Correlation functions for Hermitian many-body systems: Necessary conditions

International Nuclear Information System (INIS)

Brown, E.B.

1994-01-01

Lee [Phys. Rev. B 47, 8293 (1993)] has shown that the odd-numbered derivatives of the Kubo autocorrelation function vanish at t=0. We show that this condition is based on a more general property of nondiagonal Kubo correlation functions. This general property provides that certain functional forms (e.g., simple exponential decay) are not admissible for any symmetric or antisymmetric Kubo correlation function in a Hermitian many-body system. Lee's result emerges as a special case of this result. Applications to translationally invariant systems and systems with rotational symmetries are also demonstrated

Tensor contraction engine: Abstraction and automated parallel implementation of configuration-interaction, coupled-cluster, and many-body perturbation theories

International Nuclear Information System (INIS)

Hirata, So

2003-01-01

We develop a symbolic manipulation program and program generator (Tensor Contraction Engine or TCE) that automatically derives the working equations of a well-defined model of second-quantized many-electron theories and synthesizes efficient parallel computer programs on the basis of these equations. Provided an ansatz of a many-electron theory model, TCE performs valid contractions of creation and annihilation operators according to Wick's theorem, consolidates identical terms, and reduces the expressions into the form of multiple tensor contractions acted by permutation operators. Subsequently, it determines the binary contraction order for each multiple tensor contraction with the minimal operation and memory cost, factorizes common binary contractions (defines intermediate tensors), and identifies reusable intermediates. The resulting ordered list of binary tensor contractions, additions, and index permutations is translated into an optimized program that is combined with the NWChem and UTChem computational chemistry software packages. The programs synthesized by TCE take advantage of spin symmetry, Abelian point-group symmetry, and index permutation symmetry at every stage of calculations to minimize the number of arithmetic operations and storage requirement, adjust the peak local memory usage by index range tiling, and support parallel I/O interfaces and dynamic load balancing for parallel executions. We demonstrate the utility of TCE through automatic derivation and implementation of parallel programs for various models of configuration-interaction theory (CISD, CISDT, CISDTQ), many-body perturbation theory[MBPT(2), MBPT(3), MBPT(4)], and coupled-cluster theory (LCCD, CCD, LCCSD, CCSD, QCISD, CCSDT, and CCSDTQ)

A quantum information perspective of fermionic quantum many-body systems

Energy Technology Data Exchange (ETDEWEB)

Kraus, Christina V.

2009-11-02

In this Thesis fermionic quantum many-body system are theoretically investigated from a quantum information perspective. Quantum correlations in fermionic many-body systems, though central to many of the most fascinating effects of condensed matter physics, are poorly understood from a theoretical perspective. Even the notion of ''paired'' fermions which is widely used in the theory of superconductivity and has a clear physical meaning there, is not a concept of a systematic and mathematical theory so far. Applying concepts and tools from entanglement theory, we close this gap, developing a pairing theory allowing to unambiguously characterize paired states. We develop methods for the detection and quantification of pairing according to our definition which are applicable to current experimental setups. Pairing is shown to be a quantum correlation distinct from any notion of entanglement proposed for fermionic systems, giving further understanding of the structure of highly correlated quantum states. In addition, we show the resource character of paired states for precision metrology, proving that BCS-states allow phase measurements at the Heisenberg limit. Next, the power of fermionic systems is considered in the context of quantum simulations, where we study the possibility to simulate Hamiltonian time evolutions on a cubic lattice under the constraint of translational invariance. Given a set of translationally invariant local Hamiltonians and short range interactions we determine time evolutions which can and those which can not be simulated. Bosonic and finite-dimensional quantum systems (''spins'') are included in our investigations. Furthermore, we develop new techniques for the classical simulation of fermionic many-body systems. First, we introduce a new family of states, the fermionic Projected Entangled Pair States (fPEPS) on lattices in arbitrary spatial dimension. These are the natural generalization of the PEPS

A quantum information perspective of fermionic quantum many-body systems

International Nuclear Information System (INIS)

Kraus, Christina V.

2009-01-01

In this Thesis fermionic quantum many-body system are theoretically investigated from a quantum information perspective. Quantum correlations in fermionic many-body systems, though central to many of the most fascinating effects of condensed matter physics, are poorly understood from a theoretical perspective. Even the notion of ''paired'' fermions which is widely used in the theory of superconductivity and has a clear physical meaning there, is not a concept of a systematic and mathematical theory so far. Applying concepts and tools from entanglement theory, we close this gap, developing a pairing theory allowing to unambiguously characterize paired states. We develop methods for the detection and quantification of pairing according to our definition which are applicable to current experimental setups. Pairing is shown to be a quantum correlation distinct from any notion of entanglement proposed for fermionic systems, giving further understanding of the structure of highly correlated quantum states. In addition, we show the resource character of paired states for precision metrology, proving that BCS-states allow phase measurements at the Heisenberg limit. Next, the power of fermionic systems is considered in the context of quantum simulations, where we study the possibility to simulate Hamiltonian time evolutions on a cubic lattice under the constraint of translational invariance. Given a set of translationally invariant local Hamiltonians and short range interactions we determine time evolutions which can and those which can not be simulated. Bosonic and finite-dimensional quantum systems (''spins'') are included in our investigations. Furthermore, we develop new techniques for the classical simulation of fermionic many-body systems. First, we introduce a new family of states, the fermionic Projected Entangled Pair States (fPEPS) on lattices in arbitrary spatial dimension. These are the natural generalization of the PEPS known for spin systems, and they

PERMutation Using Transposase Engineering (PERMUTE): A Simple Approach for Constructing Circularly Permuted Protein Libraries.

Science.gov (United States)

Jones, Alicia M; Atkinson, Joshua T; Silberg, Jonathan J

2017-01-01

Rearrangements that alter the order of a protein's sequence are used in the lab to study protein folding, improve activity, and build molecular switches. One of the simplest ways to rearrange a protein sequence is through random circular permutation, where native protein termini are linked together and new termini are created elsewhere through random backbone fission. Transposase mutagenesis has emerged as a simple way to generate libraries encoding different circularly permuted variants of proteins. With this approach, a synthetic transposon (called a permuteposon) is randomly inserted throughout a circularized gene to generate vectors that express different permuted variants of a protein. In this chapter, we outline the protocol for constructing combinatorial libraries of circularly permuted proteins using transposase mutagenesis, and we describe the different permuteposons that have been developed to facilitate library construction.

A many-particle adiabatic invariant of strongly magnetized pure electron plasmas

International Nuclear Information System (INIS)

Hjorth, P.G.

1988-01-01

A pure electron plasma is said to be strongly magnetized if the cyclotron radius of the electrons is much smaller than the classical distance of closest approach. In this parameter regime a many-particle adiabatic invariant constrains the collisional dynamics. For the case of a uniform magnetic field, the adiabatic invariant is the total kinetic energy associated with the electron velocity components that are perpendicular to the magnetic field (i.e., Σ j mv 2 j perpendicular/2). Were the adiabatic invariant an exact constant of the motion, no exchange of energy would be possible between the parallel and the perpendicular degrees of freedom, and the plasma could develop and maintain two different temperatures T parallel and T perpendicular. An adiabatic invariant, however, is not strictly conserved. In the present case, each collision produces an exponentially small exchange of energy between the parallel and the perpendicular degrees of freedom, and these act cumulatively in such a way that T parallel and T perpendicular eventually relax to a common value. The rate of equilibrium is calculated, both in the case where the collisions are described by classical mechanics and in the case where the collisions are described by quantum mechanics, the two calculations giving essentially the same result. A molecular dynamics simulation has been carried out, verifying the existence of this unusual invariant, and verifying the theoretically predicted rate equation

The magic of universal quantum computing with permutations

OpenAIRE

Planat, Michel; Rukhsan-Ul-Haq

2017-01-01

The role of permutation gates for universal quantum computing is investigated. The \\lq magic' of computation is clarified in the permutation gates, their eigenstates, the Wootters discrete Wigner function and state-dependent contextuality (following many contributions on this subject). A first classification of main types of resulting magic states in low dimensions $d \\le 9$ is performed.

Translationally invariant multipartite Bell inequalities involving only two-body correlators

International Nuclear Information System (INIS)

Tura, J; B Sainz, A; Acín, A; Lewenstein, M; Augusiak, R; Vértesi, T

2014-01-01

Bell inequalities are natural tools that allow one to certify the presence of nonlocality in quantum systems. The known constructions of multipartite Bell inequalities contain, however, correlation functions involving all observers, making their experimental implementation difficult. The main purpose of this work is to explore the possibility of witnessing nonlocality in multipartite quantum states from the easiest-to-measure quantities, that is, the two-body correlations. In particular, we determine all three- and four-partite Bell inequalities constructed from one- and two-body expectation values that obey translational symmetry, and show that they reveal nonlocality in multipartite states. Also, by providing a particular example of a five-partite Bell inequality, we show that nonlocality can be detected from two-body correlators involving only nearest neighbours. Finally, we demonstrate that any translationally invariant Bell inequality can be maximally violated by a translationally invariant state and the same set of observables at all sites. We provide a numerical algorithm allowing one to seek for maximal violation of a translationally invariant Bell inequality. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell’s theorem’. (paper)

Perception of biological motion from size-invariant body representations

Directory of Open Access Journals (Sweden)

Markus eLappe

2015-03-01

Full Text Available The visual recognition of action is one of the socially most important and computationally demanding capacities of the human visual system. It combines visual shape recognition with complex non-rigid motion perception. Action presented as a point-light animation is a striking visual experience for anyone who sees it for the first time. Information about the shape and posture of the human body is sparse in point-light animations, but it is essential for action recognition. In the posturo-temporal filter model of biological motion perception posture information is picked up by visual neurons tuned to the form of the human body before body motion is calculated. We tested whether point-light stimuli are processed through posture recognition of the human body form by using a typical feature of form recognition, namely size invariance. We constructed a point-light stimulus that can only be perceived through a size-invariant mechanism. This stimulus changes rapidly in size from one image to the next. It thus disrupts continuity of early visuo-spatial properties but maintains continuity of the body posture representation. Despite this massive manipulation at the visuo-spatial level, size-changing point-light figures are spontaneously recognized by naive observers, and support discrimination of human body motion.

The Magic of Universal Quantum Computing with Permutations

Directory of Open Access Journals (Sweden)

Michel Planat

2017-01-01

Full Text Available The role of permutation gates for universal quantum computing is investigated. The “magic” of computation is clarified in the permutation gates, their eigenstates, the Wootters discrete Wigner function, and state-dependent contextuality (following many contributions on this subject. A first classification of a few types of resulting magic states in low dimensions d≤9 is performed.

Time-dependent, many-body scattering theory and nuclear reaction applications

International Nuclear Information System (INIS)

Levin, F.S.

1977-01-01

The channel component state form of the channel coupling array theory of many-body scattering is briefly reviewed. These states obey a non-hermitian matrix equation whose exact solution yields the Schroedinger eigenstates, eigenvalues and scattering amplitudes. A time-dependent formulation of the theory is introduced in analogy to the time-dependent Schrodinger equation and several consequences of the development are noted. These include an interaction picture, a single (matrix) S operator, and the usual connection between the t = 0 time-dependent and the time-independent scattering states. Finally, the channel component states (psi/sub j/) are shown to have the useful property that only psi/sub j/ has (two-body) outgoing waves in channel j: psi/sub m/, m not equal to j, is asymptotically zero in two-body channel j. This formalism is then considered as a means for direct nuclear reaction analysis. Typical bound state approximations are introduced and it is shown that a DWBA amplitude occurs in only one channel. The non-time-reversal invariance of the approximate theory is noted. Results of calculations based on a realistic model for two sets of light-ion induced, one-particle transfer reactions are discussed and compared with the coupled reaction channel (CRC) results using the CRC procedure of Cotanch and Vincent. Angular distributions for the two calculational methods are found to be similar in shape and magnitude. Higher ordercorrections are small as are time-reversal non-invariant effects. Post- and prior-type CRC calculations are seen to differ; the latter are closer to the full CRC results

Symmetry analysis of many-body wave functions, with applications to the nuclear shell model

International Nuclear Information System (INIS)

Novoselsky, A.; Katriel, J.

1995-01-01

The weights of the different permutational symmetry components of a nonsymmetry-adapted many-particle wave function are evaluated in terms of the expectation values of the symmetric-group class sums. This facilitates the evaluation of the weights without the construction of a complete set of symmetry adapted functions. Subspace projection operators are introduced, to be used when prior knowledge about the symmetry-species composition of a wave function is available. The permutational weight analysis of a recursively angular-momentum coupled (shell model) wave function is presented as an illustration

Possible generalization of Yang variables for the study of many particle final states

International Nuclear Information System (INIS)

Becker, L.; Schiller, H.

1976-01-01

Starting from a discussion of constraints on invariant variables a generalization of the so called Yang-variables is discussed for the case of 5 and 6 particles in the final states. The obtained Lorentz-invariant variables are ''quasi permutation invariant'' with respect to the final state particles. The influence of Gram determinants is discussed in the context of the application of a cluster algorithm. (author)

A chronicle of permutation statistical methods 1920–2000, and beyond

CERN Document Server

Berry, Kenneth J; Mielke Jr , Paul W

2014-01-01

The focus of this book is on the birth and historical development of permutation statistical methods from the early 1920s to the near present. Beginning with the seminal contributions of R.A. Fisher, E.J.G. Pitman, and others in the 1920s and 1930s, permutation statistical methods were initially introduced to validate the assumptions of classical statistical methods. Permutation methods have advantages over classical methods in that they are optimal for small data sets and non-random samples, are data-dependent, and are free of distributional assumptions. Permutation probability values may be exact, or estimated via moment- or resampling-approximation procedures. Because permutation methods are inherently computationally-intensive, the evolution of computers and computing technology that made modern permutation methods possible accompanies the historical narrative. Permutation analogs of many well-known statistical tests are presented in a historical context, including multiple correlation and regression, ana...

Quantized Hall conductance as a topological invariant

International Nuclear Information System (INIS)

Niu, Q.; Thouless, Ds.J.; Wu, Y.S.

1984-10-01

Whenever the Fermi level lies in a gap (or mobility gap) the bulk Hall conductance can be expressed in a topologically invariant form showing the quantization explicitly. The new formulation generalizes the earlier result by TKNN to the situation where many body interaction and substrate disorder are also present. When applying to the fractional quantized Hall effect we draw the conclusion that there must be a symmetry breaking in the many body ground state. The possibility of writing the fractionally quantized Hall conductance as a topological invariant is also carefully discussed. 19 references

Aspects of Strongly Correlated Many-Body Fermi Systems

Science.gov (United States)

Porter, William J., III

A, by now, well-known signal-to-noise problem plagues Monte Carlo calculations of quantum-information-theoretic observables in systems of interacting fermions, particularly the Renyi entanglement entropies Sn, even in many cases where the infamous sign problem does not appear. Several methods have been put forward to circumvent this affliction including ensemble-switching techniques using auxiliary partition-function ratios. This dissertation presents an algorithm that modifies the recently proposed free-fermion decomposition in an essential way: we incorporate the entanglement-sensitive correlations directly into the probability measure in a natural way. Implementing this algorithm, we demonstrate that it is compatible with the hybrid Monte Carlo algorithm, the workhorse of the lattice quantum chromodynamics community and an essential tool for studying gauge theories that contain dynamical fermions. By studying a simple one-dimensional Hubbard model, we demonstrate that our method does not exhibit the same debilitating numerical difficulties that naive attempts to study entanglement often encounter. Following that, we illustrate some key probabilistic insights, using intuition derived from the previous method and its successes to construct a simpler, better behaved, and more elegant algorithm. Using this method, in combination with new identities which allow us to avoid seemingly necessary numerical difficulties, the inversion of the restricted one-body density matrices, we compute high order Renyi entropies and perform a thorough comparison to this new algorithm's predecessor using the Hubbard model mentioned before. Finally, we characterize non-perturbatively the Renyi entropies of degree n = 2,3,4, and 5 of three-dimensional, strongly coupled many-fermion systems in the scale-invariant regime of short interaction range and large scattering length, i.e. in the unitary limit using the algorithms detailed herein. We also detail an exact, few-body projective method

Supersymmetric many-body systems from partial symmetries — integrability, localization and scrambling

Energy Technology Data Exchange (ETDEWEB)

Padmanabhan, Pramod [Fields, Gravity & Strings, CTPU, Institute for Basic Science,Daejeon 34037 (Korea, Republic of); Rey, Soo-Jong [Fields, Gravity & Strings, CTPU, Institute for Basic Science,Daejeon 34037 (Korea, Republic of); School of Physics and Astronomy & Center for Theoretical Physics, Seoul National University,Seoul 06544 (Korea, Republic of); Department of Basic Sciences, University of Science and Technology, Daejeon 34113 (Korea, Republic of); Teixeira, Daniel; Trancanelli, Diego [Institute of Physics, University of São Paulo, 05314-970 São Paulo (Brazil)

2017-05-25

Partial symmetries are described by generalized group structures known as symmetric inverse semigroups. We use the algebras arising from these structures to realize supersymmetry in (0+1) dimensions and to build many-body quantum systems on a chain. This construction consists in associating appropriate supercharges to chain sites, in analogy to what is done in spin chains. For simple enough choices of supercharges, we show that the resulting states have a finite non-zero Witten index, which is invariant under perturbations, therefore defining supersymmetric phases of matter protected by the index. The Hamiltonians we obtain are integrable and display a spectrum containing both product and entangled states. By introducing disorder and studying the out-of-time-ordered correlators (OTOC), we find that these systems are in the many-body localized phase and do not thermalize. Finally, we reformulate a theorem relating the growth of the second Rényi entropy to the OTOC on a thermal state in terms of partial symmetries.

Permutation statistical methods an integrated approach

CERN Document Server

Berry, Kenneth J; Johnston, Janis E

2016-01-01

This research monograph provides a synthesis of a number of statistical tests and measures, which, at first consideration, appear disjoint and unrelated. Numerous comparisons of permutation and classical statistical methods are presented, and the two methods are compared via probability values and, where appropriate, measures of effect size. Permutation statistical methods, compared to classical statistical methods, do not rely on theoretical distributions, avoid the usual assumptions of normality and homogeneity of variance, and depend only on the data at hand. This text takes a unique approach to explaining statistics by integrating a large variety of statistical methods, and establishing the rigor of a topic that to many may seem to be a nascent field in statistics. This topic is new in that it took modern computing power to make permutation methods available to people working in the mainstream of research. This research monograph addresses a statistically-informed audience, and can also easily serve as a ...

Many-body localization in disorder-free systems: The importance of finite-size constraints

Energy Technology Data Exchange (ETDEWEB)

Papić, Z., E-mail: zpapic@perimeterinstitute.ca [School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT (United Kingdom); Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5 (Canada); Stoudenmire, E. Miles [Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5 (Canada); Abanin, Dmitry A. [Department of Theoretical Physics, University of Geneva, 24 quai Ernest-Ansermet, 1211 Geneva (Switzerland); Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5 (Canada)

2015-11-15

Recently it has been suggested that many-body localization (MBL) can occur in translation-invariant systems, and candidate 1D models have been proposed. We find that such models, in contrast to MBL systems with quenched disorder, typically exhibit much more severe finite-size effects due to the presence of two or more vastly different energy scales. In a finite system, this can artificially split the density of states (DOS) into bands separated by large gaps. We argue for such models to faithfully represent the thermodynamic limit behavior, the ratio of relevant coupling must exceed a certain system-size depedent cutoff, chosen such that various bands in the DOS overlap one another. Setting the parameters this way to minimize finite-size effects, we study several translation-invariant MBL candidate models using exact diagonalization. Based on diagnostics including entanglement and local observables, we observe thermal (ergodic), rather than MBL-like behavior. Our results suggest that MBL in translation-invariant systems with two or more very different energy scales is less robust than perturbative arguments suggest, possibly pointing to the importance of non-perturbative effects which induce delocalization in the thermodynamic limit.

Many-body formalism for fermions: The partition function

Science.gov (United States)

Watson, D. K.

2017-09-01

The partition function, a fundamental tenet in statistical thermodynamics, contains in principle all thermodynamic information about a system. It encapsulates both microscopic information through the quantum energy levels and statistical information from the partitioning of the particles among the available energy levels. For identical particles, this statistical accounting is complicated by the symmetry requirements of the allowed quantum states. In particular, for Fermi systems, the enforcement of the Pauli principle is typically a numerically demanding task, responsible for much of the cost of the calculations. The interplay of these three elements—the structure of the many-body spectrum, the statistical partitioning of the N particles among the available levels, and the enforcement of the Pauli principle—drives the behavior of mesoscopic and macroscopic Fermi systems. In this paper, we develop an approach for the determination of the partition function, a numerically difficult task, for systems of strongly interacting identical fermions and apply it to a model system of harmonically confined, harmonically interacting fermions. This approach uses a recently introduced many-body method that is an extension of the symmetry-invariant perturbation method (SPT) originally developed for bosons. It uses group theory and graphical techniques to avoid the heavy computational demands of conventional many-body methods which typically scale exponentially with the number of particles. The SPT application of the Pauli principle is trivial to implement since it is done "on paper" by imposing restrictions on the normal-mode quantum numbers at first order in the perturbation. The method is applied through first order and represents an extension of the SPT method to excited states. Our method of determining the partition function and various thermodynamic quantities is accurate and efficient and has the potential to yield interesting insight into the role played by the Pauli

Visual recognition of permuted words

Science.gov (United States)

Rashid, Sheikh Faisal; Shafait, Faisal; Breuel, Thomas M.

2010-02-01

In current study we examine how letter permutation affects in visual recognition of words for two orthographically dissimilar languages, Urdu and German. We present the hypothesis that recognition or reading of permuted and non-permuted words are two distinct mental level processes, and that people use different strategies in handling permuted words as compared to normal words. A comparison between reading behavior of people in these languages is also presented. We present our study in context of dual route theories of reading and it is observed that the dual-route theory is consistent with explanation of our hypothesis of distinction in underlying cognitive behavior for reading permuted and non-permuted words. We conducted three experiments in lexical decision tasks to analyze how reading is degraded or affected by letter permutation. We performed analysis of variance (ANOVA), distribution free rank test, and t-test to determine the significance differences in response time latencies for two classes of data. Results showed that the recognition accuracy for permuted words is decreased 31% in case of Urdu and 11% in case of German language. We also found a considerable difference in reading behavior for cursive and alphabetic languages and it is observed that reading of Urdu is comparatively slower than reading of German due to characteristics of cursive script.

Fast algorithms for transforming back and forth between a signed permutation and its equivalent simple permutation.

Science.gov (United States)

Gog, Simon; Bader, Martin

2008-10-01

The problem of sorting signed permutations by reversals is a well-studied problem in computational biology. The first polynomial time algorithm was presented by Hannenhalli and Pevzner in 1995. The algorithm was improved several times, and nowadays the most efficient algorithm has a subquadratic running time. Simple permutations played an important role in the development of these algorithms. Although the latest result of Tannier et al. does not require simple permutations, the preliminary version of their algorithm as well as the first polynomial time algorithm of Hannenhalli and Pevzner use the structure of simple permutations. More precisely, the latter algorithms require a precomputation that transforms a permutation into an equivalent simple permutation. To the best of our knowledge, all published algorithms for this transformation have at least a quadratic running time. For further investigations on genome rearrangement problems, the existence of a fast algorithm for the transformation could be crucial. Another important task is the back transformation, i.e. if we have a sorting on the simple permutation, transform it into a sorting on the original permutation. Again, the naive approach results in an algorithm with quadratic running time. In this paper, we present a linear time algorithm for transforming a permutation into an equivalent simple permutation, and an O(n log n) algorithm for the back transformation of the sorting sequence.

Many-Body Quantum Chaos: Analytic Connection to Random Matrix Theory

Science.gov (United States)

Kos, Pavel; Ljubotina, Marko; Prosen, Tomaž

2018-04-01

A key goal of quantum chaos is to establish a relationship between widely observed universal spectral fluctuations of clean quantum systems and random matrix theory (RMT). Most prominent features of such RMT behavior with respect to a random spectrum, both encompassed in the spectral pair correlation function, are statistical suppression of small level spacings (correlation hole) and enhanced stiffness of the spectrum at large spectral ranges. For single-particle systems with fully chaotic classical counterparts, the problem has been partly solved by Berry [Proc. R. Soc. A 400, 229 (1985), 10.1098/rspa.1985.0078] within the so-called diagonal approximation of semiclassical periodic-orbit sums, while the derivation of the full RMT spectral form factor K (t ) (Fourier transform of the spectral pair correlation function) from semiclassics has been completed by Müller et al. [Phys. Rev. Lett. 93, 014103 (2004), 10.1103/PhysRevLett.93.014103]. In recent years, the questions of long-time dynamics at high energies, for which the full many-body energy spectrum becomes relevant, are coming to the forefront even for simple many-body quantum systems, such as locally interacting spin chains. Such systems display two universal types of behaviour which are termed the "many-body localized phase" and "ergodic phase." In the ergodic phase, the spectral fluctuations are excellently described by RMT, even for very simple interactions and in the absence of any external source of disorder. Here we provide a clear theoretical explanation for these observations. We compute K (t ) in the leading two orders in t and show its agreement with RMT for nonintegrable, time-reversal invariant many-body systems without classical counterparts, a generic example of which are Ising spin-1 /2 models in a periodically kicking transverse field. In particular, we relate K (t ) to partition functions of a class of twisted classical Ising models on a ring of size t ; hence, the leading-order RMT behavior

Many body calculations in atomic physics

International Nuclear Information System (INIS)

Kelly, H.P.

1985-01-01

The use of the many-body perturbation theory for atomic calculations are reviewed. The major emphasis is on the use of the linked-cluster many-body perturbation theory derived by Brueckner and Goldstone. Applications of many-body theory to calculations of hyperfine structure are examined. Auger rates and parity violation are discussed. Photoionization is reviewed, and the authors show how many-body perturbation theory can be applied to problems ranging from structural properties such as correlation energies and hyperfine structure to dynamical properties such as transitions induced by weak neutral currents and photoionization cross sections

Three-body interactions in many-body effective field theory

International Nuclear Information System (INIS)

Furnstahl, R.J.

2004-01-01

This contribution is an advertisement for applying effective field theory (EFT) to many-body problems, including nuclei and cold atomic gases. Examples involving three-body interactions are used to illustrate how EFT's quantify and systematically eliminate model dependence, and how they make many-body calculations simpler and more powerful

Opposition-Based Memetic Algorithm and Hybrid Approach for Sorting Permutations by Reversals.

Science.gov (United States)

Soncco-Álvarez, José Luis; Muñoz, Daniel M; Ayala-Rincón, Mauricio

2018-02-21

Sorting unsigned permutations by reversals is a difficult problem; indeed, it was proved to be NP-hard by Caprara (1997). Because of its high complexity, many approximation algorithms to compute the minimal reversal distance were proposed until reaching the nowadays best-known theoretical ratio of 1.375. In this article, two memetic algorithms to compute the reversal distance are proposed. The first one uses the technique of opposition-based learning leading to an opposition-based memetic algorithm; the second one improves the previous algorithm by applying the heuristic of two breakpoint elimination leading to a hybrid approach. Several experiments were performed with one-hundred randomly generated permutations, single benchmark permutations, and biological permutations. Results of the experiments showed that the proposed OBMA and Hybrid-OBMA algorithms achieve the best results for practical cases, that is, for permutations of length up to 120. Also, Hybrid-OBMA showed to improve the results of OBMA for permutations greater than or equal to 60. The applicability of our proposed algorithms was checked processing permutations based on biological data, in which case OBMA gave the best average results for all instances.

Anyonic self-induced disorder in a stabilizer code: Quasi many-body localization in a translational invariant model

Science.gov (United States)

Yarloo, H.; Langari, A.; Vaezi, A.

2018-02-01

We enquire into the quasi many-body localization in topologically ordered states of matter, revolving around the case of Kitaev toric code on the ladder geometry, where different types of anyonic defects carry different masses induced by environmental errors. Our study verifies that the presence of anyons generates a complex energy landscape solely through braiding statistics, which suffices to suppress the diffusion of defects in such clean, multicomponent anyonic liquid. This nonergodic dynamics suggests a promising scenario for investigation of quasi many-body localization. Computing standard diagnostics evidences that a typical initial inhomogeneity of anyons gives birth to a glassy dynamics with an exponentially diverging time scale of the full relaxation. Our results unveil how self-generated disorder ameliorates the vulnerability of topological order away from equilibrium. This setting provides a new platform which paves the way toward impeding logical errors by self-localization of anyons in a generic, high energy state, originated exclusively in their exotic statistics.

Permutation Tests for Stochastic Ordering and ANOVA

CERN Document Server

Basso, Dario; Salmaso, Luigi; Solari, Aldo

2009-01-01

Permutation testing for multivariate stochastic ordering and ANOVA designs is a fundamental issue in many scientific fields such as medicine, biology, pharmaceutical studies, engineering, economics, psychology, and social sciences. This book presents advanced methods and related R codes to perform complex multivariate analyses

Nucleon many-body problem using quantum-mechanical few-body technique

International Nuclear Information System (INIS)

Horiuchi, Wataru

2016-01-01

A nucleus is treated as a quantum-mechanical many-body system consisting of protons and neutrons that interact with each other by nuclear force. This paper explains the variational calculation using the correlated basis function as a powerful technique for obtaining the precise solution of Schroedinger equation of many-body, and tries to understand the nucleon many-body system from the viewpoint of a few-body through the application cases of various nuclear systems. It describes the important correlation that characterizes the nucleon many-body system such as the mean field, cluster, and tensor of bound state, and shows that non-bound state is also describable. Since such precise theory is mantic, it is essential for explaining the nature of unknown unstable nuclei, and for determining the nuclear reaction rate under the environment of the stars difficult for experiment. The method is general and flexible, and can be applied to various quantum-mechanical many-body problems. For example, the multi-body calculation of atoms and molecules, hypernuclei, and hadron spectroscopy can be carried out only by changing the potential and particles. (A.O.)

Introduction to many-body physics

CERN Document Server

Coleman, Piers

2015-01-01

A modern, graduate-level introduction to many-body physics in condensed matter, this textbook explains the tools and concepts needed for a research-level understanding of the correlated behavior of quantum fluids. Starting with an operator-based introduction to the quantum field theory of many-body physics, this textbook presents the Feynman diagram approach, Green's functions and finite-temperature many body physics before developing the path integral approach to interacting systems. Special chapters are devoted to the concepts of Fermi liquid theory, broken symmetry, conduction in disordered systems, superconductivity and the physics of local-moment metals. A strong emphasis on concepts and numerous exercises make this an invaluable course book for graduate students in condensed matter physics. It will also interest students in nuclear, atomic and particle physics.

From few- to many-body quantum systems

OpenAIRE

Schiulaz, Mauro; Távora, Marco; Santos, Lea F.

2018-01-01

How many particles are necessary to make a many-body quantum system? To answer this question, we take as reference for the many-body limit a quantum system at half-filling and compare its properties with those of a system with $N$ particles, gradually increasing $N$ from 1. We show that the convergence of the static properties of the system with few particles to the many-body limit is fast. For $N \\gtrsim 4$, the density of states is already very close to Gaussian and signatures of many-body ...

Molecular symmetry: Why permutation-inversion (PI) groups don't render the point groups obsolete

Science.gov (United States)

Groner, Peter

2018-01-01

The analysis of spectra of molecules with internal large-amplitude motions (LAMs) requires molecular symmetry (MS) groups that are larger than and significantly different from the more familiar point groups. MS groups are described often by the permutation-inversion (PI) group method. It is shown that point groups still can and should play a significant role together with the PI groups for a class of molecules with internal rotors. In molecules of this class, several simple internal rotors are attached to a rigid molecular frame. The PI groups for this class are semidirect products like H ^ F, where the invariant subgroup H is a direct product of cyclic groups and F is a point group. This result is used to derive meaningful labels for MS groups, and to derive correlation tables between MS groups and point groups. MS groups of this class have many parallels to space groups of crystalline solids.

Permutation orbifolds and chaos

NARCIS (Netherlands)

Belin, A.

2017-01-01

We study out-of-time-ordered correlation functions in permutation orbifolds at large central charge. We show that they do not decay at late times for arbitrary choices of low-dimension operators, indicating that permutation orbifolds are non-chaotic theories. This is in agreement with the fact they

Gray Code for Cayley Permutations

Directory of Open Access Journals (Sweden)

J.-L. Baril

2003-10-01

Full Text Available A length-n Cayley permutation p of a total ordered set S is a length-n sequence of elements from S, subject to the condition that if an element x appears in p then all elements y < x also appear in p . In this paper, we give a Gray code list for the set of length-n Cayley permutations. Two successive permutations in this list differ at most in two positions.

Sorting permutations by prefix and suffix rearrangements.

Science.gov (United States)

Lintzmayer, Carla Negri; Fertin, Guillaume; Dias, Zanoni

2017-02-01

Some interesting combinatorial problems have been motivated by genome rearrangements, which are mutations that affect large portions of a genome. When we represent genomes as permutations, the goal is to transform a given permutation into the identity permutation with the minimum number of rearrangements. When they affect segments from the beginning (respectively end) of the permutation, they are called prefix (respectively suffix) rearrangements. This paper presents results for rearrangement problems that involve prefix and suffix versions of reversals and transpositions considering unsigned and signed permutations. We give 2-approximation and ([Formula: see text])-approximation algorithms for these problems, where [Formula: see text] is a constant divided by the number of breakpoints (pairs of consecutive elements that should not be consecutive in the identity permutation) in the input permutation. We also give bounds for the diameters concerning these problems and provide ways of improving the practical results of our algorithms.

An Affine Invariant Bivariate Version of the Sign Test.

Science.gov (United States)

1987-06-01

words: affine invariance, bivariate quantile, bivariate symmetry, model,. generalized median, influence function , permutation test, normal efficiency...calculate a bivariate version of the influence function , and the resulting form is bounded, as is the case for the univartate sign test, and shows the...terms of a blvariate analogue of IHmpel’s (1974) influence function . The latter, though usually defined as a von-Mises derivative of certain

Many-body theory

International Nuclear Information System (INIS)

Hubbard, J.

1980-01-01

The evolution of the discipline of many-body theory during the past 25 years is outlined and the developments originated in the Theoretical Physics Division, AERE, are discussed. Topics considered include; the connection between plasma oscillations and the dielectric properties of an electron gas, superconductivity, Fermi levels, ferromagnetism in metals, phase transformations, scaling laws, and quasi-one-dimensional solids. (UK)

General variational many-body theory with complete self-consistency for trapped bosonic systems

International Nuclear Information System (INIS)

Streltsov, Alexej I.; Alon, Ofir E.; Cederbaum, Lorenz S.

2006-01-01

In this work we develop a complete variational many-body theory for a system of N trapped bosons interacting via a general two-body potential. The many-body solution of this system is expanded over orthogonal many-body basis functions (configurations). In this theory both the many-body basis functions and the respective expansion coefficients are treated as variational parameters. The optimal variational parameters are obtained self-consistently by solving a coupled system of noneigenvalue--generally integro-differential--equations to get the one-particle functions and by diagonalizing the secular matrix problem to find the expansion coefficients. We call this theory multiconfigurational Hartree theory for bosons or MCHB(M), where M specifies explicitly the number of one-particle functions used to construct the configurations. General rules for evaluating the matrix elements of one- and two-particle operators are derived and applied to construct the secular Hamiltonian matrix. We discuss properties of the derived equations. We show that in the limiting cases of one configuration the theory boils down to the well-known Gross-Pitaevskii and the recently developed multi-orbital mean fields. The invariance of the complete solution with respect to unitary transformations of the one-particle functions is utilized to find the solution with the minimal number of contributing configurations. In the second part of our work we implement and apply the developed theory. It is demonstrated that for any practical computation where the configurational space is restricted, the description of trapped bosonic systems strongly depends on the choice of the many-body basis set used, i.e., self-consistency is of great relevance. As illustrative examples we consider bosonic systems trapped in one- and two-dimensional symmetric and asymmetric double well potentials. We demonstrate that self-consistency has great impact on the predicted physical properties of the ground and excited states

Few-body correlations in many-body physics

Energy Technology Data Exchange (ETDEWEB)

Barth, Marcus

2015-12-01

In this thesis, various systems are analyzed in parameter regimes where the few-body aspects are dominant over the many-body behavior. Using the Operator Product Expansion from Quantum Field Theory, exact relations for observables of the electron gas as well as two-dimensional Fermi gases are derived. In addition, properties of both two-dimensional and three-dimensional cold quantum gases at small to moderate degeneracy are determined by means of a diagrammatic virial expansion.

Invariant exchange perturbation theory for multicenter systems: Time-dependent perturbations

International Nuclear Information System (INIS)

Orlenko, E. V.; Evstafev, A. V.; Orlenko, F. E.

2015-01-01

A formalism of exchange perturbation theory (EPT) is developed for the case of interactions that explicitly depend on time. Corrections to the wave function obtained in any order of perturbation theory and represented in an invariant form include exchange contributions due to intercenter electron permutations in complex multicenter systems. For collisions of atomic systems with an arbitrary type of interaction, general expressions are obtained for the transfer (T) and scattering (S) matrices in which intercenter electron permutations between overlapping nonorthogonal states belonging to different centers (atoms) are consistently taken into account. The problem of collision of alpha particles with lithium atoms accompanied by the redistribution of electrons between centers is considered. The differential and total charge-exchange cross sections of lithium are calculated

Some considerations on the restoration of Galilei invariance in the nuclear many-body problem. Pt. I. Mathematical tools, spectral functions and spectroscopic factors of simple bound states

International Nuclear Information System (INIS)

Schmid, K.W.

2001-01-01

The mathematical tools to restore Galilei invariance in the nuclear many-body problem with the help of projection techniques are presented. For simple oscillator configurations recursion relations for the various elementary contractions are derived. The method is then applied to simple configurations for the ground states of 4 He, 16 O and 40 Ca as well as to the corresponding one-hole and one-particle states. As a first application the spectral functions and spectroscopic factors for the above-mentioned doubly even nuclei are investigated. It turns out that the conventional picture of an uncorrelated system underestimates the single-particle strengths of the hole states from the last occupied shell while that of the higher excited hole states is overestimated considerably. These results are in complete agreement with those derived by Dieperink and de Forest using different methods. Similar effects are seen for the particle states which have not been studied before. All the calculations presented here are performed analytically and thus can be checked explicitly by the interested reader. (orig.)

EPC: A Provably Secure Permutation Based Compression Function

DEFF Research Database (Denmark)

Bagheri, Nasour; Gauravaram, Praveen; Naderi, Majid

2010-01-01

The security of permutation-based hash functions in the ideal permutation model has been studied when the input-length of compression function is larger than the input-length of the permutation function. In this paper, we consider permutation based compression functions that have input lengths sh...

Nuclear collision theory with many-body correlations, 1

International Nuclear Information System (INIS)

Kurihara, Yukio.

1984-11-01

A generalized many-body correlation operator is introduced, following the Feshbach's formalism. Especially, the many-body correlation induced by the strong repulsion and attraction of the realistic NN interaction is concerned and the Feshbach's formalism is reformulated to describe such a many-body correlation well. And a method to estimate the many-body correlation operator is given from the multiple-scattering picture. The present formalism is compared with the resonating-group method. (author)

Finally! A valid test of configural invariance using permutation in multigroup CFA

NARCIS (Netherlands)

Jorgensen, T.D.; Kite, B.A.; Chen, P.-Y.; Short, S.D.; van der Ark, L.A.; Wiberg, M.; Culpepper, S.A.; Douglas, J.A.; Wang, W.-C.

2017-01-01

In multigroup factor analysis, configural measurement invariance is accepted as tenable when researchers either (a) fail to reject the null hypothesis of exact fit using a χ2 test or (b) conclude that a model fits approximately well enough, according to one or more alternative fit indices (AFIs).

Status of many-body theory

International Nuclear Information System (INIS)

Brueckner, K.A.

1980-01-01

This paper reviews the major steps in the development of many-body theory since the early 1950's. Very few systems permit an exact solution by selective diagram summation or by exact solution of a truncated Hamiltonian. Formal methods have usually had little success for real physical systems. Examples are all the quantum liquids such as nuclear matter, liquid He 3 , liquid He 4 , superconductors and metallic conductors. Atomic and molecular systems and finite nuclei present additional problems. Many-body theory has probably had its greatest success in the application to atomic properties and the development in recent years is reviewed. (Auth.)

Many-body orthogonal polynomial systems

International Nuclear Information System (INIS)

Witte, N.S.

1997-03-01

The fundamental methods employed in the moment problem, involving orthogonal polynomial systems, the Lanczos algorithm, continued fraction analysis and Pade approximants has been combined with a cumulant approach and applied to the extensive many-body problem in physics. This has yielded many new exact results for many-body systems in the thermodynamic limit - for the ground state energy, for excited state gaps, for arbitrary ground state avenges - and are of a nonperturbative nature. These results flow from a confluence property of the three-term recurrence coefficients arising and define a general class of many-body orthogonal polynomials. These theorems constitute an analytical solution to the Lanczos algorithm in that they are expressed in terms of the three-term recurrence coefficients α and β. These results can also be applied approximately for non-solvable models in the form of an expansion, in a descending series of the system size. The zeroth order order this expansion is just the manifestation of the central limit theorem in which a Gaussian measure and hermite polynomials arise. The first order represents the first non-trivial order, in which classical distribution functions like the binomial distributions arise and the associated class of orthogonal polynomials are Meixner polynomials. Amongst examples of systems which have infinite order in the expansion are q-orthogonal polynomials where q depends on the system size in a particular way. (author)

Vortex matter stabilized by many-body interactions

Science.gov (United States)

Wolf, S.; Vagov, A.; Shanenko, A. A.; Axt, V. M.; Aguiar, J. Albino

2017-10-01

This work investigates interactions of vortices in superconducting materials between standard types I and II, in the domain of the so-called intertype (IT) superconductivity. Contrary to common expectations, the many-body (many-vortex) contribution is not a correction to the pair-vortex interaction here but plays a crucial role in the formation of the IT vortex matter. In particular, the many-body interactions stabilize vortex clusters that otherwise could not exist. Furthermore, clusters with large numbers of vortices become more stable when approaching the boundary between the intertype domain and type I. This indicates that IT superconductors develop a peculiar unconventional type of the vortex matter governed by the many-body interactions of vortices.

Review of many-body calculations

International Nuclear Information System (INIS)

Kelly, H.P.

1981-01-01

A brief review is given of many-body perturbation theory and its application to atomic physics. Particular attention is given to the choice of single-particle potential used to generate excited states. Applications to many atomic properties are discussed including hyperfine structure, photoabsorption including multiple processes, and parity non-conserving transitions in heavy atoms

1-Colored Archetypal Permutations and Strings of Degree n

Directory of Open Access Journals (Sweden)

Gheorghe Eduard Tara

2012-10-01

Full Text Available New notions related to permutations are introduced here. We present the string of a 1-colored permutation as a closed planar curve, the fundamental 1-colored permutation as an equivalence class related to the equivalence in strings of the 1-colored permutations. We give formulas for the number of the 1-colored archetypal permutations of degree n. We establish an algorithm to identify the 1- colored archetypal permutations of degree n and we present the atlas of the 1-colored archetypal strings of degree n, n ≤ 7, based on this algorithm.

Dynamically induced many-body localization

Science.gov (United States)

Choi, Soonwon; Abanin, Dmitry A.; Lukin, Mikhail D.

2018-03-01

We show that a quantum phase transition from ergodic to many-body localized (MBL) phases can be induced via periodic pulsed manipulation of spin systems. Such a transition is enabled by the interplay between weak disorder and slow heating rates. Specifically, we demonstrate that the Hamiltonian of a weakly disordered ergodic spin system can be effectively engineered, by using sufficiently fast coherent controls, to yield a stable MBL phase, which in turn completely suppresses the energy absorption from external control field. Our results imply that a broad class of existing many-body systems can be used to probe nonequilibrium phases of matter for a long time, limited only by coupling to external environment.

Tensor Permutation Matrices in Finite Dimensions

OpenAIRE

Christian, Rakotonirina

2005-01-01

We have generalised the properties with the tensor product, of one 4x4 matrix which is a permutation matrix, and we call a tensor commutation matrix. Tensor commutation matrices can be constructed with or without calculus. A formula allows us to construct a tensor permutation matrix, which is a generalisation of tensor commutation matrix, has been established. The expression of an element of a tensor commutation matrix has been generalised in the case of any element of a tensor permutation ma...

Many-body forces in nuclear shell-model

International Nuclear Information System (INIS)

Rath, P.K.

1985-01-01

In the microscopic derivation of the effective Hamiltonian for the nuclear shell model many-body forces between the valence nucleons occur. These many-body forces can be discriminated in ''real'' many-body forces, which can be related to mesonic and internal degrees of freedom of the nucleons, and ''effective'' many-body forces, which arise by the confinement of the nucleonic Hilbert space to the finite-dimension shell-model space. In the present thesis the influences of such three-body forces on the spectra of sd-shell nuclei are studied. For this the two common techniques for shell-model calculations (Oak Ridge-Rochester and Glasgow representation) are extended in such way that a general three-body term in the Hamiltonian can be regarded. The studies show that the repulsive contributions of the considered three-nucleon forces become more important with increasing number of valence nucleons. By this the particle-number dependence of empirical two-nucleon forces can be qualitatively explained. A special kind of effective many-body force occurs in the folded diagram expansion of the energy-dependent effective Hamiltonian for the shell model. Thereby it is shown that the contributions of the folded diagrams with three nucleons are just as important as those with two nucleons. Thus it is to be suspected that the folded diagram expansion contains many-particle terms with arbitrary particle number. The present studies however show that four nucleon effects are neglegible so that the folded diagram expansion can be confined to two- and three-particle terms. In shell-model calculations which extend over several main shells the influences of the spurious center-of-mass motion must be regarded. A procedure is discussed by which these spurious degrees of freedom can be exactly separated. (orig.) [de

The coupling analysis between stock market indices based on permutation measures

Science.gov (United States)

Shi, Wenbin; Shang, Pengjian; Xia, Jianan; Yeh, Chien-Hung

2016-04-01

Many information-theoretic methods have been proposed for analyzing the coupling dependence between time series. And it is significant to quantify the correlation relationship between financial sequences since the financial market is a complex evolved dynamic system. Recently, we developed a new permutation-based entropy, called cross-permutation entropy (CPE), to detect the coupling structures between two synchronous time series. In this paper, we extend the CPE method to weighted cross-permutation entropy (WCPE), to address some of CPE's limitations, mainly its inability to differentiate between distinct patterns of a certain motif and the sensitivity of patterns close to the noise floor. It shows more stable and reliable results than CPE does when applied it to spiky data and AR(1) processes. Besides, we adapt the CPE method to infer the complexity of short-length time series by freely changing the time delay, and test it with Gaussian random series and random walks. The modified method shows the advantages in reducing deviations of entropy estimation compared with the conventional one. Finally, the weighted cross-permutation entropy of eight important stock indices from the world financial markets is investigated, and some useful and interesting empirical results are obtained.

NDPA: A generalized efficient parallel in-place N-Dimensional Permutation Algorithm

Directory of Open Access Journals (Sweden)

Muhammad Elsayed Ali

2015-09-01

Full Text Available N-dimensional transpose/permutation is a very important operation in many large-scale data intensive and scientific applications. These applications include but not limited to oil industry i.e. seismic data processing, nuclear medicine, media production, digital signal processing and business intelligence. This paper proposes an efficient in-place N-dimensional permutation algorithm. The algorithm is based on a novel 3D transpose algorithm that was published recently. The proposed algorithm has been tested on 3D, 4D, 5D, 6D and 7D data sets as a proof of concept. This is the first contribution which is breaking the dimensions’ limitation of the base algorithm. The suggested algorithm exploits the idea of mixing both logical and physical permutations together. In the logical permutation, the address map is transposed for each data unit access. In the physical permutation, actual data elements are swapped. Both permutation levels exploit the fast on-chip memory bandwidth by transferring large amount of data and allowing for fine-grain SIMD (Single Instruction, Multiple Data operations. Thus, the performance is improved as evident from the experimental results section. The algorithm is implemented on NVidia GeForce GTS 250 GPU (Graphics Processing Unit containing 128 cores. The rapid increase in GPUs performance coupled with the recent and continuous improvements in its programmability proved that GPUs are the right choice for computationally demanding tasks. The use of GPUs is the second contribution which reflects how strongly they fit for high performance tasks. The third contribution is improving the proposed algorithm performance to its peak as discussed in the results section.

Sorting signed permutations by short operations.

Science.gov (United States)

Galvão, Gustavo Rodrigues; Lee, Orlando; Dias, Zanoni

2015-01-01

During evolution, global mutations may alter the order and the orientation of the genes in a genome. Such mutations are referred to as rearrangement events, or simply operations. In unichromosomal genomes, the most common operations are reversals, which are responsible for reversing the order and orientation of a sequence of genes, and transpositions, which are responsible for switching the location of two contiguous portions of a genome. The problem of computing the minimum sequence of operations that transforms one genome into another - which is equivalent to the problem of sorting a permutation into the identity permutation - is a well-studied problem that finds application in comparative genomics. There are a number of works concerning this problem in the literature, but they generally do not take into account the length of the operations (i.e. the number of genes affected by the operations). Since it has been observed that short operations are prevalent in the evolution of some species, algorithms that efficiently solve this problem in the special case of short operations are of interest. In this paper, we investigate the problem of sorting a signed permutation by short operations. More precisely, we study four flavors of this problem: (i) the problem of sorting a signed permutation by reversals of length at most 2; (ii) the problem of sorting a signed permutation by reversals of length at most 3; (iii) the problem of sorting a signed permutation by reversals and transpositions of length at most 2; and (iv) the problem of sorting a signed permutation by reversals and transpositions of length at most 3. We present polynomial-time solutions for problems (i) and (iii), a 5-approximation for problem (ii), and a 3-approximation for problem (iv). Moreover, we show that the expected approximation ratio of the 5-approximation algorithm is not greater than 3 for random signed permutations with more than 12 elements. Finally, we present experimental results that show

Exact many-body dynamics with stochastic one-body density matrix evolution

International Nuclear Information System (INIS)

Lacroix, D.

2004-05-01

In this article, we discuss some properties of the exact treatment of the many-body problem with stochastic Schroedinger equation (SSE). Starting from the SSE theory, an equivalent reformulation is proposed in terms of quantum jumps in the density matrix space. The technical details of the derivation a stochastic version of the Liouville von Neumann equation are given. It is shown that the exact Many-Body problem could be replaced by an ensemble of one-body density evolution, where each density matrix evolves according to its own mean-field augmented by a one-body noise. (author)

Statistical analysis of complex systems with nonclassical invariant measures

KAUST Repository

Fratalocchi, Andrea

2011-01-01

I investigate the problem of finding a statistical description of a complex many-body system whose invariant measure cannot be constructed stemming from classical thermodynamics ensembles. By taking solitons as a reference system and by employing a

Non-equilibrium many body dynamics

International Nuclear Information System (INIS)

Creutz, M.; Gyulassy, M.

1997-01-01

This Riken BNL Research Center Symposium on Non-Equilibrium Many Body Physics was held on September 23-25, 1997 as part of the official opening ceremony of the Center at Brookhaven National Lab. A major objective of theoretical work at the center is to elaborate on the full spectrum of strong interaction physics based on QCD, including the physics of confinement and chiral symmetry breaking, the parton structure of hadrons and nuclei, and the phenomenology of ultra-relativistic nuclear collisions related to the up-coming experiments at RHIC. The opportunities and challenges of nuclear and particle physics in this area naturally involve aspects of the many body problem common to many other fields. The aim of this symposium was to find common theoretical threads in the area of non-equilibrium physics and modern transport theories. The program consisted of invited talks on a variety topics from the fields of atomic, condensed matter, plasma, astrophysics, cosmology, and chemistry, in addition to nuclear and particle physics. Separate abstracts have been indexed into the database for contributions to this workshop

Non-equilibrium many body dynamics

Energy Technology Data Exchange (ETDEWEB)

Creutz, M.; Gyulassy, M.

1997-09-22

This Riken BNL Research Center Symposium on Non-Equilibrium Many Body Physics was held on September 23-25, 1997 as part of the official opening ceremony of the Center at Brookhaven National Lab. A major objective of theoretical work at the center is to elaborate on the full spectrum of strong interaction physics based on QCD, including the physics of confinement and chiral symmetry breaking, the parton structure of hadrons and nuclei, and the phenomenology of ultra-relativistic nuclear collisions related to the up-coming experiments at RHIC. The opportunities and challenges of nuclear and particle physics in this area naturally involve aspects of the many body problem common to many other fields. The aim of this symposium was to find common theoretical threads in the area of non-equilibrium physics and modern transport theories. The program consisted of invited talks on a variety topics from the fields of atomic, condensed matter, plasma, astrophysics, cosmology, and chemistry, in addition to nuclear and particle physics. Separate abstracts have been indexed into the database for contributions to this workshop.

Permutation parity machines for neural synchronization

International Nuclear Information System (INIS)

Reyes, O M; Kopitzke, I; Zimmermann, K-H

2009-01-01

Synchronization of neural networks has been studied in recent years as an alternative to cryptographic applications such as the realization of symmetric key exchange protocols. This paper presents a first view of the so-called permutation parity machine, an artificial neural network proposed as a binary variant of the tree parity machine. The dynamics of the synchronization process by mutual learning between permutation parity machines is analytically studied and the results are compared with those of tree parity machines. It will turn out that for neural synchronization, permutation parity machines form a viable alternative to tree parity machines

The Tucson-Melbourne Three-Body Force in a Translationally-Invariant Harmonic Oscillator Basis

Science.gov (United States)

Marsden, David; Navratil, Petr; Barrett, Bruce

2000-09-01

A translationally-invariant three-body basis set has been employed in shell model calculations on ^3H and ^3He including the Tucson-Melbourne form of the real nuclear three-body force. The basis consists of harmonic oscillators in Jacobi coordinates, explicitly avoiding the centre of mass drift problem in the calculations. The derivation of the three-body matrix elements and the results of large basis effective interaction shell model calculations will be presented. J. L. Friar, B. F. Gibson, G. L. Payne and S. A. Coon; Few Body Systems 5, 13 (1988) P. Navratil, G.P. Kamuntavicius and B.R. Barrett; Phys. Rev. C. 61, 044001 (2000)

Complete permutation Gray code implemented by finite state machine

Directory of Open Access Journals (Sweden)

Li Peng

2014-09-01

Full Text Available An enumerating method of complete permutation array is proposed. The list of n! permutations based on Gray code defined over finite symbol set Z(n = {1, 2, …, n} is implemented by finite state machine, named as n-RPGCF. An RPGCF can be used to search permutation code and provide improved lower bounds on the maximum cardinality of a permutation code in some cases.

A transposase strategy for creating libraries of circularly permuted proteins.

Science.gov (United States)

Mehta, Manan M; Liu, Shirley; Silberg, Jonathan J

2012-05-01

A simple approach for creating libraries of circularly permuted proteins is described that is called PERMutation Using Transposase Engineering (PERMUTE). In PERMUTE, the transposase MuA is used to randomly insert a minitransposon that can function as a protein expression vector into a plasmid that contains the open reading frame (ORF) being permuted. A library of vectors that express different permuted variants of the ORF-encoded protein is created by: (i) using bacteria to select for target vectors that acquire an integrated minitransposon; (ii) excising the ensemble of ORFs that contain an integrated minitransposon from the selected vectors; and (iii) circularizing the ensemble of ORFs containing integrated minitransposons using intramolecular ligation. Construction of a Thermotoga neapolitana adenylate kinase (AK) library using PERMUTE revealed that this approach produces vectors that express circularly permuted proteins with distinct sequence diversity from existing methods. In addition, selection of this library for variants that complement the growth of Escherichia coli with a temperature-sensitive AK identified functional proteins with novel architectures, suggesting that PERMUTE will be useful for the directed evolution of proteins with new functions.

Discrete Bat Algorithm for Optimal Problem of Permutation Flow Shop Scheduling

Science.gov (United States)

Luo, Qifang; Zhou, Yongquan; Xie, Jian; Ma, Mingzhi; Li, Liangliang

2014-01-01

A discrete bat algorithm (DBA) is proposed for optimal permutation flow shop scheduling problem (PFSP). Firstly, the discrete bat algorithm is constructed based on the idea of basic bat algorithm, which divide whole scheduling problem into many subscheduling problems and then NEH heuristic be introduced to solve subscheduling problem. Secondly, some subsequences are operated with certain probability in the pulse emission and loudness phases. An intensive virtual population neighborhood search is integrated into the discrete bat algorithm to further improve the performance. Finally, the experimental results show the suitability and efficiency of the present discrete bat algorithm for optimal permutation flow shop scheduling problem. PMID:25243220

Discrete bat algorithm for optimal problem of permutation flow shop scheduling.

Science.gov (United States)

Luo, Qifang; Zhou, Yongquan; Xie, Jian; Ma, Mingzhi; Li, Liangliang

2014-01-01

A discrete bat algorithm (DBA) is proposed for optimal permutation flow shop scheduling problem (PFSP). Firstly, the discrete bat algorithm is constructed based on the idea of basic bat algorithm, which divide whole scheduling problem into many subscheduling problems and then NEH heuristic be introduced to solve subscheduling problem. Secondly, some subsequences are operated with certain probability in the pulse emission and loudness phases. An intensive virtual population neighborhood search is integrated into the discrete bat algorithm to further improve the performance. Finally, the experimental results show the suitability and efficiency of the present discrete bat algorithm for optimal permutation flow shop scheduling problem.

Many-body localization from one particle density matrix

Energy Technology Data Exchange (ETDEWEB)

Bera, Soumya; Bardarson, Jens [Max Planck Institute for the Physics of Complex Systems, Dresden (Germany); Schomerus, Henning [Lancaster University, Lancaster (United Kingdom); Heidrich-Meisner, Fabian [Ludwig-Maximilians-Universitaet Muenchen (Germany)

2016-07-01

We show that the one-particle density matrix ρ can be used to characterize the interaction-driven many-body localization transition in isolated fermionic systems. The natural orbitals (the eigenstates) are localized in the many-body localized phase and spread out when one enters the delocalized phase, while the occupation spectrum (the set of eigenvalues) reveals the distinctive Fock- space structure of the many-body eigenstates, exhibiting a step-like discontinuity in the localized phase. The associated one-particle occupation entropy is small in the localized phase and large in the delocalized phase, with diverging fluctuations at the transition.

Thermodynamical and Green function many-body Wick theorems

International Nuclear Information System (INIS)

Westwanski, B.

1987-01-01

The thermodynamical and Green function many-body reduction theorems of Wick type are proved for the arbitrary mixtures of the fermion, boson and spin systems. ''Many-body'' means that the operators used are the products of the arbitrary number of one-body standard basis operators [of the fermion or (and) spin types] with different site (wave vector) indices, but having the same ''time'' (in the interaction representation). The method of proving is based on'' 1) the first-order differential equation of Schwinger type for: 1a) anti T-product of operators; 1b) its average value; 2) KMS boundary conditions for this average. It is shown that the fermion, boson and spin systems can be unified in the many-body formulation (bosonification of the fermion systems). It is impossible in the one-body approach. Both of the many-body versions of the Wick theorem have the recurrent feature: nth order moment diagrams for the free energy or Green functions can be expressed by the (n-1)th order ones. This property corresponds to the automatic realization of: (i) summations over Bose-Einstein or (and) Fermi-Dirac frequencies; (ii) elimination of Bose-Einstein or (and) Fermi-Dirac distributions. The procedures (i) and (ii), being the results of using the Green function one-body reduction theorem, have constituted the significant difficulty up to now in the treatment of quantum systems. (orig.)

Defects and permutation branes in the Liouville field theory

DEFF Research Database (Denmark)

Sarkissian, Gor

2009-01-01

The defects and permutation branes for the Liouville field theory are considered. By exploiting cluster condition, equations satisfied by permutation branes and defects reflection amplitudes are obtained. It is shown that two types of solutions exist, discrete and continuous families.......The defects and permutation branes for the Liouville field theory are considered. By exploiting cluster condition, equations satisfied by permutation branes and defects reflection amplitudes are obtained. It is shown that two types of solutions exist, discrete and continuous families....

Atoms as many-body systems

International Nuclear Information System (INIS)

Amusia, M Ya

2011-01-01

Contrary to common wisdom, not everything is clear and simple in the structure of many-electron atoms. Complexity in atoms is mainly a result of interelectron interaction that leads to rather unusual behaviour. Most transparently this is manifested in photo-ionization processes of many-electron atoms and some multi-atomic objects e.g. endohedrals. Particular attention will be given to the approach describing the interaction of photons with many-electron atoms in the frame of the many-body theory based on the Feynman diagrams technique. As a suitable one-electron approximation the Hartree - Fock (HF) approach will be presented. On its ground we will include the so-called electron correlation effects and discuss the frequently used Random Phase Approximation with Exchange - RPAE. Some results of recent calculations will be presented.

Atoms as many-body systems

Energy Technology Data Exchange (ETDEWEB)

Amusia, M Ya, E-mail: amusia@vms.huji.ac.il [Racah Institute of Physics, The Hebrew University, Jerusalem (Israel); Ioffe Physical-technical Institute, RAS, St. Petersburg (Russian Federation)

2011-09-16

Contrary to common wisdom, not everything is clear and simple in the structure of many-electron atoms. Complexity in atoms is mainly a result of interelectron interaction that leads to rather unusual behaviour. Most transparently this is manifested in photo-ionization processes of many-electron atoms and some multi-atomic objects e.g. endohedrals. Particular attention will be given to the approach describing the interaction of photons with many-electron atoms in the frame of the many-body theory based on the Feynman diagrams technique. As a suitable one-electron approximation the Hartree - Fock (HF) approach will be presented. On its ground we will include the so-called electron correlation effects and discuss the frequently used Random Phase Approximation with Exchange - RPAE. Some results of recent calculations will be presented.

Mathematical methods of many-body quantum field theory

CERN Document Server

Lehmann, Detlef

2004-01-01

Mathematical Methods of Many-Body Quantum Field Theory offers a comprehensive, mathematically rigorous treatment of many-body physics. It develops the mathematical tools for describing quantum many-body systems and applies them to the many-electron system. These tools include the formalism of second quantization, field theoretical perturbation theory, functional integral methods, bosonic and fermionic, and estimation and summation techniques for Feynman diagrams. Among the physical effects discussed in this context are BCS superconductivity, s-wave and higher l-wave, and the fractional quantum Hall effect. While the presentation is mathematically rigorous, the author does not focus solely on precise definitions and proofs, but also shows how to actually perform the computations.Presenting many recent advances and clarifying difficult concepts, this book provides the background, results, and detail needed to further explore the issue of when the standard approximation schemes in this field actually work and wh...

Nuclear many-body correlation dynamics--a nonperturbative approach in quantum many-body theory

International Nuclear Information System (INIS)

Wang Shunjin

1996-01-01

Based on the experimental results and theoretical experience in nuclear physics, the article has explored the basic physical ideas and theoretical methods in nuclear and quantum many-body correlation dynamics. The main theoretical results and important applications are introduced briefly. The paper addresses the fundamental ingredients and physical interpretation of theoretical results in a comprehensive way. Recent new results about correlation dynamics in quantum field theories are also presented. The perspectives of further application are viewed. (91 refs.)

Spectrum of quantum transfer matrices via classical many-body systems

Energy Technology Data Exchange (ETDEWEB)

Gorsky, A. [ITEP,Bolshaya Cheremushkinskaya str. 25, 117218, Moscow (Russian Federation); MIPT,Inststitutskii per. 9, 141700, Dolgoprudny, Moscow region (Russian Federation); Zabrodin, A. [ITEP,Bolshaya Cheremushkinskaya str. 25, 117218, Moscow (Russian Federation); MIPT,Inststitutskii per. 9, 141700, Dolgoprudny, Moscow region (Russian Federation); Institute of Biochemical Physics,Kosygina str. 4, 119991, Moscow (Russian Federation); National Research University Higher School of Economics,Myasnitskaya str. 20, 101000, Moscow (Russian Federation); Zotov, A. [ITEP,Bolshaya Cheremushkinskaya str. 25, 117218, Moscow (Russian Federation); MIPT,Inststitutskii per. 9, 141700, Dolgoprudny, Moscow region (Russian Federation); Steklov Mathematical Institute, RAS,Gubkina str. 8, 119991, Moscow (Russian Federation)

2014-01-15

In this paper we clarify the relationship between inhomogeneous quantum spin chains and classical integrable many-body systems. It provides an alternative (to the nested Bethe ansatz) method for computation of spectra of the spin chains. Namely, the spectrum of the quantum transfer matrix for the inhomogeneous gl{sub n}-invariant XXX spin chain on N sites with twisted boundary conditions can be found in terms of velocities of particles in the rational N-body Ruijsenaars-Schneider model. The possible values of the velocities are to be found from intersection points of two Lagrangian submanifolds in the phase space of the classical model. One of them is the Lagrangian hyperplane corresponding to fixed coordinates of all N particles and the other one is an N-dimensional Lagrangian submanifold obtained by fixing levels of N classical Hamiltonians in involution. The latter are determined by eigenvalues of the twist matrix. To support this picture, we give a direct proof that the eigenvalues of the Lax matrix for the classical Ruijsenaars-Schneider model, where velocities of particles are substituted by eigenvalues of the spin chain Hamiltonians, calculated through the Bethe equations, coincide with eigenvalues of the twist matrix, with certain multiplicities. We also prove a similar statement for the gl{sub n} Gaudin model with N marked points (on the quantum side) and the Calogero-Moser system with N particles (on the classical side). The realization of the results obtained in terms of branes and supersymmetric gauge theories is also discussed.

Permutation parity machines for neural cryptography.

Science.gov (United States)

Reyes, Oscar Mauricio; Zimmermann, Karl-Heinz

2010-06-01

Recently, synchronization was proved for permutation parity machines, multilayer feed-forward neural networks proposed as a binary variant of the tree parity machines. This ability was already used in the case of tree parity machines to introduce a key-exchange protocol. In this paper, a protocol based on permutation parity machines is proposed and its performance against common attacks (simple, geometric, majority and genetic) is studied.

Permutation parity machines for neural cryptography

International Nuclear Information System (INIS)

Reyes, Oscar Mauricio; Zimmermann, Karl-Heinz

2010-01-01

Recently, synchronization was proved for permutation parity machines, multilayer feed-forward neural networks proposed as a binary variant of the tree parity machines. This ability was already used in the case of tree parity machines to introduce a key-exchange protocol. In this paper, a protocol based on permutation parity machines is proposed and its performance against common attacks (simple, geometric, majority and genetic) is studied.

Permutations of massive vacua

Energy Technology Data Exchange (ETDEWEB)

Bourget, Antoine [Department of Physics, Universidad de Oviedo, Avenida Calvo Sotelo 18, 33007 Oviedo (Spain); Troost, Jan [Laboratoire de Physique Théorique de l’É cole Normale Supérieure, CNRS,PSL Research University, Sorbonne Universités, 75005 Paris (France)

2017-05-09

We discuss the permutation group G of massive vacua of four-dimensional gauge theories with N=1 supersymmetry that arises upon tracing loops in the space of couplings. We concentrate on superconformal N=4 and N=2 theories with N=1 supersymmetry preserving mass deformations. The permutation group G of massive vacua is the Galois group of characteristic polynomials for the vacuum expectation values of chiral observables. We provide various techniques to effectively compute characteristic polynomials in given theories, and we deduce the existence of varying symmetry breaking patterns of the duality group depending on the gauge algebra and matter content of the theory. Our examples give rise to interesting field extensions of spaces of modular forms.

Short history of nuclear many-body problem

International Nuclear Information System (INIS)

Köhler, H.S.

2014-01-01

This is a very short presentation regarding developments in the theory of nuclear many-body problems, as seen and experienced by the author during the past 60 years with particular emphasis on the contributions of Gerry Brown and his research-group. Much of his work was based on Brueckner's formulation of the nuclear many-body problem. It is reviewed briefly together with the Moszkowski–Scott separation method that was an important part of his early work. The core polarisation and his work related to effective interactions in general are also addressed

Analyzing Permutations for AES-like Ciphers: Understanding ShiftRows

DEFF Research Database (Denmark)

Beierle, Christof; Jovanovic, Philipp; Lauridsen, Martin Mehl

2015-01-01

Designing block ciphers and hash functions in a manner that resemble the AES in many aspects has been very popular since Rijndael was adopted as the Advanced Encryption Standard. However, in sharp contrast to the MixColumns operation, the security implications of the way the state is permuted...... by the operation resembling ShiftRows has never been studied in depth. Here, we provide the first structured study of the influence of ShiftRows-like operations, or more generally, word-wise permutations, in AES-like ciphers with respect to diffusion properties and resistance towards differential- and linear...... normal form. Using a mixed-integer linear programming approach, we obtain optimal parameters for a wide range of AES-like ciphers, and show improvements on parameters for Rijndael-192, Rijndael-256, PRIMATEs-80 and Prøst-128. As a separate result, we show for specific cases of the state geometry...

Effective linear two-body method for many-body problems in atomic and nuclear physics

International Nuclear Information System (INIS)

Kim, Y.E.; Zubarev, A.L.

2000-01-01

We present an equivalent linear two-body method for the many body problem, which is based on an approximate reduction of the many-body Schroedinger equation by the use of a variational principle. The method is applied to several problems in atomic and nuclear physics. (author)

Many-Body Quantum Chaos and Entanglement in a Quantum Ratchet

Science.gov (United States)

Valdez, Marc Andrew; Shchedrin, Gavriil; Heimsoth, Martin; Creffield, Charles E.; Sols, Fernando; Carr, Lincoln D.

2018-06-01

We uncover signatures of quantum chaos in the many-body dynamics of a Bose-Einstein condensate-based quantum ratchet in a toroidal trap. We propose measures including entanglement, condensate depletion, and spreading over a fixed basis in many-body Hilbert space, which quantitatively identify the region in which quantum chaotic many-body dynamics occurs, where random matrix theory is limited or inaccessible. With these tools, we show that many-body quantum chaos is neither highly entangled nor delocalized in the Hilbert space, contrary to conventionally expected signatures of quantum chaos.

Many-body localization of bosons in optical lattices

Science.gov (United States)

Sierant, Piotr; Zakrzewski, Jakub

2018-04-01

Many-body localization for a system of bosons trapped in a one-dimensional lattice is discussed. Two models that may be realized for cold atoms in optical lattices are considered. The model with a random on-site potential is compared with previously introduced random interactions model. While the origin and character of the disorder in both systems is different they show interesting similar properties. In particular, many-body localization appears for a sufficiently large disorder as verified by a time evolution of initial density wave states as well as using statistical properties of energy levels for small system sizes. Starting with different initial states, we observe that the localization properties are energy-dependent which reveals an inverted many-body localization edge in both systems (that finding is also verified by statistical analysis of energy spectrum). Moreover, we consider computationally challenging regime of transition between many body localized and extended phases where we observe a characteristic algebraic decay of density correlations which may be attributed to subdiffusion (and Griffiths-like regions) in the studied systems. Ergodicity breaking in the disordered Bose–Hubbard models is compared with the slowing-down of the time evolution of the clean system at large interactions.

Thermalization dynamics in a quenched many-body state

Science.gov (United States)

Kaufman, Adam; Preiss, Philipp; Tai, Eric; Lukin, Alex; Rispoli, Matthew; Schittko, Robert; Greiner, Markus

2016-05-01

Quantum and classical many-body systems appear to have disparate behavior due to the different mechanisms that govern their evolution. The dynamics of a classical many-body system equilibrate to maximally entropic states and quickly re-thermalize when perturbed. The assumptions of ergodicity and unbiased configurations lead to a successful framework of describing classical systems by a sampling of thermal ensembles that are blind to the system's microscopic details. By contrast, an isolated quantum many-body system is governed by unitary evolution: the system retains memory of past dynamics and constant global entropy. However, even with differing characteristics, the long-term behavior for local observables in quenched, non-integrable quantum systems are often well described by the same thermal framework. We explore the onset of this convergence in a many-body system of bosonic atoms in an optical lattice. Our system's finite size allows us to verify full state purity and measure local observables. We observe rapid growth and saturation of the entanglement entropy with constant global purity. The combination of global purity and thermalized local observables agree with the Eigenstate Thermalization Hypothesis in the presence of a near-volume law in the entanglement entropy.

Relativistic Many-Body Theory A New Field-Theoretical Approach

CERN Document Server

Lindgren, Ingvar

2011-01-01

Relativistic Many-Body Theory treats — for the first time — the combination of relativistic atomic many-body theory with quantum-electrodynamics (QED) in a unified manner. This book can be regarded as a continuation of the book by Lindgren and Morrison, Atomic Many-Body Theory (Springer 1986), which deals with the non-relativistic theory of many-electron systems, describing several means of treating the electron correlation to essentially all orders of perturbation theory. The treatment of the present book is based upon quantum-field theory, and demonstrates that when the procedure is carried to all orders of perturbation theory, two-particle systems are fully compatible with the relativistically covariant Bethe-Salpeter equation. This procedure can be applied to arbitrary open-shell systems, in analogy with the standard many-body theory, and it is also applicable to systems with more than two particles. Presently existing theoretical procedures for treating atomic systems are, in several cases, insuffici...

The quantum mechanics of many-body systems

CERN Document Server

Thouless, David James; Brueckner, Keith A

1961-01-01

The Quantum Mechanics of Many-Body Systems provides an introduction to that field of theoretical physics known as """"many-body theory."""" It is concerned with problems that are common to nuclear physics, atomic physics, the electron theory of metals, and to the theories of liquid helium three and four, and it describes the methods which have recently been developed to solve such problems. The aim has been to produce a unified account of the field, rather than to describe all the parallel methods that have been developed; as a result, a number of important papers are not mentioned. The main

A translationally invariant RPA-calculation for 16O on the basis of an algebraic solution of the many-body oscillator problem

International Nuclear Information System (INIS)

Schwesinger, B.

1978-01-01

The solution of the many-body oscillator problem is used as a basis for a RPA-calculation of 16 O. The calculation is performed in a LS-coupling scheme with an interaction containing central, spin-orbit and tensor forces. The main differences with conventional RPA-calculations occur for the transition probabilities. (orig.) [de

Set-Based Discrete Particle Swarm Optimization Based on Decomposition for Permutation-Based Multiobjective Combinatorial Optimization Problems.

Science.gov (United States)

Yu, Xue; Chen, Wei-Neng; Gu, Tianlong; Zhang, Huaxiang; Yuan, Huaqiang; Kwong, Sam; Zhang, Jun

2017-08-07

This paper studies a specific class of multiobjective combinatorial optimization problems (MOCOPs), namely the permutation-based MOCOPs. Many commonly seen MOCOPs, e.g., multiobjective traveling salesman problem (MOTSP), multiobjective project scheduling problem (MOPSP), belong to this problem class and they can be very different. However, as the permutation-based MOCOPs share the inherent similarity that the structure of their search space is usually in the shape of a permutation tree, this paper proposes a generic multiobjective set-based particle swarm optimization methodology based on decomposition, termed MS-PSO/D. In order to coordinate with the property of permutation-based MOCOPs, MS-PSO/D utilizes an element-based representation and a constructive approach. Through this, feasible solutions under constraints can be generated step by step following the permutation-tree-shaped structure. And problem-related heuristic information is introduced in the constructive approach for efficiency. In order to address the multiobjective optimization issues, the decomposition strategy is employed, in which the problem is converted into multiple single-objective subproblems according to a set of weight vectors. Besides, a flexible mechanism for diversity control is provided in MS-PSO/D. Extensive experiments have been conducted to study MS-PSO/D on two permutation-based MOCOPs, namely the MOTSP and the MOPSP. Experimental results validate that the proposed methodology is promising.

Slow dynamics in translation-invariant quantum lattice models

Science.gov (United States)

Michailidis, Alexios A.; Žnidarič, Marko; Medvedyeva, Mariya; Abanin, Dmitry A.; Prosen, Tomaž; Papić, Z.

2018-03-01

Many-body quantum systems typically display fast dynamics and ballistic spreading of information. Here we address the open problem of how slow the dynamics can be after a generic breaking of integrability by local interactions. We develop a method based on degenerate perturbation theory that reveals slow dynamical regimes and delocalization processes in general translation invariant models, along with accurate estimates of their delocalization time scales. Our results shed light on the fundamental questions of the robustness of quantum integrable systems and the possibility of many-body localization without disorder. As an example, we construct a large class of one-dimensional lattice models where, despite the absence of asymptotic localization, the transient dynamics is exceptionally slow, i.e., the dynamics is indistinguishable from that of many-body localized systems for the system sizes and time scales accessible in experiments and numerical simulations.

Nonlinear Quantum Metrology of Many-Body Open Systems

Science.gov (United States)

Beau, M.; del Campo, A.

2017-07-01

We introduce general bounds for the parameter estimation error in nonlinear quantum metrology of many-body open systems in the Markovian limit. Given a k -body Hamiltonian and p -body Lindblad operators, the estimation error of a Hamiltonian parameter using a Greenberger-Horne-Zeilinger state as a probe is shown to scale as N-[k -(p /2 )], surpassing the shot-noise limit for 2 k >p +1 . Metrology equivalence between initial product states and maximally entangled states is established for p ≥1 . We further show that one can estimate the system-environment coupling parameter with precision N-(p /2 ), while many-body decoherence enhances the precision to N-k in the noise-amplitude estimation of a fluctuating k -body Hamiltonian. For the long-range Ising model, we show that the precision of this parameter beats the shot-noise limit when the range of interactions is below a threshold value.

Ab initio translationally invariant nonlocal one-body densities from no-core shell-model theory

Science.gov (United States)

Burrows, M.; Elster, Ch.; Popa, G.; Launey, K. D.; Nogga, A.; Maris, P.

2018-02-01

Background: It is well known that effective nuclear interactions are in general nonlocal. Thus if nuclear densities obtained from ab initio no-core shell-model (NCSM) calculations are to be used in reaction calculations, translationally invariant nonlocal densities must be available. Purpose: Though it is standard to extract translationally invariant one-body local densities from NCSM calculations to calculate local nuclear observables like radii and transition amplitudes, the corresponding nonlocal one-body densities have not been considered so far. A major reason for this is that the procedure for removing the center-of-mass component from NCSM wave functions up to now has only been developed for local densities. Results: A formulation for removing center-of-mass contributions from nonlocal one-body densities obtained from NCSM and symmetry-adapted NCSM (SA-NCSM) calculations is derived, and applied to the ground state densities of 4He, 6Li, 12C, and 16O. The nonlocality is studied as a function of angular momentum components in momentum as well as coordinate space. Conclusions: We find that the nonlocality for the ground state densities of the nuclei under consideration increases as a function of the angular momentum. The relative magnitude of those contributions decreases with increasing angular momentum. In general, the nonlocal structure of the one-body density matrices we studied is given by the shell structure of the nucleus, and cannot be described with simple functional forms.

Detecting a many-body mobility edge with quantum quenches

Directory of Open Access Journals (Sweden)

Piero Naldesi, Elisa Ercolessi, Tommaso Roscilde

2016-10-01

Full Text Available The many-body localization (MBL transition is a quantum phase transition involving highly excited eigenstates of a disordered quantum many-body Hamiltonian, which evolve from "extended/ergodic" (exhibiting extensive entanglement entropies and fluctuations to "localized" (exhibiting area-law scaling of entanglement and fluctuations. The MBL transition can be driven by the strength of disorder in a given spectral range, or by the energy density at fixed disorder - if the system possesses a many-body mobility edge. Here we propose to explore the latter mechanism by using "quantum-quench spectroscopy", namely via quantum quenches of variable width which prepare the state of the system in a superposition of eigenstates of the Hamiltonian within a controllable spectral region. Studying numerically a chain of interacting spinless fermions in a quasi-periodic potential, we argue that this system has a many-body mobility edge; and we show that its existence translates into a clear dynamical transition in the time evolution immediately following a quench in the strength of the quasi-periodic potential, as well as a transition in the scaling properties of the quasi-stationary state at long times. Our results suggest a practical scheme for the experimental observation of many-body mobility edges using cold-atom setups.

Q-deformed algebras and many-body physics

Energy Technology Data Exchange (ETDEWEB)

Galetti, D; Lunardi, J T; Pimentel, B M [Instituto de Fisica Teorica (IFT), Sao Paulo, SP (Brazil); Lima, C L [Sao Paulo Univ., SP (Brazil). Inst. de Fisica

1995-11-01

A review is presented of some applications of q-deformed algebras to many-body systems. The rotational and pairing nuclear problems will be discussed in the context of q-deformed algebras, before presenting a more microscopically based application of q-deformed concepts to many-fermion systems. (author). 30 refs., 5 figs.

Permutations avoiding an increasing number of length-increasing forbidden subsequences

Directory of Open Access Journals (Sweden)

Elena Barcucci

2000-12-01

Full Text Available A permutation π is said to be τ-avoiding if it does not contain any subsequence having all the same pairwise comparisons as τ. This paper concerns the characterization and enumeration of permutations which avoid a set F j of subsequences increasing both in number and in length at the same time. Let F j be the set of subsequences of the form σ(j+1(j+2, σ being any permutation on {1,...,j}. For j=1 the only subsequence in F 1 is 123 and the 123-avoiding permutations are enumerated by the Catalan numbers; for j=2 the subsequences in F 2 are 1234 2134 and the (1234,2134 avoiding permutations are enumerated by the Schröder numbers; for each other value of j greater than 2 the subsequences in F j are j! and their length is (j+2 the permutations avoiding these j! subsequences are enumerated by a number sequence {a n } such that C n ≤ a n ≤ n!, C n being the n th Catalan number. For each j we determine the generating function of permutations avoiding the subsequences in F j according to the length, to the number of left minima and of non-inversions.

An AUC-based permutation variable importance measure for random forests.

Science.gov (United States)

Janitza, Silke; Strobl, Carolin; Boulesteix, Anne-Laure

2013-04-05

The random forest (RF) method is a commonly used tool for classification with high dimensional data as well as for ranking candidate predictors based on the so-called random forest variable importance measures (VIMs). However the classification performance of RF is known to be suboptimal in case of strongly unbalanced data, i.e. data where response class sizes differ considerably. Suggestions were made to obtain better classification performance based either on sampling procedures or on cost sensitivity analyses. However to our knowledge the performance of the VIMs has not yet been examined in the case of unbalanced response classes. In this paper we explore the performance of the permutation VIM for unbalanced data settings and introduce an alternative permutation VIM based on the area under the curve (AUC) that is expected to be more robust towards class imbalance. We investigated the performance of the standard permutation VIM and of our novel AUC-based permutation VIM for different class imbalance levels using simulated data and real data. The results suggest that the new AUC-based permutation VIM outperforms the standard permutation VIM for unbalanced data settings while both permutation VIMs have equal performance for balanced data settings. The standard permutation VIM loses its ability to discriminate between associated predictors and predictors not associated with the response for increasing class imbalance. It is outperformed by our new AUC-based permutation VIM for unbalanced data settings, while the performance of both VIMs is very similar in the case of balanced classes. The new AUC-based VIM is implemented in the R package party for the unbiased RF variant based on conditional inference trees. The codes implementing our study are available from the companion website: http://www.ibe.med.uni-muenchen.de/organisation/mitarbeiter/070_drittmittel/janitza/index.html.

Some topics on permutable subgroups in infinite groups

OpenAIRE

Ialenti, Roberto

2017-01-01

The aim of this thesis is to study permutability in different aspects of the theory of infinite groups. In particular, it will be studied the structure of groups in which all the members of a relevant system of subgroups satisfy a suitable generalized condition of permutability.

Seniority in quantum many-body systems

International Nuclear Information System (INIS)

Van Isacker, P.

2010-01-01

The use of the seniority quantum number in many-body systems is reviewed. A brief summary is given of its introduction by Racah in the context of atomic spectroscopy. Several extensions of Racah's original idea are discussed: seniority for identical nucleons in a single-j shell, its extension to the case of many, non-degenerate j shells and to systems with neutrons and protons. To illustrate its usefulness to this day, a recent application of seniority is presented in Bose-Einstein condensates of atoms with spin.

Probing many-body localization with neural networks

Science.gov (United States)

Schindler, Frank; Regnault, Nicolas; Neupert, Titus

2017-06-01

We show that a simple artificial neural network trained on entanglement spectra of individual states of a many-body quantum system can be used to determine the transition between a many-body localized and a thermalizing regime. Specifically, we study the Heisenberg spin-1/2 chain in a random external field. We employ a multilayer perceptron with a single hidden layer, which is trained on labeled entanglement spectra pertaining to the fully localized and fully thermal regimes. We then apply this network to classify spectra belonging to states in the transition region. For training, we use a cost function that contains, in addition to the usual error and regularization parts, a term that favors a confident classification of the transition region states. The resulting phase diagram is in good agreement with the one obtained by more conventional methods and can be computed for small systems. In particular, the neural network outperforms conventional methods in classifying individual eigenstates pertaining to a single disorder realization. It allows us to map out the structure of these eigenstates across the transition with spatial resolution. Furthermore, we analyze the network operation using the dreaming technique to show that the neural network correctly learns by itself the power-law structure of the entanglement spectra in the many-body localized regime.

Circular Permutation of a Chaperonin Protein: Biophysics and Application to Nanotechnology

Science.gov (United States)

Paavola, Chad; Chan, Suzanne; Li, Yi-Fen; McMillan, R. Andrew; Trent, Jonathan

2004-01-01

We have designed five circular permutants of a chaperonin protein derived from the hyperthermophilic organism Sulfolobus shibatae. These permuted proteins were expressed in E. coli and are well-folded. Furthermore, all the permutants assemble into 18-mer double rings of the same form as the wild-type protein. We characterized the thermodynamics of folding for each permutant by both guanidine denaturation and differential scanning calorimetry. We also examined the assembly of chaperonin rings into higher order structures that may be used as nanoscale templates. The results show that circular permutation can be used to tune the thermodynamic properties of a protein template as well as facilitating the fusion of peptides, binding proteins or enzymes onto nanostructured templates.

A semiclassical approach to many-body interference in Fock-space

Energy Technology Data Exchange (ETDEWEB)

Engl, Thomas

2015-11-01

Many-body systems draw ever more physicists' attention. Such an increase of interest often comes along with the development of new theoretical methods. In this thesis, a non-perturbative semiclassical approach is developed, which allows to analytically study many-body interference effects both in bosonic and fermionic Fock space and is expected to be applicable to many research areas in physics ranging from Quantum Optics and Ultracold Atoms to Solid State Theory and maybe even High Energy Physics. After the derivation of the semiclassical approximation, which is valid in the limit of large total number of particles, first applications manifesting the presence of many-body interference effects are shown. Some of them are confirmed numerically thus verifying the semiclassical predictions. Among these results are coherent back-/forward-scattering in bosonic and fermionic Fock space as well as a many-body spin echo, to name only the two most important ones.

Three-body forces mandated by Poincare invariance

International Nuclear Information System (INIS)

Coester, F.

1986-01-01

Poincare invariant models for the three-nucleon system are examined which have the same heuristic relation to field theories as the nonrelativistic nuclear models. The generators of the infinitesimal dynamical transformations can be obtained as functions of the kinematic generators, the invariant mass operator of the interacting system, and additional operators. These additional operators are the components of the Newton-Wigner position operator in the instant form, and the transverse components of the spin in the front form. The relativistic dynamics of Poincare transformations is examined, and then these concepts are applied to two-nucleon systems. The transition to a fully interacting three-nucleon system is made

The relativistic atomic many-body problem

International Nuclear Information System (INIS)

Brown, G.E.

1987-01-01

Problems connected with the infinite negative energy sea of electrons in the atomic many-body problem are discussed. It is shown that as long as one works in mean-field approximations, wave functions do not need to suffer from continuum dissociation. Various effects from virtual pairs in the wave functions are discussed. (orig.)

Many body perturbation calculations of photoionization

International Nuclear Information System (INIS)

Kelly, H.P.

1979-01-01

The application of many body perturbation theory to the calculation of atomic photoionization cross sections is reviewed. The choice of appropriate potential for the single-particle state is discussed and results are presented for several atoms including resonance structure. In addition to single photoionization, the process of double photoionization is considered and is found to be significant. (Auth.)

Quasiparticle many-body dynamics of the Anderson model

International Nuclear Information System (INIS)

Kuzemskij, A.L.

1996-01-01

The paper addresses the many-body quasiparticle dynamics of the Anderson impurity model at finite temperatures in the framework of the equation-of-motion method. We find a new exact identity relating the one-particle and many-particle Green's Functions. Using this identity we present a consistent and general scheme for a construction of generalised mean fields (elastic scattering corrections) and self-energy (inelastic scattering) in terms of the Dyson equation. A new approach for the complex expansion for the single-particle propagator in terms of the Coulomb repulsion U and hybridization V is proposed. Using the exact identity, the essentially new many-body dynamical solution of SIAM has been derived. This approach offers a new way for the systematic construction of the approximative interpolating dynamical solutions of the strongly correlated electron systems. 47 refs

Permutation orbifolds

International Nuclear Information System (INIS)

Bantay, P.

2002-01-01

A general theory of permutation orbifolds is developed for arbitrary twist groups. Explicit expressions for the number of primaries, the partition function, the genus one characters, the matrix elements of modular transformations and for fusion rule coefficients are presented, together with the relevant mathematical concepts, such as Λ-matrices and twisted dimensions. The arithmetic restrictions implied by the theory for the allowed modular representations in CFT are discussed. The simplest nonabelian example with twist group S 3 is described to illustrate the general theory

Ballistic near-field heat transport in dense many-body systems

Science.gov (United States)

Latella, Ivan; Biehs, Svend-Age; Messina, Riccardo; Rodriguez, Alejandro W.; Ben-Abdallah, Philippe

2018-01-01

Radiative heat transport mediated by near-field interactions is known to be superdiffusive in dilute, many-body systems. Here we use a generalized Landauer theory of radiative heat transfer in many-body planar systems to demonstrate a nonmonotonic transition from superdiffusive to ballistic transport in dense systems. We show that such a transition is associated to a change of the polarization of dominant modes. Our findings are complemented by a quantitative study of the relaxation dynamics of the system in the different regimes of heat transport. This result could have important consequences on thermal management at nanoscale of many-body systems.

Gauge invariance rediscovered

International Nuclear Information System (INIS)

Moriyasu, K.

1978-01-01

A pedagogical approach to gauge invariance is presented which is based on the analogy between gauge transformations and relativity. By using the concept of an internal space, purely geometrical arguments are used to teach the physical ideas behind gauge invariance. Many of the results are applicable to general gauge theories

A permutations representation that knows what " Eulerian" means

Directory of Open Access Journals (Sweden)

Roberto Mantaci

2001-12-01

Full Text Available Eulerian numbers (and ``Alternate Eulerian numbers'' are often interpreted as distributions of statistics defined over the Symmetric group. The main purpose of this paper is to define a way to represent permutations that provides some other combinatorial interpretations of these numbers. This representation uses a one-to-one correspondence between permutations and the so-called subexceedant functions.

General coordinate invariance in quantum many-body systems

Czech Academy of Sciences Publication Activity Database

Brauner, Tomáš; Endlich, S.; Monin, A.; Penco, R.

2014-01-01

Roč. 90, č. 10 (2014), s. 105016 ISSN 1550-7998 Institutional support: RVO:61389005 Keywords : Chiral Perturbation-Theory * Planar Galilei Group * Lagrangians Subject RIV: BE - Theoretical Physics Impact factor: 4.643, year: 2014

Atomic many-body theory of giant resonances

International Nuclear Information System (INIS)

Kelly, H.P.; Altun, Z.

1987-01-01

In this paper the use of many-body perturbation theory (MBPT) to include effects of electron correlations is discussed. The various physical processes contributing to the broad photoionization cross sections of the rare gases are studied in terms of the relevant many-body diagrams. Use of the random phase approximation with exchange (RPAE) is discussed by Amusia and Cherepkov. Calculations using the relativistic RPAE are reviewed by Johnson. In addition, many-body perturbation theory (MBPT) is used to study resonances which are due to excitation of bound states degenerate with the continuum. Very interesting giant resonance structure can occur when an inner shell electron is excited into a vacant open-shell orbital of the same principal quantum number. A particular example which is studied is the neutral manganese atom 3p 6 3d 5 4s 2 ( 6 S), in which the spins of the five 3d electrons are aligned. A very large resonance occurs in the 3d and 4s cross sections due to 3p → 3d excitation near 51 eV, and calculations of this resonance by MBPT and RPAE are discussed. A second example of this type of resonance occurs in open-shell rare-earth atoms with configurations 4d 10 4f/sup n/5s 2 5p 6 s 2 . Calculations and experimental results will be discussed for the case of europium with a half-filled sub-shell 4f 7 . 71 references, 15 figures

Young module multiplicities and classifying the indecomposable Young permutation modules

OpenAIRE

Gill, Christopher C.

2012-01-01

We study the multiplicities of Young modules as direct summands of permutation modules on cosets of Young subgroups. Such multiplicities have become known as the p-Kostka numbers. We classify the indecomposable Young permutation modules, and, applying the Brauer construction for p-permutation modules, we give some new reductions for p-Kostka numbers. In particular we prove that p-Kostka numbers are preserved under multiplying partitions by p, and strengthen a known reduction given by Henke, c...

Many-body interactions in quasi-freestanding graphene

Energy Technology Data Exchange (ETDEWEB)

Siegel, David; Park, Cheol-Hwan; Hwang, Choongyu; Deslippe, Jack; Fedorov, Alexei; Louie, Steven; Lanzara, Alessandra

2011-06-03

The Landau-Fermi liquid picture for quasiparticles assumes that charge carriers are dressed by many-body interactions, forming one of the fundamental theories of solids. Whether this picture still holds for a semimetal such as graphene at the neutrality point, i.e., when the chemical potential coincides with the Dirac point energy, is one of the long-standing puzzles in this field. Here we present such a study in quasi-freestanding graphene by using high-resolution angle-resolved photoemission spectroscopy. We see the electron-electron and electron-phonon interactions go through substantial changes when the semimetallic regime is approached, including renormalizations due to strong electron-electron interactions with similarities to marginal Fermi liquid behavior. These findings set a new benchmark in our understanding of many-body physics in graphene and a variety of novel materials with Dirac fermions.

The Structure of a Thermophilic Kinase Shapes Fitness upon Random Circular Permutation.

Science.gov (United States)

Jones, Alicia M; Mehta, Manan M; Thomas, Emily E; Atkinson, Joshua T; Segall-Shapiro, Thomas H; Liu, Shirley; Silberg, Jonathan J

2016-05-20

Proteins can be engineered for synthetic biology through circular permutation, a sequence rearrangement in which native protein termini become linked and new termini are created elsewhere through backbone fission. However, it remains challenging to anticipate a protein's functional tolerance to circular permutation. Here, we describe new transposons for creating libraries of randomly circularly permuted proteins that minimize peptide additions at their termini, and we use transposase mutagenesis to study the tolerance of a thermophilic adenylate kinase (AK) to circular permutation. We find that libraries expressing permuted AKs with either short or long peptides amended to their N-terminus yield distinct sets of active variants and present evidence that this trend arises because permuted protein expression varies across libraries. Mapping all sites that tolerate backbone cleavage onto AK structure reveals that the largest contiguous regions of sequence that lack cleavage sites are proximal to the phosphotransfer site. A comparison of our results with a range of structure-derived parameters further showed that retention of function correlates to the strongest extent with the distance to the phosphotransfer site, amino acid variability in an AK family sequence alignment, and residue-level deviations in superimposed AK structures. Our work illustrates how permuted protein libraries can be created with minimal peptide additions using transposase mutagenesis, and it reveals a challenge of maintaining consistent expression across permuted variants in a library that minimizes peptide additions. Furthermore, these findings provide a basis for interpreting responses of thermophilic phosphotransferases to circular permutation by calibrating how different structure-derived parameters relate to retention of function in a cellular selection.

Many-body physics with circuit quantum electrodynamics

International Nuclear Information System (INIS)

Leib, Martin H.

2015-01-01

We present proposals to simulate many-body physics with superconducting circuits. The ''body'' to work with for superconducting circuits is the microwave photon and interaction is induced by the nonlinearity of the Josephson effect. We present two different approaches to simulate Bose-Hubbard physics, one based on a polariton scheme and another with nonlinear resonators. We also present a Dicke-model like simulator for ultrastrongly coupled Josephson junctions to a resonator and show a scheme for implementing long range interactions.

Permutation groups

CERN Document Server

Passman, Donald S

2012-01-01

This volume by a prominent authority on permutation groups consists of lecture notes that provide a self-contained account of distinct classification theorems. A ready source of frequently quoted but usually inaccessible theorems, it is ideally suited for professional group theorists as well as students with a solid background in modern algebra.The three-part treatment begins with an introductory chapter and advances to an economical development of the tools of basic group theory, including group extensions, transfer theorems, and group representations and characters. The final chapter feature

Many-body forces and stability of the alkaline-earth tetramers

International Nuclear Information System (INIS)

Diaz-Torrejon, C.C.; Kaplan, Ilya G.

2011-01-01

Graphical abstract: Many-body forces effect. In a three-particle system, the two-body interaction energies depend upon coordinates of all three particles. The comparative study of the interaction energy and its many-body decomposition for alkaline-earths tetramers Be 4 , Mg 4 , and Ca 4 at the all-electron CCSD(T)/aug-cc-pVQZ level is performed. For study of dependence of the binding energy and the orbital population on the cluster size the corresponding dimers and trimers were also calculated at the same level of theory. In comparison with weakly bound dimers, the binding energy in trimers and, especially, in tetramers drastically increases; e.g., E b /N in Be 3 is 7 times larger and in Be 4 is 18.4 times larger than in Be 2 . This sharp increase is explained as a manifestation of many-body forces. The trimers and tetramers are stabilized by the three-body forces, whereas the two- and four-body forces are repulsive. The attractive contribution to the three-body forces has a three-atom electron exchange origin. The natural bond orbital (NBO) population analysis reveals a relatively large np-population in trimers and tetramers. The population of the valence np-orbitals leads to the sp-hybridization providing the covalent bonding. Research highlights: → The alkaline-earths trimers and tetramers are stabilized by the three-body forces. → Two- and four-body forces are repulsive for trimers and tetramers. → The attractive contribution to the three-body forces has a three-atom electron exchange origin. → The population of the np-orbitals leads to the sp-hybridization providing the covalent bonding. - Abstract: The comparative study of the interaction energy and its many-body decomposition for Be 4 , Mg 4 , and Ca 4 at the all-electron CCSD(T)/aug-cc-pVQZ level is performed. For study of dependence of the binding energy and the orbital population on the cluster size the corresponding dimers and trimers were also calculated at the same level of theory. In

Universal Properties of Many-Body Delocalization Transitions

Directory of Open Access Journals (Sweden)

Andrew C. Potter

2015-09-01

Full Text Available We study the dynamical melting of “hot” one-dimensional many-body localized systems. As disorder is weakened below a critical value, these nonthermal quantum glasses melt via a continuous dynamical phase transition into classical thermal liquids. By accounting for collective resonant tunneling processes, we derive and numerically solve an effective model for such quantum-to-classical transitions and compute their universal critical properties. Notably, the classical thermal liquid exhibits a broad regime of anomalously slow subdiffusive equilibration dynamics and energy transport. The subdiffusive regime is characterized by a continuously evolving dynamical critical exponent that diverges with a universal power at the transition. Our approach elucidates the universal long-distance, low-energy scaling structure of many-body delocalization transitions in one dimension, in a way that is transparently connected to the underlying microscopic physics. We discuss experimentally testable signatures of the predicted scaling properties.

Many body quantum physics at the condensed matter

International Nuclear Information System (INIS)

Llano, M. de

1981-01-01

The non-relativistic, continuous (as opposed to spin) many-body problem as it relates to condensed matter at absolute zero temperature is reviewed in simple, non-technical terms, mainly from the standpoint of infinite order perturbation theory, for physical systems where all the particles have the same mass but which otherwise interact with arbitrary short- or long-ranged two-body forces. (author)

Permutation based decision making under fuzzy environment using Tabu search

Directory of Open Access Journals (Sweden)

Mahdi Bashiri

2012-04-01

Full Text Available One of the techniques, which are used for Multiple Criteria Decision Making (MCDM is the permutation. In the classical form of permutation, it is assumed that weights and decision matrix components are crisp. However, when group decision making is under consideration and decision makers could not agree on a crisp value for weights and decision matrix components, fuzzy numbers should be used. In this article, the fuzzy permutation technique for MCDM problems has been explained. The main deficiency of permutation is its big computational time, so a Tabu Search (TS based algorithm has been proposed to reduce the computational time. A numerical example has illustrated the proposed approach clearly. Then, some benchmark instances extracted from literature are solved by proposed TS. The analyses of the results show the proper performance of the proposed method.

Many-body localization dynamics from a one-particle perspective

Energy Technology Data Exchange (ETDEWEB)

Lezama Mergold Love, Talia; Bera, Soumya; Bardarson, Jens Hjorleifur [Max Planck Institute for the Physics of Complex Systems, Dresden (Germany)

2016-07-01

Systems exhibiting many-body localization (Anderson insulators in the presence of interactions) present a novel class of nonergodic phases of matter. The study of entanglement, in terms of both exact eigenstates and its time evolution after quenches, has been useful to reveal the salient signatures of these systems. Similarly to the entanglement entropy of exact eigenstates, the one-particle density matrix can be used as a tool to characterize the many-body localization transition with its eigenvalues showing a Fermi-liquid like step discontinuity in the localized phase. However, this analysis distinguishes the Fock-space structure of the eigenstates from the real space. Here, we present numerical evidence for dynamical signatures of the many-body localized phase for a closed fermionic system, using the one-particle density matrix and its time evolution after a global quench. We discuss and compare our results with the well-known logarithmic spreading of entanglement (a dynamical signature of this phase, absent in the Anderson insulator).

Entanglement between noncomplementary parts of many-body systems

International Nuclear Information System (INIS)

Wichterich, Hannu Christian

2011-01-01

This thesis investigates the structure and behaviour of entanglement, the purely quantum mechanical part of correlations, in many-body systems, employing both numerical and analytical techniques at the interface of condensed matter theory and quantum information theory. Entanglement can be seen as a precious resource which, for example, enables the noiseless and instant transmission of quantum information, provided the communicating parties share a sufficient ''amount'' of it. Furthermore, measures of entanglement of a quantum mechanical state are perceived as useful probes of collective properties of many-body systems. For instance, certain measures are capable of detecting and classifying ground-state phases and, particularly, transition (or critical) points separating such phases. Chapters 2 and 3 focus on entanglement in many-body systems and its use as a potential resource for communication protocols. They address the questions of how a substantial amount of entanglement can be established between distant subsystems, and how efficiently this entanglement could be ''harvested'' by way of measurements. The subsequent chapters 4 and 5 are devoted to universality of entanglement between large collections of particles undergoing a quantum phase transition, where, despite the enormous complexity of these systems, collective properties including entanglement no longer depend crucially on the microscopic details. (orig.)

Encoding Sequential Information in Semantic Space Models: Comparing Holographic Reduced Representation and Random Permutation

Directory of Open Access Journals (Sweden)

Gabriel Recchia

2015-01-01

Full Text Available Circular convolution and random permutation have each been proposed as neurally plausible binding operators capable of encoding sequential information in semantic memory. We perform several controlled comparisons of circular convolution and random permutation as means of encoding paired associates as well as encoding sequential information. Random permutations outperformed convolution with respect to the number of paired associates that can be reliably stored in a single memory trace. Performance was equal on semantic tasks when using a small corpus, but random permutations were ultimately capable of achieving superior performance due to their higher scalability to large corpora. Finally, “noisy” permutations in which units are mapped to other units arbitrarily (no one-to-one mapping perform nearly as well as true permutations. These findings increase the neurological plausibility of random permutations and highlight their utility in vector space models of semantics.

Many body effects in the van der Waals force

International Nuclear Information System (INIS)

Perez, P.; Claro, F.

1985-08-01

A classical model of fluctuating dipoles is proposed for the evaluation of many-body effects in the van der Waals force between neutral polarizable particles. The method is applied to solid xenon giving the correct low temperature stable structure, unlike the usual two-body potential result. (author)

Topological Invariants and Ground-State Wave functions of Topological Insulators on a Torus

Directory of Open Access Journals (Sweden)

Zhong Wang

2014-01-01

Full Text Available We define topological invariants in terms of the ground-state wave functions on a torus. This approach leads to precisely defined formulas for the Hall conductance in four dimensions and the topological magnetoelectric θ term in three dimensions, and their generalizations in higher dimensions. They are valid in the presence of arbitrary many-body interactions and disorder. These topological invariants systematically generalize the two-dimensional Niu-Thouless-Wu formula and will be useful in numerical calculations of disordered topological insulators and strongly correlated topological insulators, especially fractional topological insulators.

A Fast Algorithm for Generating Permutation Distribution of Ranks in ...

African Journals Online (AJOL)

... function of the distribution of the ranks. This further gives insight into the permutation distribution of a rank statistics. The algorithm is implemented with the aid of the computer algebra system Mathematica. Key words: Combinatorics, generating function, permutation distribution, rank statistics, partitions, computer algebra.

Properties of exponential many-body interatomic potentials

Czech Academy of Sciences Publication Activity Database

Ostapovets, Andrej; Paidar, Václav

2009-01-01

Roč. 47, č. 3 (2009), s. 193-199 ISSN 0023-432X R&D Projects: GA AV ČR IAA100100920 Institutional research plan: CEZ:AV0Z10100520 Keywords : many-body potentials * elastic constants * multilayer surface relaxations Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.345, year: 2007

Energy Distributions from Three-Body Decaying Many-Body Resonances

International Nuclear Information System (INIS)

Alvarez-Rodriguez, R.; Jensen, A. S.; Fedorov, D. V.; Fynbo, H. O. U.; Garrido, E.

2007-01-01

We compute energy distributions of three particles emerging from decaying many-body resonances. We reproduce the measured energy distributions from decays of two archetypal states chosen as the lowest 0 + and 1 + resonances in 12 C populated in β decays. These states are dominated by sequential, through the 8 Be ground state, and direct decays, respectively. These decay mechanisms are reflected in the ''dynamic'' evolution from small, cluster or shell-model states, to large distances, where the coordinate or momentum space continuum wave functions are accurately computed

EDITORIAL: Focus on Quantum Information and Many-Body Theory

Science.gov (United States)

Eisert, Jens; Plenio, Martin B.

2010-02-01

Quantum many-body models describing natural systems or materials and physical systems assembled piece by piece in the laboratory for the purpose of realizing quantum information processing share an important feature: intricate correlations that originate from the coherent interaction between a large number of constituents. In recent years it has become manifest that the cross-fertilization between research devoted to quantum information science and to quantum many-body physics leads to new ideas, methods, tools, and insights in both fields. Issues of criticality, quantum phase transitions, quantum order and magnetism that play a role in one field find relations to the classical simulation of quantum systems, to error correction and fault tolerance thresholds, to channel capacities and to topological quantum computation, to name but a few. The structural similarities of typical problems in both fields and the potential for pooling of ideas then become manifest. Notably, methods and ideas from quantum information have provided fresh approaches to long-standing problems in strongly correlated systems in the condensed matter context, including both numerical methods and conceptual insights. Focus on quantum information and many-body theory Contents TENSOR NETWORKS Homogeneous multiscale entanglement renormalization ansatz tensor networks for quantum critical systems M Rizzi, S Montangero, P Silvi, V Giovannetti and Rosario Fazio Concatenated tensor network states R Hübener, V Nebendahl and W Dür Entanglement renormalization in free bosonic systems: real-space versus momentum-space renormalization group transforms G Evenbly and G Vidal Finite-size geometric entanglement from tensor network algorithms Qian-Qian Shi, Román Orús, John Ove Fjærestad and Huan-Qiang Zhou Characterizing symmetries in a projected entangled pair state D Pérez-García, M Sanz, C E González-Guillén, M M Wolf and J I Cirac Matrix product operator representations B Pirvu, V Murg, J I Cirac

Statistical analysis of complex systems with nonclassical invariant measures

KAUST Repository

Fratalocchi, Andrea

2011-02-28

I investigate the problem of finding a statistical description of a complex many-body system whose invariant measure cannot be constructed stemming from classical thermodynamics ensembles. By taking solitons as a reference system and by employing a general formalism based on the Ablowitz-Kaup-Newell-Segur scheme, I demonstrate how to build an invariant measure and, within a one-dimensional phase space, how to develop a suitable thermodynamics. A detailed example is provided with a universal model of wave propagation, with reference to a transparent potential sustaining gray solitons. The system shows a rich thermodynamic scenario, with a free-energy landscape supporting phase transitions and controllable emergent properties. I finally discuss the origin of such behavior, trying to identify common denominators in the area of complex dynamics.

Quantile-based permutation thresholds for quantitative trait loci hotspots.

Science.gov (United States)

Neto, Elias Chaibub; Keller, Mark P; Broman, Andrew F; Attie, Alan D; Jansen, Ritsert C; Broman, Karl W; Yandell, Brian S

2012-08-01

Quantitative trait loci (QTL) hotspots (genomic locations affecting many traits) are a common feature in genetical genomics studies and are biologically interesting since they may harbor critical regulators. Therefore, statistical procedures to assess the significance of hotspots are of key importance. One approach, randomly allocating observed QTL across the genomic locations separately by trait, implicitly assumes all traits are uncorrelated. Recently, an empirical test for QTL hotspots was proposed on the basis of the number of traits that exceed a predetermined LOD value, such as the standard permutation LOD threshold. The permutation null distribution of the maximum number of traits across all genomic locations preserves the correlation structure among the phenotypes, avoiding the detection of spurious hotspots due to nongenetic correlation induced by uncontrolled environmental factors and unmeasured variables. However, by considering only the number of traits above a threshold, without accounting for the magnitude of the LOD scores, relevant information is lost. In particular, biologically interesting hotspots composed of a moderate to small number of traits with strong LOD scores may be neglected as nonsignificant. In this article we propose a quantile-based permutation approach that simultaneously accounts for the number and the LOD scores of traits within the hotspots. By considering a sliding scale of mapping thresholds, our method can assess the statistical significance of both small and large hotspots. Although the proposed approach can be applied to any type of heritable high-volume "omic" data set, we restrict our attention to expression (e)QTL analysis. We assess and compare the performances of these three methods in simulations and we illustrate how our approach can effectively assess the significance of moderate and small hotspots with strong LOD scores in a yeast expression data set.

Quantum Markov processes and applications in many-body systems

International Nuclear Information System (INIS)

Temme, P. K.

2010-01-01

This thesis is concerned with the investigation of quantum as well as classical Markov processes and their application in the field of strongly correlated many-body systems. A Markov process is a special kind of stochastic process, which is determined by an evolution that is independent of its history and only depends on the current state of the system. The application of Markov processes has a long history in the field of statistical mechanics and classical many-body theory. Not only are Markov processes used to describe the dynamics of stochastic systems, but they predominantly also serve as a practical method that allows for the computation of fundamental properties of complex many-body systems by means of probabilistic algorithms. The aim of this thesis is to investigate the properties of quantum Markov processes, i.e. Markov processes taking place in a quantum mechanical state space, and to gain a better insight into complex many-body systems by means thereof. Moreover, we formulate a novel quantum algorithm which allows for the computation of the thermal and ground states of quantum many-body systems. After a brief introduction to quantum Markov processes we turn to an investigation of their convergence properties. We find bounds on the convergence rate of the quantum process by generalizing geometric bounds found for classical processes. We generalize a distance measure that serves as the basis for our investigations, the chi-square divergence, to non-commuting probability spaces. This divergence allows for a convenient generalization of the detailed balance condition to quantum processes. We then devise the quantum algorithm that can be seen as the natural generalization of the ubiquitous Metropolis algorithm to simulate quantum many-body Hamiltonians. By this we intend to provide further evidence, that a quantum computer can serve as a fully-fledged quantum simulator, which is not only capable of describing the dynamical evolution of quantum systems, but

Permutation groups and transformation semigroups : results and problems

OpenAIRE

Araujo, Joao; Cameron, Peter Jephson

2015-01-01

J.M. Howie, the influential St Andrews semigroupist, claimed that we value an area of pure mathematics to the extent that (a) it gives rise to arguments that are deep and elegant, and (b) it has interesting interconnections with other parts of pure mathematics. This paper surveys some recent results on the transformation semigroup generated by a permutation group $G$ and a single non-permutation $a$. Our particular concern is the influence that properties of $G$ (related to homogeneity, trans...

Many-body physics and the capacity of quantum channels with memory

International Nuclear Information System (INIS)

Plenio, M B; Virmani, S

2008-01-01

In most studies of the capacity of quantum channels, it is assumed that the errors in the use of each channel are independent. However, recent work has begun to investigate the effects of memory or correlations in the error, and has led to suggestions that there can be interesting non-analytic behaviour in the capacity of such channels. In a previous paper, we pursued this issue by connecting the study of channel capacities under correlated error to the study of critical behaviour in many-body physics. This connection enables the use of techniques from many-body physics to either completely solve or understand qualitatively a number of interesting models of correlated error with analogous behaviour to associated many-body systems. However, in order for this approach to work rigorously, there are a number of technical properties that need to be established for the lattice systems being considered. In this paper, we discuss these properties in detail, and establish them for some classes of many-body system

Classical many-body theory with retarded interactions: Dynamical irreversibility and determinism without probabilities

Energy Technology Data Exchange (ETDEWEB)

Zakharov, A.Yu., E-mail: Anatoly.Zakharov@novsu.ru; Zakharov, M.A., E-mail: ma_zakharov@list.ru

2016-01-28

The exact equations of motion for microscopic density of classical many-body system with account of inter-particle retarded interactions is derived. It is shown that interactions retardation leads to irreversible behavior of many-body systems. - Highlights: • A new form of equation of motion of classical many-body system is proposed. • Interactions retardation as one of the mechanisms of many-body system irreversibility. • Irreversibility and determinism without probabilities. • The possible way to microscopic foundation of thermodynamics.

Determination of Pavement Rehabilitation Activities through a Permutation Algorithm

Directory of Open Access Journals (Sweden)

Sangyum Lee

2013-01-01

Full Text Available This paper presents a mathematical programming model for optimal pavement rehabilitation planning. The model maximized the rehabilitation area through a newly developed permutation algorithm, based on the procedures outlined in the harmony search (HS algorithm. Additionally, the proposed algorithm was based on an optimal solution method for the problem of multilocation rehabilitation activities on pavement structure, using empirical deterioration and rehabilitation effectiveness models, according to a limited maintenance budget. Thus, nonlinear pavement performance and rehabilitation activity decision models were used to maximize the objective functions of the rehabilitation area within a limited budget, through the permutation algorithm. Our results showed that the heuristic permutation algorithm provided a good optimum in terms of maximizing the rehabilitation area, compared with a method of the worst-first maintenance currently used in Seoul.

Probing quantum and thermal noise in an interacting many-body system

DEFF Research Database (Denmark)

Hofferberth, S.; Lesanovsky, Igor; Schumm, Thorsten

2008-01-01

of the shot-to-shot variations of interference-fringe contrast for pairs of independently created one-dimensional Bose condensates. Analysing different system sizes, we observe the crossover from thermal to quantum noise, reflected in a characteristic change in the distribution functions from poissonian......The probabilistic character of the measurement process is one of the most puzzling and fascinating aspects of quantum mechanics. In many-body systems quantum-mechanical noise reveals non-local correlations of the underlying many-body states. Here, we provide a complete experimental analysis....... Furthermore, our experiments constitute the first analysis of the full distribution of quantum noise in an interacting many-body system....

A Permutation Approach for Selecting the Penalty Parameter in Penalized Model Selection

Science.gov (United States)

Sabourin, Jeremy A; Valdar, William; Nobel, Andrew B

2015-01-01

Summary We describe a simple, computationally effcient, permutation-based procedure for selecting the penalty parameter in LASSO penalized regression. The procedure, permutation selection, is intended for applications where variable selection is the primary focus, and can be applied in a variety of structural settings, including that of generalized linear models. We briefly discuss connections between permutation selection and existing theory for the LASSO. In addition, we present a simulation study and an analysis of real biomedical data sets in which permutation selection is compared with selection based on the following: cross-validation (CV), the Bayesian information criterion (BIC), Scaled Sparse Linear Regression, and a selection method based on recently developed testing procedures for the LASSO. PMID:26243050

Time dependent mean field approximation to the many-body S-matrix

International Nuclear Information System (INIS)

Alhassid, Y.; Koonin, S.E.

1980-01-01

Time-dependent Hartree-Fock (TDHF) calculations are a good description of some inclusive properties of deep inelastic heavy-ion collisions. The first steps toward a mean-field theory that approximates specific elements of the many-body S matrix are presented. A many-body system with pairwise interactions excited by an external, time-dependent one-body field is considered. The methods are used to solve the forced Lipkin model. The moduli of elastic and excitation amplitudes are plotted. 3 figures

Many-body perturbation theory for ab initio nuclear structure

International Nuclear Information System (INIS)

Tichai, Alexander

2017-01-01

The solution of the quantum many-body problem for medium-mass nuclei using realistic nuclear interactions poses a superbe challenge for nuclear structure research. Because an exact solution can only be provided for the lightest nuclei, one has to rely on approximate solutions when proceeding to heavier systems. Over the past years, tremendous progress has been made in the development and application of systematically improvable expansion methods and an accurate description of nuclear observables has become viable up to mass number A ∼ 100. While closed-shell systems are consistently described via a plethora of different many-body methods, the extension to genuine open-shell systems still remains a major challenge and up to now there is no ab initio many-body method which applies equally well to systems with even and odd mass numbers. The goal of this thesis is the development and implementation of innovative perturbative approaches with genuine open-shell capabilities. This requires the extension of well-known single-reference approaches to more general vacua. In this work we choose two complementary routes for the usage of generalized reference states. First, we derive a new ab initio approach based on multi-configurational reference states that are conveniently derived from a prior no-core shell model calculation. Perturbative corrections are derived via second-order many-body perturbation theory, thus, merging configuration interaction and many-body perturbation theory. The generality of this ansatz enables for a treatment of medium-mass systems with arbitrary mass number, as well as the extension to low-lying excited states such that ground and excited states are treated on an equal footing. In a complementary approach, we use reference states that break a symmetry of the underlying Hamiltonian. In the simplest case this corresponds to the expansion around a particle-number-broken Hartree-Fock-Bogolyubov vacuum which is obtained from a mean-field calculation

Some exact solutions to the translation-invariant N-body problem

International Nuclear Information System (INIS)

Hall, R.L.

1978-01-01

It is shown that Schroedinger's equation for a translation-invariant system consisting of N particles with arbitrary masses interacting via Hooke's law pair potentials with the same coupling constant can be solved exactly; explicit solutions are found for the case N = 3. Exact solutions are also found explicitly for the translation-invariant problem in which a particle with mass m 0 interacts with N identical particles of mass m 1 via Hooke's law pair potential with coupling constant k 0 2 , and the identical particles interact with each other via Hooke's law pair potentials with coupling constant k 1 2 . The latter solution provides a basis problem for an energy lower-bound method for translation-invariant atom-like systems. (author)

Porter-Thomas distribution in unstable many-body systems

International Nuclear Information System (INIS)

Volya, Alexander

2011-01-01

We use the continuum shell model approach to explore the resonance width distribution in unstable many-body systems. The single-particle nature of a decay, the few-body character of the interaction Hamiltonian, and the collectivity that emerges in nonstationary systems due to the coupling to the continuum of reaction states are discussed. Correlations between the structures of the parent and daughter nuclear systems in the common Fock space are found to result in deviations of decay width statistics from the Porter-Thomas distribution.

Many Body Structure of Strongly Interacting Systems

CERN Document Server

Arenhövel, Hartmuth; Drechsel, Dieter; Friedrich, Jörg; Kaiser, Karl-Heinz; Walcher, Thomas; Symposium on 20 Years of Physics at the Mainz Microtron MAMI

2006-01-01

This carefully edited proceedings volume provides an extensive review and analysis of the work carried out over the past 20 years at the Mainz Microtron (MAMI). This research centered around the application of Quantum Chromodynamics in the strictly nonperturbative regime at hadronic scales of about 1 fm. Due to the many degrees of freedom in hadrons at this scale the leitmotiv of this research is "Many body structure of strongly interacting systems". Further, an outlook on the research with the forthcoming upgrade of MAMI is given. This volume is an authoritative source of reference for everyone interested in the field of the electro-weak probing of the structure of hadrons.

Genuine quantum correlations in quantum many-body systems: a review of recent progress.

Science.gov (United States)

De Chiara, Gabriele; Sanpera, Anna

2018-04-19

Quantum information theory has considerably helped in the understanding of quantum many-body systems. The role of quantum correlations and in particular, bipartite entanglement, has become crucial to characterise, classify and simulate quantum many body systems. Furthermore, the scaling of entanglement has inspired modifications to numerical techniques for the simulation of many-body systems leading to the, now established, area of tensor networks. However, the notions and methods brought by quantum information do not end with bipartite entanglement. There are other forms of correlations embedded in the ground, excited and thermal states of quantum many-body systems that also need to be explored and might be utilised as potential resources for quantum technologies. The aim of this work is to review the most recent developments regarding correlations in quantum many-body systems focussing on multipartite entanglement, quantum nonlocality, quantum discord, mutual information but also other non classical measures of correlations based on quantum coherence. Moreover, we also discuss applications of quantum metrology in quantum many-body systems. © 2018 IOP Publishing Ltd.

Many-body quantum chaos: Recent developments and applications to nuclei

International Nuclear Information System (INIS)

Gomez, J.M.G.; Kar, K.; Kota, V.K.B.; Molina, R.A.; Relano, A.; Retamosa, J.

2011-01-01

In the last decade, there has been an increasing interest in the analysis of energy level spectra and wave functions of nuclei, particles, atoms and other quantum many-body systems by means of statistical methods and random matrix ensembles. The concept of quantum chaos plays a central role for understanding the universal properties of the energy spectrum of quantum systems. Since these properties concern the whole spectrum, statistical methods become an essential tool. Besides random matrix theory, new theoretical developments making use of information theory, time series analysis, and the merging of thermodynamics and the semiclassical approximation are emphasized. Applications of these methods to quantum systems, especially to atomic nuclei, are reviewed. We focus on recent developments like the study of 'imperfect spectra' to estimate the degree of symmetry breaking or the fraction of missing levels, the existence of chaos remnants in nuclear masses, the onset of chaos in nuclei, and advances in the comprehension of the Hamiltonian structure in many-body systems. Finally, some applications of statistical spectroscopy methods generated by many-body chaos and two-body random matrix ensembles are described, with emphasis on Gamow-Teller strength sums and beta decay rates for stellar evolution and supernovae.

Solvable Family of Driven-Dissipative Many-Body Systems

Science.gov (United States)

Foss-Feig, Michael; Young, Jeremy T.; Albert, Victor V.; Gorshkov, Alexey V.; Maghrebi, Mohammad F.

2017-11-01

Exactly solvable models have played an important role in establishing the sophisticated modern understanding of equilibrium many-body physics. Conversely, the relative scarcity of solutions for nonequilibrium models greatly limits our understanding of systems away from thermal equilibrium. We study a family of nonequilibrium models, some of which can be viewed as dissipative analogues of the transverse-field Ising model, in that an effectively classical Hamiltonian is frustrated by dissipative processes that drive the system toward states that do not commute with the Hamiltonian. Surprisingly, a broad and experimentally relevant subset of these models can be solved efficiently. We leverage these solutions to compute the effects of decoherence on a canonical trapped-ion-based quantum computation architecture, and to prove a no-go theorem on steady-state phase transitions in a many-body model that can be realized naturally with Rydberg atoms or trapped ions.

Paradeisos: A perfect hashing algorithm for many-body eigenvalue problems

Science.gov (United States)

Jia, C. J.; Wang, Y.; Mendl, C. B.; Moritz, B.; Devereaux, T. P.

2018-03-01

We describe an essentially perfect hashing algorithm for calculating the position of an element in an ordered list, appropriate for the construction and manipulation of many-body Hamiltonian, sparse matrices. Each element of the list corresponds to an integer value whose binary representation reflects the occupation of single-particle basis states for each element in the many-body Hilbert space. The algorithm replaces conventional methods, such as binary search, for locating the elements of the ordered list, eliminating the need to store the integer representation for each element, without increasing the computational complexity. Combined with the "checkerboard" decomposition of the Hamiltonian matrix for distribution over parallel computing environments, this leads to a substantial savings in aggregate memory. While the algorithm can be applied broadly to many-body, correlated problems, we demonstrate its utility in reducing total memory consumption for a series of fermionic single-band Hubbard model calculations on small clusters with progressively larger Hilbert space dimension.

Permutation-based inference for the AUC: A unified approach for continuous and discontinuous data.

Science.gov (United States)

Pauly, Markus; Asendorf, Thomas; Konietschke, Frank

2016-11-01

We investigate rank-based studentized permutation methods for the nonparametric Behrens-Fisher problem, that is, inference methods for the area under the ROC curve. We hereby prove that the studentized permutation distribution of the Brunner-Munzel rank statistic is asymptotically standard normal, even under the alternative. Thus, incidentally providing the hitherto missing theoretical foundation for the Neubert and Brunner studentized permutation test. In particular, we do not only show its consistency, but also that confidence intervals for the underlying treatment effects can be computed by inverting this permutation test. In addition, we derive permutation-based range-preserving confidence intervals. Extensive simulation studies show that the permutation-based confidence intervals appear to maintain the preassigned coverage probability quite accurately (even for rather small sample sizes). For a convenient application of the proposed methods, a freely available software package for the statistical software R has been developed. A real data example illustrates the application. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Almost conserved operators in nearly many-body localized systems

Science.gov (United States)

Pancotti, Nicola; Knap, Michael; Huse, David A.; Cirac, J. Ignacio; Bañuls, Mari Carmen

2018-03-01

We construct almost conserved local operators, that possess a minimal commutator with the Hamiltonian of the system, near the many-body localization transition of a one-dimensional disordered spin chain. We collect statistics of these slow operators for different support sizes and disorder strengths, both using exact diagonalization and tensor networks. Our results show that the scaling of the average of the smallest commutators with the support size is sensitive to Griffiths effects in the thermal phase and the onset of many-body localization. Furthermore, we demonstrate that the probability distributions of the commutators can be analyzed using extreme value theory and that their tails reveal the difference between diffusive and subdiffusive dynamics in the thermal phase.

Probing many-body interactions in an optical lattice clock

Energy Technology Data Exchange (ETDEWEB)

Rey, A.M., E-mail: arey@jilau1.colorado.edu [JILA, NIST and University of Colorado, Department of Physics, Boulder, CO 80309 (United States); Gorshkov, A.V. [Joint Quantum Institute, NIST and University of Maryland, Department of Physics, College Park, MD 20742 (United States); Kraus, C.V. [Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck (Austria); Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck (Austria); Martin, M.J. [JILA, NIST and University of Colorado, Department of Physics, Boulder, CO 80309 (United States); Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125 (United States); Bishof, M.; Swallows, M.D.; Zhang, X.; Benko, C.; Ye, J. [JILA, NIST and University of Colorado, Department of Physics, Boulder, CO 80309 (United States); Lemke, N.D.; Ludlow, A.D. [National Institute of Standards and Technology, Boulder, CO 80305 (United States)

2014-01-15

We present a unifying theoretical framework that describes recently observed many-body effects during the interrogation of an optical lattice clock operated with thousands of fermionic alkaline earth atoms. The framework is based on a many-body master equation that accounts for the interplay between elastic and inelastic p-wave and s-wave interactions, finite temperature effects and excitation inhomogeneity during the quantum dynamics of the interrogated atoms. Solutions of the master equation in different parameter regimes are presented and compared. It is shown that a general solution can be obtained by using the so called Truncated Wigner Approximation which is applied in our case in the context of an open quantum system. We use the developed framework to model the density shift and decay of the fringes observed during Ramsey spectroscopy in the JILA {sup 87}Sr and NIST {sup 171}Yb optical lattice clocks. The developed framework opens a suitable path for dealing with a variety of strongly-correlated and driven open-quantum spin systems. -- Highlights: •Derived a theoretical framework that describes many-body effects in a lattice clock. •Validated the analysis with recent experimental measurements. •Demonstrated the importance of beyond mean field corrections in the dynamics.

Spin-dependent electron many-body effects in GaAs

Science.gov (United States)

Nemec, P.; Kerachian, Y.; van Driel, H. M.; Smirl, Arthur L.

2005-12-01

Time- and polarization-resolved differential transmission measurements employing same and oppositely circularly polarized 150fs optical pulses are used to investigate spin characteristics of conduction band electrons in bulk GaAs at 295K . Electrons and holes with densities in the 2×1016cm-3-1018cm-3 range are generated and probed with pulses whose center wavelength is between 865 and 775nm . The transmissivity results can be explained in terms of the spin sensitivity of both phase-space filling and many-body effects (band-gap renormalization and screening of the Coulomb enhancement factor). For excitation and probing at 865nm , just above the band-gap edge, the transmissivity changes mainly reflect spin-dependent phase-space filling which is dominated by the electron Fermi factors. However, for 775nm probing, the influence of many-body effects on the induced transmission change are comparable with those from reduced phase space filling, exposing the spin dependence of the many-body effects. If one does not take account of these spin-dependent effects one can misinterpret both the magnitude and time evolution of the electron spin polarization. For suitable measurements we find that the electron spin relaxation time is 130ps .

Image encryption based on permutation-substitution using chaotic map and Latin Square Image Cipher

Science.gov (United States)

Panduranga, H. T.; Naveen Kumar, S. K.; Kiran, HASH(0x22c8da0)

2014-06-01

In this paper we presented a image encryption based on permutation-substitution using chaotic map and Latin square image cipher. The proposed method consists of permutation and substitution process. In permutation process, plain image is permuted according to chaotic sequence generated using chaotic map. In substitution process, based on secrete key of 256 bit generate a Latin Square Image Cipher (LSIC) and this LSIC is used as key image and perform XOR operation between permuted image and key image. The proposed method can applied to any plain image with unequal width and height as well and also resist statistical attack, differential attack. Experiments carried out for different images of different sizes. The proposed method possesses large key space to resist brute force attack.

Adjusted permutation method for multiple attribute decision making with meta-heuristic solution approaches

Directory of Open Access Journals (Sweden)

Hossein Karimi

2011-04-01

Full Text Available The permutation method of multiple attribute decision making has two significant deficiencies: high computational time and wrong priority output in some problem instances. In this paper, a novel permutation method called adjusted permutation method (APM is proposed to compensate deficiencies of conventional permutation method. We propose Tabu search (TS and particle swarm optimization (PSO to find suitable solutions at a reasonable computational time for large problem instances. The proposed method is examined using some numerical examples to evaluate the performance of the proposed method. The preliminary results show that both approaches provide competent solutions in relatively reasonable amounts of time while TS performs better to solve APM.

A novel particle swarm optimization algorithm for permutation flow-shop scheduling to minimize makespan

International Nuclear Information System (INIS)

Lian Zhigang; Gu Xingsheng; Jiao Bin

2008-01-01

It is well known that the flow-shop scheduling problem (FSSP) is a branch of production scheduling and is NP-hard. Now, many different approaches have been applied for permutation flow-shop scheduling to minimize makespan, but current algorithms even for moderate size problems cannot be solved to guarantee optimality. Some literatures searching PSO for continuous optimization problems are reported, but papers searching PSO for discrete scheduling problems are few. In this paper, according to the discrete characteristic of FSSP, a novel particle swarm optimization (NPSO) algorithm is presented and successfully applied to permutation flow-shop scheduling to minimize makespan. Computation experiments of seven representative instances (Taillard) based on practical data were made, and comparing the NPSO with standard GA, we obtain that the NPSO is clearly more efficacious than standard GA for FSSP to minimize makespan

Secure physical layer using dynamic permutations in cognitive OFDMA systems

DEFF Research Database (Denmark)

Meucci, F.; Wardana, Satya Ardhy; Prasad, Neeli R.

2009-01-01

This paper proposes a novel lightweight mechanism for a secure Physical (PHY) layer in Cognitive Radio Network (CRN) using Orthogonal Frequency Division Multiplexing (OFDM). User's data symbols are mapped over the physical subcarriers with a permutation formula. The PHY layer is secured...... with a random and dynamic subcarrier permutation which is based on a single pre-shared information and depends on Dynamic Spectrum Access (DSA). The dynamic subcarrier permutation is varying over time, geographical location and environment status, resulting in a very robust protection that ensures...... confidentiality. The method is shown to be effective also for existing non-cognitive systems. The proposed mechanism is effective against eavesdropping even if the eavesdropper adopts a long-time patterns analysis, thus protecting cryptography techniques of higher layers. The correlation properties...

Photoionization cross sections and Auger rates calculated by many-body perturbation theory

International Nuclear Information System (INIS)

Kelly, H.P.

1976-01-01

Methods for applying the many body perturbation theory to atomic calculations are discussed with particular emphasis on calculation of photoionization cross sections and Auger rates. Topics covered include: Rayleigh--Schroedinger theory; many body perturbation theory; calculations of photoionization cross sections; and Auger rates

Quantum theory of many-body systems techniques and applications

CERN Document Server

Zagoskin, Alexandre

2014-01-01

This text presents a self-contained treatment of the physics of many-body systems from the point of view of condensed matter. The approach, quite traditionally, uses the mathematical formalism of quasiparticles and Green’s functions. In particular, it covers all the important diagram techniques for normal and superconducting systems, including the zero-temperature perturbation theory and the Matsubara, Keldysh and Nambu-Gor'kov formalism, as well as an introduction to Feynman path integrals. This new edition contains an introduction to the methods of theory of one-dimensional systems (bosonization and conformal field theory) and their applications to many-body problems.   Intended for graduate students in physics and related fields, the aim is not to be exhaustive, but to present enough detail to enable the student to follow the current research literature, or to apply the techniques to new problems. Many of the examples are drawn from mesoscopic physics, which deals with systems small enough that quantum...

Relativistic many-body theory a new field-theoretical approach

CERN Document Server

Lindgren, Ingvar

2016-01-01

This revised second edition of the author’s classic text offers readers a comprehensively updated review of relativistic atomic many-body theory, covering the many developments in the field since the publication of the original title.  In particular, a new final section extends the scope to cover the evaluation of QED effects for dynamical processes. The treatment of the book is based upon quantum-field theory, and demonstrates that when the procedure is carried to all orders of perturbation theory, two-particle systems are fully compatible with the relativistically covariant Bethe-Salpeter equation. This procedure can be applied to arbitrary open-shell systems, in analogy with the standard many-body theory, and it is also applicable to systems with more than two particles. Presently existing theoretical procedures for treating atomic systems are, in several cases, insufficient to explain the accurate experimental data recently obtained, particularly for highly charged ions. The main text is divided into...

Nuclear, particle and many body physics

CERN Document Server

Morse, Philip M; Feshbach, Herman

2013-01-01

Nuclear, Particle and Many Body Physics, Volume II, is the second of two volumes dedicated to the memory of physicist Amos de-Shalit. The contributions in this volume are a testament to the respect he earned as a physicist and of the warm and rich affection he commanded as a personal friend. The book contains 41 chapters and begins with a study on the renormalization of rational Lagrangians. Separate chapters cover the scattering of high energy protons by light nuclei; approximation of the dynamics of proton-neutron systems; the scattering amplitude for the Gaussian potential; Coulomb excitati

Theory of many-body localization in periodically driven systems

International Nuclear Information System (INIS)

Abanin, Dmitry A.; De Roeck, Wojciech; Huveneers, François

2016-01-01

We present a theory of periodically driven, many-body localized (MBL) systems. We argue that MBL persists under periodic driving at high enough driving frequency: The Floquet operator (evolution operator over one driving period) can be represented as an exponential of an effective time-independent Hamiltonian, which is a sum of quasi-local terms and is itself fully MBL. We derive this result by constructing a sequence of canonical transformations to remove the time-dependence from the original Hamiltonian. When the driving evolves smoothly in time, the theory can be sharpened by estimating the probability of adiabatic Landau–Zener transitions at many-body level crossings. In all cases, we argue that there is delocalization at sufficiently low frequency. We propose a phase diagram of driven MBL systems.

Fifth International Conference on Recent Progress in Many-Body Theories

CERN Document Server

Pajanne, E; Bishop, R; Recent Progress in MANY-BODY THEORIES

1988-01-01

The present volume contains the texts of the invited talks delivered at the Fifth International Conference on Recent Progress in Many-Body Theories held in Oulu, Finland during the period 3-8 August 1987. The general format and style of the meeting followed closely those which had evolved from the earlier conferences in the series: Trieste 1978, Oaxtepec 1981, Altenberg 1983 and San Francisco 1985. Thus, the conferences in this series are in­ tended, as far as is practicable, to cover in a broad and balanced fashion both the entire spectrum of theoretical tools developed to tackle the quan­ tum many-body problem, and their major fields of· application. One of the major aims of the series is to foster the exchange of ideas and techniques among physicists working in such diverse areas of application of many-body theories as nucleon-nucleon interactions, nuclear physics, astronomy, atomic and molecular physics, quantum chemistry, quantum fluids and plasmas, and solid-state and condensed matter physics. A spec...

Diagonalization and Many-Body Localization for a Disordered Quantum Spin Chain

OpenAIRE

Imbrie, John Z

2016-01-01

We consider a weakly interacting quantum spin chain with random local interactions. We prove that many-body localization follows from a physically reasonable assumption that limits the extent of level attraction in the statistics of eigenvalues. In a KAM-style construction, a sequence of local unitary transformations is used to diagonalize the Hamiltonian by deforming the initial tensor product basis into a complete set of exact many-body eigenfunctions.

Permutational symmetries for coincidence rates in multimode multiphotonic interferometry

Science.gov (United States)

Khalid, Abdullah; Spivak, Dylan; Sanders, Barry C.; de Guise, Hubert

2018-06-01

We obtain coincidence rates for passive optical interferometry by exploiting the permutational symmetries of partially distinguishable input photons, and our approach elucidates qualitative features of multiphoton coincidence landscapes. We treat the interferometer input as a product state of any number of photons in each input mode with photons distinguished by their arrival time. Detectors at the output of the interferometer count photons from each output mode over a long integration time. We generalize and prove the claim of Tillmann et al. [Phys. Rev. X 5, 041015 (2015), 10.1103/PhysRevX.5.041015] that coincidence rates can be elegantly expressed in terms of immanants. Immanants are functions of matrices that exhibit permutational symmetries and the immanants appearing in our coincidence-rate expressions share permutational symmetries with the input state. Our results are obtained by employing representation theory of the symmetric group to analyze systems of an arbitrary number of photons in arbitrarily sized interferometers.

On the many-body foundation of the nuclear field theory

International Nuclear Information System (INIS)

Bes, D.R.; Dussel, G.G.; Liotta, R.J.; Perazzo, R.P.J.; Broglia, R.A.

1976-01-01

The equivalence between the description of the many-body finite nuclear system in terms of Feynman diagrams involving only the fermion degrees of freedom and of Feynman diagrams involving fermion and phonon degrees of freedom is proved for intermediate states in the case of a general two-body residual interaction. (Auth.)

An examination of the factor structure and sex invariance of a French translation of the Body Appreciation Scale-2 in university students.

Science.gov (United States)

Kertechian, Sevag; Swami, Viren

2017-06-01

The Body Appreciation Scale-2 (BAS-2) is a measure of positive body image that has been found that have a one-dimensional factor structure in a number of different cultural groups. Here, we examined the factor structure and sex-based measurement invariance of a French translation of the BAS-2. A total of 652 university students (age M=21.33, SD=3.18) completed a newly-translated French version of the BAS-2. Exploratory factor analyses with a randomly selected split-half subsample revealed that the BAS-2 had a one-dimensional factor structure in both sexes. Confirmatory factor analyses with a second split-half subsample indicated that the one-dimensional factor structure had adequate fit following modifications and was invariant across sex. French BAS-2 scores had adequate internal consistency and men had significantly higher body appreciation than women (ds=.16-.23). These results provide preliminary support for the factorial validity of the French BAS-2. Copyright © 2017 Elsevier Ltd. All rights reserved.

Microscopic optical potentials derived from ab initio translationally invariant nonlocal one-body densities

Science.gov (United States)

Gennari, Michael; Vorabbi, Matteo; Calci, Angelo; Navrátil, Petr

2018-03-01

Background: The nuclear optical potential is a successful tool for the study of nucleon-nucleus elastic scattering and its use has been further extended to inelastic scattering and other nuclear reactions. The nuclear density of the target nucleus is a fundamental ingredient in the construction of the optical potential and thus plays an important role in the description of the scattering process. Purpose: In this paper we derive a microscopic optical potential for intermediate energies using ab initio translationally invariant nonlocal one-body nuclear densities computed within the no-core shell model (NCSM) approach utilizing two- and three-nucleon chiral interactions as the only input. Methods: The optical potential is derived at first order within the spectator expansion of the nonrelativistic multiple scattering theory by adopting the impulse approximation. Nonlocal nuclear densities are derived from the NCSM one-body densities calculated in the second quantization. The translational invariance is generated by exactly removing the spurious center-of-mass (COM) component from the NCSM eigenstates. Results: The ground-state local and nonlocal densities of He 4 ,6 ,8 , 12C, and 16O are calculated and applied to optical potential construction. The differential cross sections and the analyzing powers for the elastic proton scattering off these nuclei are then calculated for different values of the incident proton energy. The impact of nonlocality and the COM removal is discussed. Conclusions: The use of nonlocal densities has a substantial impact on the differential cross sections and improves agreement with experiment in comparison to results generated with the local densities especially for light nuclei. For the halo nuclei 6He and 8He, the results for the differential cross section are in a reasonable agreement with the data although a more sophisticated model for the optical potential is required to properly describe the analyzing powers.

Integrals of motion in the many-body localized phase

Directory of Open Access Journals (Sweden)

V. Ros

2015-02-01

Full Text Available We construct a complete set of quasi-local integrals of motion for the many-body localized phase of interacting fermions in a disordered potential. The integrals of motion can be chosen to have binary spectrum {0,1}, thus constituting exact quasiparticle occupation number operators for the Fermi insulator. We map the problem onto a non-Hermitian hopping problem on a lattice in operator space. We show how the integrals of motion can be built, under certain approximations, as a convergent series in the interaction strength. An estimate of its radius of convergence is given, which also provides an estimate for the many-body localization–delocalization transition. Finally, we discuss how the properties of the operator expansion for the integrals of motion imply the presence or absence of a finite temperature transition.

Theory of many-body radiative heat transfer without the constraint of reciprocity

Science.gov (United States)

Zhu, Linxiao; Guo, Yu; Fan, Shanhui

2018-03-01

Using a self-consistent scattered field approach based on fluctuational electrodynamics, we develop compact formulas for radiative heat transfer in many-body systems without the constraint of reciprocity. The formulas allow for efficient numerical calculation for a system consisting of a large number of bodies, and are in principle exact. As a demonstration, for a nonreciprocal many-body system, we investigate persistent heat current at thermal equilibrium and directional heat transfer when the system is away from thermal equilibrium.

Bell Correlations in a Many-Body System with Finite Statistics

Science.gov (United States)

Wagner, Sebastian; Schmied, Roman; Fadel, Matteo; Treutlein, Philipp; Sangouard, Nicolas; Bancal, Jean-Daniel

2017-10-01

A recent experiment reported the first violation of a Bell correlation witness in a many-body system [Science 352, 441 (2016)]. Following discussions in this Letter, we address here the question of the statistics required to witness Bell correlated states, i.e., states violating a Bell inequality, in such experiments. We start by deriving multipartite Bell inequalities involving an arbitrary number of measurement settings, two outcomes per party and one- and two-body correlators only. Based on these inequalities, we then build up improved witnesses able to detect Bell correlated states in many-body systems using two collective measurements only. These witnesses can potentially detect Bell correlations in states with an arbitrarily low amount of spin squeezing. We then establish an upper bound on the statistics needed to convincingly conclude that a measured state is Bell correlated.

Photon Subtraction by Many-Body Decoherence

DEFF Research Database (Denmark)

Murray, C. R.; Mirgorodskiy, I.; Tresp, C.

2018-01-01

We experimentally and theoretically investigate the scattering of a photonic quantum field from another stored in a strongly interacting atomic Rydberg ensemble. Considering the many-body limit of this problem, we derive an exact solution to the scattering-induced spatial decoherence of multiple...... stored photons, allowing for a rigorous understanding of the underlying dissipative quantum dynamics. Combined with our experiments, this analysis reveals a correlated coherence-protection process in which the scattering from one excitation can shield all others from spatial decoherence. We discuss how...... this effect can be used to manipulate light at the quantum level, providing a robust mechanism for single-photon subtraction, and experimentally demonstrate this capability....

Prethermalization in an isolated many body system

International Nuclear Information System (INIS)

Gring, M.

2012-01-01

Understanding the relaxation dynamics of complex non-equilibrium many-body quantum systems is a fundamental problem, arising in many areas of physics. However, experimental examples of non-equilibrium systems that are both controllable and suitable for detailed study are extremely rare. In this thesis one such example in the form of a coherently split one-dimensional (1d) ultra cold Bose gas in a double-well potential is studied in detail. Typical for the analysis of non-equilibrium systems, the key challenge in this study is the characterization of the complex transient states of the system. In the presented work this task is solved by employing measurements of the time evolution of the full quantum mechanical probability distribution functions (FDFs) of time-of-flight matter-wave interference patterns between the two halves of the split system. The dynamics of the FDFs reveal two distinct regimes of relaxation clearly demonstrating the multi-mode nature of 1d Bose gases. Moreover, after an initial rapid evolution, the FDFs exhibit the approach towards a thermal-like steady state of the system which however does not correspond to the true thermal equilibrium of the system. This surprising behaviour is also predicted by a recent theoretical work which puts the observations in a much broader context and classifies them as an example of prethermalization. Prethermalization is a general concept from relativistic quantum field theory and is currently the subject of intense theoretical research. Accordingly prethermalized states were recently predicted for a series of other many-body quantum systems. The work presented in this thesis represents a direct experimental observation of this phenomenon of prethermalization. (author) [de

Many-Body Mean-Field Equations: Parallel implementation

International Nuclear Information System (INIS)

Vallieres, M.; Umar, S.; Chinn, C.; Strayer, M.

1993-01-01

We describe the implementation of Hartree-Fock Many-Body Mean-Field Equations on a Parallel Intel iPSC/860 hypercube. We first discuss the Nuclear Mean-Field approach in physical terms. Then we describe our parallel implementation of this approach on the Intel iPSC/860 hypercube. We discuss and compare the advantages and disadvantages of the domain partition versus the Hilbert space partition for this problem. We conclude by discussing some timing experiments on various computing platforms

Structure of the many-body wavefunction for scattering

International Nuclear Information System (INIS)

L'Huillier, M.; Redish, E.F.; Tandy, P.C.

1978-01-01

We show that the scattered part of the many-body wavefunction initiated by two incoming clusters is given by a fully connected operator acting on the initial channel state. The structure of this operator suggests a division of the full wavefunction into two-cluster components. A set of coupled equations in both the differential and integral form is then derived for these components. These equations have structure and properties similar to the three-body equations of Faddeev. We demonstrate that each component has outgoing waves in a unique two-cluster partition. The transition amplitude for any final arrangement can therefore be extracted directly from the outgoing waves in the relevant components

Efficient tomography of a quantum many-body system

Science.gov (United States)

Lanyon, B. P.; Maier, C.; Holzäpfel, M.; Baumgratz, T.; Hempel, C.; Jurcevic, P.; Dhand, I.; Buyskikh, A. S.; Daley, A. J.; Cramer, M.; Plenio, M. B.; Blatt, R.; Roos, C. F.

2017-12-01

Quantum state tomography is the standard technique for estimating the quantum state of small systems. But its application to larger systems soon becomes impractical as the required resources scale exponentially with the size. Therefore, considerable effort is dedicated to the development of new characterization tools for quantum many-body states. Here we demonstrate matrix product state tomography, which is theoretically proven to allow for the efficient and accurate estimation of a broad class of quantum states. We use this technique to reconstruct the dynamical state of a trapped-ion quantum simulator comprising up to 14 entangled and individually controlled spins: a size far beyond the practical limits of quantum state tomography. Our results reveal the dynamical growth of entanglement and describe its complexity as correlations spread out during a quench: a necessary condition for future demonstrations of better-than-classical performance. Matrix product state tomography should therefore find widespread use in the study of large quantum many-body systems and the benchmarking and verification of quantum simulators and computers.

Many-body localization proximity effects in platforms of coupled spins and bosons

Science.gov (United States)

Marino, J.; Nandkishore, R. M.

2018-02-01

We discuss the onset of many-body localization in a one-dimensional system composed of a XXZ quantum spin chain and a Bose-Hubbard model linearly coupled together. We consider two complementary setups, depending whether spatial disorder is initially imprinted on spins or on bosons; in both cases, we explore the conditions for the disordered portion of the system to localize by proximity of the other clean half. Assuming that the dynamics of one of the two parts develops on shorter time scales than the other, we can adiabatically eliminate the fast degrees of freedom, and derive an effective Hamiltonian for the system's remainder using projection operator techniques. Performing a locator expansion on the strength of the many-body interaction term or on the hopping amplitude of the effective Hamiltonian thus derived, we present results on the stability of the many-body localized phases induced by proximity effect. We also briefly comment on the feasibility of the proposed model through modern quantum optics architectures, with the long-term perspective to realize experimentally, in composite open systems, Anderson or many-body localization proximity effects.

Mott Transition In Strongly Correlated Materials: Many-Body Methods And Realistic Materials Simulations

Science.gov (United States)

Lee, Tsung-Han

Strongly correlated materials are a class of materials that cannot be properly described by the Density Functional Theory (DFT), which is a single-particle approximation to the original many-body electronic Hamiltonian. These systems contain d or f orbital electrons, i.e., transition metals, actinides, and lanthanides compounds, for which the electron-electron interaction (correlation) effects are too strong to be described by the single-particle approximation of DFT. Therefore, complementary many-body methods have been developed, at the model Hamiltonians level, to describe these strong correlation effects. Dynamical Mean Field Theory (DMFT) and Rotationally Invariant Slave-Boson (RISB) approaches are two successful methods that can capture the correlation effects for a broad interaction strength. However, these many-body methods, as applied to model Hamiltonians, treat the electronic structure of realistic materials in a phenomenological fashion, which only allow to describe their properties qualitatively. Consequently, the combination of DFT and many body methods, e.g., Local Density Approximation augmented by RISB and DMFT (LDA+RISB and LDA+DMFT), have been recently proposed to combine the advantages of both methods into a quantitative tool to analyze strongly correlated systems. In this dissertation, we studied the possible improvements of these approaches, and tested their accuracy on realistic materials. This dissertation is separated into two parts. In the first part, we studied the extension of DMFT and RISB in three directions. First, we extended DMFT framework to investigate the behavior of the domain wall structure in metal-Mott insulator coexistence regime by studying the unstable solution describing the domain wall. We found that this solution, differing qualitatively from both the metallic and the insulating solutions, displays an insulating-like behavior in resistivity while carrying a weak metallic character in its electronic structure. Second, we

Typical Relaxation of Isolated Many-Body Systems Which Do Not Thermalize

Science.gov (United States)

Balz, Ben N.; Reimann, Peter

2017-05-01

We consider isolated many-body quantum systems which do not thermalize; i.e., expectation values approach an (approximately) steady longtime limit which disagrees with the microcanonical prediction of equilibrium statistical mechanics. A general analytical theory is worked out for the typical temporal relaxation behavior in such cases. The main prerequisites are initial conditions which appreciably populate many energy levels and do not give rise to significant spatial inhomogeneities on macroscopic scales. The theory explains very well the experimental and numerical findings in a trapped-ion quantum simulator exhibiting many-body localization, in ultracold atomic gases, and in integrable hard-core boson and X X Z models.

Coupled-channel equations and off-shell transformations in many-body scattering

International Nuclear Information System (INIS)

Cattapan, G.; Vanzani, V.

1977-01-01

The general structure and the basic features of several many-body coupled-channel integral equations, obtained by means of the channel coupling array device, are studied in a systematic way. Particular attention is paid to the employment of symmetric transition operators. The connection between different formulations has been clarified and the role played by some off-shell transformations for many-body transition operators has been discussed. Specific choices of the coupling scheme are considered and the corresponding coupled equations are compared with similar equations previously derived. Several sets of linear relations between transition operators have also been presented and used in a three-body context to derive uncoupled integral equations with connected kernel

Computing the Jones index of quadratic permutation endomorphisms of O2

DEFF Research Database (Denmark)

Szymanski, Wojciech; Conti, Roberto

2009-01-01

We compute the index of the type III1/2  factors arising from endomorphisms of the Cuntz algebra O2  associated to the rank-two permutation matrices. Udgivelsesdato: January......We compute the index of the type III1/2  factors arising from endomorphisms of the Cuntz algebra O2  associated to the rank-two permutation matrices. Udgivelsesdato: January...

Highly Enhanced Many-Body Interactions in Anisotropic 2D Semiconductors.

Science.gov (United States)

Sharma, Ankur; Yan, Han; Zhang, Linglong; Sun, Xueqian; Liu, Boqing; Lu, Yuerui

2018-05-15

Atomically thin two-dimensional (2D) semiconductors have presented a plethora of opportunities for future optoelectronic devices and photonics applications, made possible by the strong light matter interactions at the 2D quantum limit. Many body interactions between fundamental particles in 2D semiconductors are strongly enhanced compared with those in bulk semiconductors because of the reduced dimensionality and, thus, reduced dielectric screening. These enhanced many body interactions lead to the formation of robust quasi-particles, such as excitons, trions, and biexcitons, which are extremely important for the optoelectronics device applications of 2D semiconductors, such as light emitting diodes, lasers, and optical modulators, etc. Recently, the emerging anisotropic 2D semiconductors, such as black phosphorus (termed as phosphorene) and phosphorene-like 2D materials, such as ReSe 2 , 2D-perovskites, SnS, etc., show strong anisotropic optical and electrical properties, which are different from conventional isotropic 2D semiconductors, such as transition metal dichalcogenide (TMD) monolayers. This anisotropy leads to the formation of quasi-one-dimensional (quasi-1D) excitons and trions in a 2D system, which results in even stronger many body interactions in anisotropic 2D materials, arising from the further reduced dimensionality of the quasi-particles and thus reduced dielectric screening. Many body interactions have been heavily investigated in TMD monolayers in past years, but not in anisotropic 2D materials yet. The quasi-particles in anisotropic 2D materials have fractional dimensionality which makes them perfect candidates to serve as a platform to study fundamental particle interactions in fractional dimensional space. In this Account, we present our recent progress related to 2D phosphorene, a 2D system with quasi-1D excitons and trions. Phosphorene, because of its unique anisotropic properties, provides a unique 2D platform for investigating the

Many-body approaches to nuclear physics

International Nuclear Information System (INIS)

Hjorth-Jensen, M.

1993-10-01

This thesis deals with applications of perturbative many-body theories to selected nuclear systems at low and intermediate energies. Examples are the properties of neutron stars, the calculation of shell-model effective interactions and the microscopic derivation of the optical-model potential for finite nuclei. The line of research leans on the microscopic approach, i.e. an approach which aims at describing nuclear properties from the underlying free interaction between the various hadrons where parameters like meson coupling constants define the Lagrangians. The emphasis is on the behavior of the various components of the free interaction in different nuclear media in order to understand how these components are affected by the studied nuclear correlations. 159 refs

Interferometric probes of many-body localization.

Science.gov (United States)

Serbyn, M; Knap, M; Gopalakrishnan, S; Papić, Z; Yao, N Y; Laumann, C R; Abanin, D A; Lukin, M D; Demler, E A

2014-10-03

We propose a method for detecting many-body localization (MBL) in disordered spin systems. The method involves pulsed coherent spin manipulations that probe the dephasing of a given spin due to its entanglement with a set of distant spins. It allows one to distinguish the MBL phase from a noninteracting localized phase and a delocalized phase. In particular, we show that for a properly chosen pulse sequence the MBL phase exhibits a characteristic power-law decay reflecting its slow growth of entanglement. We find that this power-law decay is robust with respect to thermal and disorder averaging, provide numerical simulations supporting our results, and discuss possible experimental realizations in solid-state and cold-atom systems.

Sorting signed permutations by inversions in O(nlogn) time.

Science.gov (United States)

Swenson, Krister M; Rajan, Vaibhav; Lin, Yu; Moret, Bernard M E

2010-03-01

The study of genomic inversions (or reversals) has been a mainstay of computational genomics for nearly 20 years. After the initial breakthrough of Hannenhalli and Pevzner, who gave the first polynomial-time algorithm for sorting signed permutations by inversions, improved algorithms have been designed, culminating with an optimal linear-time algorithm for computing the inversion distance and a subquadratic algorithm for providing a shortest sequence of inversions--also known as sorting by inversions. Remaining open was the question of whether sorting by inversions could be done in O(nlogn) time. In this article, we present a qualified answer to this question, by providing two new sorting algorithms, a simple and fast randomized algorithm and a deterministic refinement. The deterministic algorithm runs in time O(nlogn + kn), where k is a data-dependent parameter. We provide the results of extensive experiments showing that both the average and the standard deviation for k are small constants, independent of the size of the permutation. We conclude (but do not prove) that almost all signed permutations can be sorted by inversions in O(nlogn) time.

Functional integral representation of the nuclear many-body grand partition function

International Nuclear Information System (INIS)

Kerman, A.K.; Troudet, T.

1984-01-01

A local functional integral formulation of the nuclear many-body problem is proposed which is a generalization of the method previously developed. Its most interesting feature is that it allows an expansion of the many-body evolution operator around any arbitrary mean-field which takes into account the pairing correlations between the nucleons. This is explicitly illustrated for the nuclear many-body grand partition function for which special attention is paid to the static temperature-dependent Hartree-Fock-Bogolyubov (H.F.B.) approximation. Indeed, the temperature-dependent H.F.B. configuration appears to be the optimal choice from a variational point of view among all the possible independent quasi-particle motion approximations. An analytic approximation of the energy level density rho (E,A) is given using explicitly the arbitrariness in the choice of the mean-field and a possible numerical application is proposed. Finally, a new compact formulation of our functional integral that might be useful for future Monte Carlo calculations is proposed

Stochastic many-body problems in ecology, evolution, neuroscience, and systems biology

Science.gov (United States)

Butler, Thomas C.

Using the tools of many-body theory, I analyze problems in four different areas of biology dominated by strong fluctuations: The evolutionary history of the genetic code, spatiotemporal pattern formation in ecology, spatiotemporal pattern formation in neuroscience and the robustness of a model circadian rhythm circuit in systems biology. In the first two research chapters, I demonstrate that the genetic code is extremely optimal (in the sense that it manages the effects of point mutations or mistranslations efficiently), more than an order of magnitude beyond what was previously thought. I further show that the structure of the genetic code implies that early proteins were probably only loosely defined. Both the nature of early proteins and the extreme optimality of the genetic code are interpreted in light of recent theory [1] as evidence that the evolution of the genetic code was driven by evolutionary dynamics that were dominated by horizontal gene transfer. I then explore the optimality of a proposed precursor to the genetic code. The results show that the precursor code has only limited optimality, which is interpreted as evidence that the precursor emerged prior to translation, or else never existed. In the next part of the dissertation, I introduce a many-body formalism for reaction-diffusion systems described at the mesoscopic scale with master equations. I first apply this formalism to spatially-extended predator-prey ecosystems, resulting in the prediction that many-body correlations and fluctuations drive population cycles in time, called quasicycles. Most of these results were previously known, but were derived using the system size expansion [2, 3]. I next apply the analytical techniques developed in the study of quasi-cycles to a simple model of Turing patterns in a predator-prey ecosystem. This analysis shows that fluctuations drive the formation of a new kind of spatiotemporal pattern formation that I name "quasi-patterns." These quasi

Many-body theory of charge transfer in hyperthermal atomic scattering

International Nuclear Information System (INIS)

Marston, J.B.; Andersson, D.R.; Behringer, E.R.; Cooper, B.H.; DiRubio, C.A.; Kimmel, G.A.; Richardson, C.

1993-01-01

We use the Newns-Anderson Hamiltonian to describe many-body electronic processes that occur when hyperthermal alkali atoms scatter off metallic surfaces. Following Brako and Newns, we expand the electronic many-body wave function in the number of particle-hole pairs (we keep terms up to and including a single particle-hole pair). We extend their earlier work by including level crossings, excited neutrals, and negative ions. The full set of equations of motion is integrated numerically, without further approximations, to obtain the many-body amplitudes as a function of time. The velocity and work-function dependence of final-state quantities such as the distribution of ion charges and excited atomic occupancies are compared with experiment. In particular, experiments that scatter alkali ions off clean Cu(001) surfaces in the energy range 5--1600 eV constrain the theory quantitatively. The neutralization probability of Na + ions shows a minimum at intermediate velocity in agreement with the theory. This behavior contrasts with that of K + , which shows virtually no neutralization, and with Li + , which exhibits a monotonically increasing neutral fraction with decreasing velocity. Particle-hole excitations are left behind in the metal during a fraction of the collision events; this dissipated energy is predicted to be quite small (on the order of tenths of an electron volt). Indeed, classical trajectory simulations of the surface dynamics account well for the observed energy loss, and thus provide some justification for our truncation of the equations of motion at the single particle-hole pair level. Li + scattering experiments off low work-function surfaces provide qualitative information on the importance of many-body effects. At sufficiently low work function, the negative ions predicted to occur are in fact observed

Chiral Floquet Phases of Many-Body Localized Bosons

Directory of Open Access Journals (Sweden)

Hoi Chun Po

2016-12-01

Full Text Available We construct and classify chiral topological phases in driven (Floquet systems of strongly interacting bosons, with finite-dimensional site Hilbert spaces, in two spatial dimensions. The construction proceeds by introducing exactly soluble models with chiral edges, which in the presence of many-body localization (MBL in the bulk are argued to lead to stable chiral phases. These chiral phases do not require any symmetry and in fact owe their existence to the absence of energy conservation in driven systems. Surprisingly, we show that they are classified by a quantized many-body index, which is well defined for any MBL Floquet system. The value of this index, which is always the logarithm of a positive rational number, can be interpreted as the entropy per Floquet cycle pumped along the edge, formalizing the notion of quantum-information flow. We explicitly compute this index for specific models and show that the nontrivial topology leads to edge thermalization, which provides an interesting link between bulk topology and chaos at the edge. We also discuss chiral Floquet phases in interacting fermionic systems and their relation to chiral bosonic phases.

On permutation polynomials over finite fields: differences and iterations

DEFF Research Database (Denmark)

Anbar Meidl, Nurdagül; Odzak, Almasa; Patel, Vandita

2017-01-01

The Carlitz rank of a permutation polynomial f over a finite field Fq is a simple concept that was introduced in the last decade. Classifying permutations over Fq with respect to their Carlitz ranks has some advantages, for instance f with a given Carlitz rank can be approximated by a rational li...

Many-Body Theory for Positronium-Atom Interactions

Science.gov (United States)

Green, D. G.; Swann, A. R.; Gribakin, G. F.

2018-05-01

A many-body-theory approach has been developed to study positronium-atom interactions. As first applications, we calculate the elastic scattering and momentum-transfer cross sections and the pickoff annihilation rate 1Zeff for Ps collisions with He and Ne. For He the cross section is in agreement with previous coupled-state calculations, while comparison with experiment for both atoms highlights discrepancies between various sets of measured data. In contrast, the calculated 1Zeff (0.13 and 0.26 for He and Ne, respectively) are in excellent agreement with the measured values.

On logarithmic extensions of local scale-invariance

International Nuclear Information System (INIS)

Henkel, Malte

2013-01-01

Ageing phenomena far from equilibrium naturally present dynamical scaling and in many situations this may be generalised to local scale-invariance. Generically, the absence of time-translation-invariance implies that each scaling operator is characterised by two independent scaling dimensions. Building on analogies with logarithmic conformal invariance and logarithmic Schrödinger-invariance, this work proposes a logarithmic extension of local scale-invariance, without time-translation-invariance. Carrying this out requires in general to replace both scaling dimensions of each scaling operator by Jordan cells. Co-variant two-point functions are derived for the most simple case of a two-dimensional logarithmic extension. Their form is compared to simulational data for autoresponse functions in several universality classes of non-equilibrium ageing phenomena

First-principles many-body theory for ultra-cold atoms

International Nuclear Information System (INIS)

Drummond, Peter D.; Hu Hui; Liu Xiaji

2010-01-01

Recent breakthroughs in the creation of ultra-cold atoms in the laboratory have ushered in unprecedented changes in physical science. These enormous changes in the coldest temperatures available in the laboratory mean that many novel experiments are possible. There is unprecedented control and simplicity in these novel systems, meaning that quantum many-body theory is now facing severe challenges in quantitatively understanding these new results. We discuss some of the new experiments and recently developed theoretical techniques required to predict the results obtained.

Harmonically trapped cold atom systems: Few-body dynamics and application to many-body thermodynamics

Science.gov (United States)

Daily, Kevin Michael

Underlying the many-body effects of ultracold atomic gases are the few-body dynamics and interparticle interactions. Moreover, the study of few-body systems on their own has accelerated due to confining few atoms in each well of a deep optical lattice or in a single microtrap. This thesis studies the microscopic properties of few-body systems under external spherically symmetric harmonic confinement and how the few-body properties translate to the many-body system. Bosonic and fermionic few-body systems are considered and the dependence of the energetics and other quantities are investigated as functions of the s-wave scattering length, the mass ratio and the temperature. It is found that the condensate fraction of a weakly-interacting trapped Bose gas depletes quadratically with the s-wave scattering length. The next order term in the depletion depends not only, as might be expected naively, on the s-wave scattering length and the effective range but additionally on a two-body parameter that is not needed to reproduce the energy of weakly-interacting trapped Bose gases. This finding has important implications for effective field theory treatments of the system. Weakly-interacting atomic and molecular two-component Fermi gases with equal masses are described using perturbative approaches. The energy shifts are tabulated and interpreted, and a measure of the molecular condensate fraction is developed. We develop a measure of the molecular condensate fraction using the two-body density matrix and we develop a model of the spherical component of the momentum distribution that agrees well with stochastic variational calculations. We establish the existence of intersystem degeneracies for equal mass two-component Fermi gases with zero-range interactions, where the eigen energies of the spin-imbalanced system are degenerate with a subset of the eigen energies of the more spin-balanced system and the same total number of fermions. For unequal mass two-component Fermi

Electron correlation in molecules: concurrent computation Many-Body Perturbation Theory (ccMBPT) calculations using macrotasking on the NEC SX-3/44 computer

International Nuclear Information System (INIS)

Moncrieff, D.; Wilson, S.

1992-06-01

The ab initio determination of the electronic structure of molecules is a many-fermion problem involving the approximate description of the motion of the electrons in the field of fixed nuclei. It is an area of research which demands considerable computational resources but having enormous potential in fields as diverse as interstellar chemistry and drug design, catalysis and solid state chemistry, molecular biology and environmental chemistry. Electronic structure calculations almost invariably divide into two main stages: the approximate solution of an independent electron model, in which each electron moves in the average field created by the other electrons in the system, and then, the more computationally demanding determination of a series of corrections to this model, the electron correlation effects. The many-body perturbation theory expansion affords a systematic description of correlation effects, which leads directly to algorithms which are suitable for concurrent computation. We term this concurrent computation Many-Body Perturbation Theory (ccMBPT). The use of a dynamic load balancing technique on the NEC SX-3/44 computer in electron correlation calculations is investigated for the calculation of the most demanding energy component in the most accurate of contemporary ab initio studies. An application to the ground state of the nitrogen molecule is described. We also briefly discuss the extent to which the calculation of the dominant corrections to such studies can be rendered computationally tractable by exploiting both the vector processing and parallel processor capabilities of the NEC SX-3/44 computer. (author)

Ordered groups and infinite permutation groups

CERN Document Server

1996-01-01

The subjects of ordered groups and of infinite permutation groups have long en­ joyed a symbiotic relationship. Although the two subjects come from very different sources, they have in certain ways come together, and each has derived considerable benefit from the other. My own personal contact with this interaction began in 1961. I had done Ph. D. work on sequence convergence in totally ordered groups under the direction of Paul Conrad. In the process, I had encountered "pseudo-convergent" sequences in an ordered group G, which are like Cauchy sequences, except that the differences be­ tween terms of large index approach not 0 but a convex subgroup G of G. If G is normal, then such sequences are conveniently described as Cauchy sequences in the quotient ordered group GIG. If G is not normal, of course GIG has no group structure, though it is still a totally ordered set. The best that can be said is that the elements of G permute GIG in an order-preserving fashion. In independent investigations around that t...

N ecklaces~ Periodic Points and Permutation Representations

Indian Academy of Sciences (India)

Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 11. Necklaces, Periodic Points and Permutation Representations - Fermat's Little Theorem. Somnath Basu Anindita Bose Sumit Kumar Sinha Pankaj Vishe. General Article Volume 6 Issue 11 November 2001 pp 18-26 ...

A Scalable Permutation Approach Reveals Replication and Preservation Patterns of Network Modules in Large Datasets.

Science.gov (United States)

Ritchie, Scott C; Watts, Stephen; Fearnley, Liam G; Holt, Kathryn E; Abraham, Gad; Inouye, Michael

2016-07-01

Network modules-topologically distinct groups of edges and nodes-that are preserved across datasets can reveal common features of organisms, tissues, cell types, and molecules. Many statistics to identify such modules have been developed, but testing their significance requires heuristics. Here, we demonstrate that current methods for assessing module preservation are systematically biased and produce skewed p values. We introduce NetRep, a rapid and computationally efficient method that uses a permutation approach to score module preservation without assuming data are normally distributed. NetRep produces unbiased p values and can distinguish between true and false positives during multiple hypothesis testing. We use NetRep to quantify preservation of gene coexpression modules across murine brain, liver, adipose, and muscle tissues. Complex patterns of multi-tissue preservation were revealed, including a liver-derived housekeeping module that displayed adipose- and muscle-specific association with body weight. Finally, we demonstrate the broader applicability of NetRep by quantifying preservation of bacterial networks in gut microbiota between men and women. Copyright © 2016 The Author(s). Published by Elsevier Inc. All rights reserved.

General many-body formalism for composite quantum particles.

Science.gov (United States)

Combescot, M; Betbeder-Matibet, O

2010-05-21

This Letter provides a formalism capable of exactly treating Pauli blocking between n-fermion particles. This formalism is based on an operator algebra made of commutators and anticommutators which contrasts with the usual scalar formalism of Green functions developed half a century ago for elementary quantum particles. We also provide the diagrams which visualize the very specific many-body physics induced by fermion exchanges between composite quantum particles.

Many-Body Coulomb Gauge Exotic and Charmed Hybrids

OpenAIRE

Llanes-Estrada, Felipe J.; Cotanch, Stephen R.

2000-01-01

Utilizing a QCD Coulomb gauge Hamiltonian with linear confinement specified by lattice, we report a relativistic many-body calculation for the light exotic and charmed hybrid mesons. The Hamiltonian successfully describes both quark and gluon sectors, with vacuum and quasiparticle properties generated by a BCS transformation and more elaborate TDA and RPA diagonalizations for the meson ($q\\bar{q}$) and glueball ($gg$) masses. Hybrids entail a computationally intense relativistic three quasipa...

Relativistic many-body perturbation-theory calculations based on Dirac-Fock-Breit wave functions

International Nuclear Information System (INIS)

Ishikawa, Y.; Quiney, H.M.

1993-01-01

A relativistic many-body perturbation theory based on the Dirac-Fock-Breit wave functions has been developed and implemented by employing analytic basis sets of Gaussian-type functions. The instantaneous Coulomb and low-frequency Breit interactions are treated using a unified formalism in both the construction of the Dirac-Fock-Breit self-consistent-field atomic potential and in the evaluation of many-body perturbation-theory diagrams. The relativistic many-body perturbation-theory calculations have been performed on the helium atom and ions of the helium isoelectronic sequence up to Z=50. The contribution of the low-frequency Breit interaction to the relativistic correlation energy is examined for the helium isoelectronic sequence

Efficient molecular dynamics simulations with many-body potentials on graphics processing units

Science.gov (United States)

Fan, Zheyong; Chen, Wei; Vierimaa, Ville; Harju, Ari

2017-09-01

Graphics processing units have been extensively used to accelerate classical molecular dynamics simulations. However, there is much less progress on the acceleration of force evaluations for many-body potentials compared to pairwise ones. In the conventional force evaluation algorithm for many-body potentials, the force, virial stress, and heat current for a given atom are accumulated within different loops, which could result in write conflict between different threads in a CUDA kernel. In this work, we provide a new force evaluation algorithm, which is based on an explicit pairwise force expression for many-body potentials derived recently (Fan et al., 2015). In our algorithm, the force, virial stress, and heat current for a given atom can be accumulated within a single thread and is free of write conflicts. We discuss the formulations and algorithms and evaluate their performance. A new open-source code, GPUMD, is developed based on the proposed formulations. For the Tersoff many-body potential, the double precision performance of GPUMD using a Tesla K40 card is equivalent to that of the LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) molecular dynamics code running with about 100 CPU cores (Intel Xeon CPU X5670 @ 2.93 GHz).

Understanding many-body physics in one dimension from the Lieb–Liniger model

International Nuclear Information System (INIS)

Jiang Yu-Zhu; Chen Yang-Yang; Guan Xi-Wen

2015-01-01

This article presents an elementary introduction on various aspects of the prototypical integrable model the Lieb–Liniger Bose gas ranging from the cooperative to the collective features of many-body phenomena. In 1963, Lieb and Liniger first solved this quantum field theory many-body problem using Bethe’s hypothesis, i.e., a particular form of wavefunction introduced by Bethe in solving the one-dimensional Heisenberg model in 1931. Despite the Lieb–Liniger model is arguably the simplest exactly solvable model, it exhibits rich quantum many-body physics in terms of the aspects of mathematical integrability and physical universality. Moreover, the Yang–Yang grand canonical ensemble description for the model provides us with a deep understanding of quantum statistics, thermodynamics, and quantum critical phenomena at the many-body physical level. Recently, such fundamental physics of this exactly solved model has been attracting growing interest in experiments. Since 2004, there have been more than 20 experimental papers that reported novel observations of different physical aspects of the Lieb–Liniger model in the laboratory. So far the observed results are in excellent agreement with results obtained using the analysis of this simplest exactly solved model. Those experimental observations reveal the unique beauty of integrability. (topical review)

Error-free holographic frames encryption with CA pixel-permutation encoding algorithm

Science.gov (United States)

Li, Xiaowei; Xiao, Dan; Wang, Qiong-Hua

2018-01-01

The security of video data is necessary in network security transmission hence cryptography is technique to make video data secure and unreadable to unauthorized users. In this paper, we propose a holographic frames encryption technique based on the cellular automata (CA) pixel-permutation encoding algorithm. The concise pixel-permutation algorithm is used to address the drawbacks of the traditional CA encoding methods. The effectiveness of the proposed video encoding method is demonstrated by simulation examples.

Quantum simulations and many-body physics with light.

Science.gov (United States)

Noh, Changsuk; Angelakis, Dimitris G

2017-01-01

In this review we discuss the works in the area of quantum simulation and many-body physics with light, from the early proposals on equilibrium models to the more recent works in driven dissipative platforms. We start by describing the founding works on Jaynes-Cummings-Hubbard model and the corresponding photon-blockade induced Mott transitions and continue by discussing the proposals to simulate effective spin models and fractional quantum Hall states in coupled resonator arrays (CRAs). We also analyse the recent efforts to study out-of-equilibrium many-body effects using driven CRAs, including the predictions for photon fermionisation and crystallisation in driven rings of CRAs as well as other dynamical and transient phenomena. We try to summarise some of the relatively recent results predicting exotic phases such as super-solidity and Majorana like modes and then shift our attention to developments involving 1D nonlinear slow light setups. There the simulation of strongly correlated phases characterising Tonks-Girardeau gases, Luttinger liquids, and interacting relativistic fermionic models is described. We review the major theory results and also briefly outline recent developments in ongoing experimental efforts involving different platforms in circuit QED, photonic crystals and nanophotonic fibres interfaced with cold atoms.

Permutation entropy of fractional Brownian motion and fractional Gaussian noise

International Nuclear Information System (INIS)

Zunino, L.; Perez, D.G.; Martin, M.T.; Garavaglia, M.; Plastino, A.; Rosso, O.A.

2008-01-01

We have worked out theoretical curves for the permutation entropy of the fractional Brownian motion and fractional Gaussian noise by using the Bandt and Shiha [C. Bandt, F. Shiha, J. Time Ser. Anal. 28 (2007) 646] theoretical predictions for their corresponding relative frequencies. Comparisons with numerical simulations show an excellent agreement. Furthermore, the entropy-gap in the transition between these processes, observed previously via numerical results, has been here theoretically validated. Also, we have analyzed the behaviour of the permutation entropy of the fractional Gaussian noise for different time delays

Intermittent many-body dynamics at equilibrium

Science.gov (United States)

Danieli, C.; Campbell, D. K.; Flach, S.

2017-06-01

The equilibrium value of an observable defines a manifold in the phase space of an ergodic and equipartitioned many-body system. A typical trajectory pierces that manifold infinitely often as time goes to infinity. We use these piercings to measure both the relaxation time of the lowest frequency eigenmode of the Fermi-Pasta-Ulam chain, as well as the fluctuations of the subsequent dynamics in equilibrium. The dynamics in equilibrium is characterized by a power-law distribution of excursion times far off equilibrium, with diverging variance. Long excursions arise from sticky dynamics close to q -breathers localized in normal mode space. Measuring the exponent allows one to predict the transition into nonergodic dynamics. We generalize our method to Klein-Gordon lattices where the sticky dynamics is due to discrete breathers localized in real space.

Current algebras and many-body physics

International Nuclear Information System (INIS)

Albertin, U.K.

1989-01-01

Several applications of current algebras in many body physics are examined. The first is the interacting Bose gas in three dimensions. Theories for phonons, vortices and rotons are all described within the current algebra formalism. Next the one dimensional electron gas is examined within the approximation of linear dispersion so that relativistic current algebra techniques may be used. The relation with Thirring strings and compactified boson models is examined, and points of enhanced symmetry in the compactified boson models are shown to lie on phase transition lines for the electron gas. Finally, mathematical aspects of the current algebra are studied. The theory of induced representations of the diffeomorphism group are used to describe the Aharanov-Bohm effect, the thermodynamics of the Bose gas, and the Bose gas in the presence of vortex filaments

Spectral statistics of chaotic many-body systems

International Nuclear Information System (INIS)

Dubertrand, Rémy; Müller, Sebastian

2016-01-01

We derive a trace formula that expresses the level density of chaotic many-body systems as a smooth term plus a sum over contributions associated to solutions of the nonlinear Schrödinger (or Gross–Pitaevski) equation. Our formula applies to bosonic systems with discretised positions, such as the Bose–Hubbard model, in the semiclassical limit as well as in the limit where the number of particles is taken to infinity. We use the trace formula to investigate the spectral statistics of these systems, by studying interference between solutions of the nonlinear Schrödinger equation. We show that in the limits taken the statistics of fully chaotic many-particle systems becomes universal and agrees with predictions from the Wigner–Dyson ensembles of random matrix theory. The conditions for Wigner–Dyson statistics involve a gap in the spectrum of the Frobenius–Perron operator, leaving the possibility of different statistics for systems with weaker chaotic properties. (paper)

A note on the estimation of the Pareto efficient set for multiobjective matrix permutation problems.

Science.gov (United States)

Brusco, Michael J; Steinley, Douglas

2012-02-01

There are a number of important problems in quantitative psychology that require the identification of a permutation of the n rows and columns of an n × n proximity matrix. These problems encompass applications such as unidimensional scaling, paired-comparison ranking, and anti-Robinson forms. The importance of simultaneously incorporating multiple objective criteria in matrix permutation applications is well recognized in the literature; however, to date, there has been a reliance on weighted-sum approaches that transform the multiobjective problem into a single-objective optimization problem. Although exact solutions to these single-objective problems produce supported Pareto efficient solutions to the multiobjective problem, many interesting unsupported Pareto efficient solutions may be missed. We illustrate the limitation of the weighted-sum approach with an example from the psychological literature and devise an effective heuristic algorithm for estimating both the supported and unsupported solutions of the Pareto efficient set. © 2011 The British Psychological Society.

Ruelle resonances in quantum many-body dynamics

International Nuclear Information System (INIS)

Prosen, Tomaz

2002-01-01

We define a quantum Perron-Frobenius master operator over a suitable normed space of translationally invariant states adjoint to the quasi-local C* algebra of quantum lattice gasses (e.g. spin chains), whose spectrum determines the exponents of decay of time correlation functions. The theoretical ideas are applied to a generic example of kicked Ising spin 1/2 chains. We show that the 'chaotic eigenmodes' corresponding to leading eigenvalue resonances have fractal structure in the basis of local operators. (letter to the editor)

Chiral symmetry and many-body forces in nuclei

International Nuclear Information System (INIS)

Nyman, E.M.; Rho, M.

1976-01-01

It is demonstrated that when quantum corrections are added, chiral Lagrangians need not generate strong many-body forces as they do in tree approximation. It is suggested that a physically reasonable procedure is to adjust the sigma-model parameters so as not to conflict with the current status of nuclear theory. As a consequence, the equilibrium density of abnormal states could be pushed up further, and the binding energy be considerably reduced. (Auth.)

Entanglement replication in driven dissipative many-body systems.

Science.gov (United States)

Zippilli, S; Paternostro, M; Adesso, G; Illuminati, F

2013-01-25

We study the dissipative dynamics of two independent arrays of many-body systems, locally driven by a common entangled field. We show that in the steady state the entanglement of the driving field is reproduced in an arbitrarily large series of inter-array entangled pairs over all distances. Local nonclassical driving thus realizes a scale-free entanglement replication and long-distance entanglement distribution mechanism that has immediate bearing on the implementation of quantum communication networks.

Lattice Methods and the Nuclear Few- and Many-Body Problem

Science.gov (United States)

Lee, Dean

This chapter builds upon the review of lattice methods and effective field theory of the previous chapter. We begin with a brief overview of lattice calculations using chiral effective field theory and some recent applications. We then describe several methods for computing scattering on the lattice. After that we focus on the main goal, explaining the theory and algorithms relevant to lattice simulations of nuclear few- and many-body systems. We discuss the exact equivalence of four different lattice formalisms, the Grassmann path integral, transfer matrix operator, Grassmann path integral with auxiliary fields, and transfer matrix operator with auxiliary fields. Along with our analysis we include several coding examples and a number of exercises for the calculations of few- and many-body systems at leading order in chiral effective field theory.

How should we understand non-equilibrium many-body steady states?

Science.gov (United States)

Maghrebi, Mohammad; Gorshkov, Alexey

: Many-body systems with both coherent dynamics and dissipation constitute a rich class of models which are nevertheless much less explored than their dissipationless counterparts. The advent of numerous experimental platforms that simulate such dynamics poses an immediate challenge to systematically understand and classify these models. In particular, nontrivial many-body states emerge as steady states under non-equilibrium dynamics. In this talk, I use a field-theoretic approach based on the Keldysh formalism to study nonequilibrium phases and phase transitions in such models. I show that an effective temperature generically emerges as a result of dissipation, and the universal behavior including the dynamics near the steady state is described by a thermodynamic universality class. In the end, I will also discuss possibilities that go beyond the paradigm of an effective thermodynamic behavior.

Many-Body Effects on the Thermodynamics of Fluids, Mixtures, and Nanoconfined Fluids.

Science.gov (United States)

Desgranges, Caroline; Delhommelle, Jerome

2015-11-10

Using expanded Wang-Landau simulations, we show that taking into account the many-body interactions results in sharp changes in the grand-canonical partition functions of single-component systems, binary mixtures, and nanoconfined fluids. The many-body contribution, modeled with a 3-body Axilrod-Teller-Muto term, results in shifts toward higher chemical potentials of the phase transitions from low-density phases to high-density phases and accounts for deviations of more than, e.g., 20% of the value of the partition function for a single-component liquid. Using the statistical mechanics formalism, we analyze how this contribution has a strong impact on some properties (e.g., pressure, coexisting densities, and enthalpy) and a moderate impact on others (e.g., Gibbs or Helmholtz free energies). We also characterize the effect of the 3-body terms on adsorption isotherms and adsorption thermodynamic properties, thereby providing a full picture of the effect of the 3-body contribution on the thermodynamics of nanoconfined fluids.

Moments of generalized Husimi distributions and complexity of many-body quantum states

International Nuclear Information System (INIS)

Sugita, Ayumu

2003-01-01

We consider generalized Husimi distributions for many-body systems, and show that their moments are good measures of complexity of many-body quantum states. Our construction of the Husimi distribution is based on the coherent state of the single-particle transformation group. Then the coherent states are independent-particle states, and, at the same time, the most localized states in the Husimi representation. Therefore delocalization of the Husimi distribution, which can be measured by the moments, is a sign of many-body correlation (entanglement). Since the delocalization of the Husimi distribution is also related to chaoticity of the dynamics, it suggests a relation between entanglement and chaos. Our definition of the Husimi distribution can be applied not only to systems of distinguishable particles, but also to those of identical particles, i.e., fermions and bosons. We derive an algebraic formula to evaluate the moments of the Husimi distribution

Construction of exact constants of motion and effective models for many-body localized systems

Science.gov (United States)

Goihl, M.; Gluza, M.; Krumnow, C.; Eisert, J.

2018-04-01

One of the defining features of many-body localization is the presence of many quasilocal conserved quantities. These constants of motion constitute a cornerstone to an intuitive understanding of much of the phenomenology of many-body localized systems arising from effective Hamiltonians. They may be seen as local magnetization operators smeared out by a quasilocal unitary. However, accurately identifying such constants of motion remains a challenging problem. Current numerical constructions often capture the conserved operators only approximately, thus restricting a conclusive understanding of many-body localization. In this work, we use methods from the theory of quantum many-body systems out of equilibrium to establish an alternative approach for finding a complete set of exact constants of motion which are in addition guaranteed to represent Pauli-z operators. By this we are able to construct and investigate the proposed effective Hamiltonian using exact diagonalization. Hence, our work provides an important tool expected to further boost inquiries into the breakdown of transport due to quenched disorder.

On Permuting Cut with Contraction

OpenAIRE

Borisavljevic, Mirjana; Dosen, Kosta; Petric, Zoran

1999-01-01

The paper presents a cut-elimination procedure for intuitionistic propositional logic in which cut is eliminated directly, without introducing the multiple-cut rule mix, and in which pushing cut above contraction is one of the reduction steps. The presentation of this procedure is preceded by an analysis of Gentzen's mix-elimination procedure, made in the perspective of permuting cut with contraction. It is also shown that in the absence of implication, pushing cut above contraction doesn't p...

Many-body localization-delocalization transition in the quantum Sherrington-Kirkpatrick model

Science.gov (United States)

Mukherjee, Sudip; Nag, Sabyasachi; Garg, Arti

2018-04-01

We analyze the many-body localization- (MBL) to-delocalization transition in the Sherrington-Kirkpatrick (SK) model of Ising spin glass in the presence of a transverse field Γ . Based on energy-resolved analysis, which is of relevance for a closed quantum system, we show that the quantum SK model has many-body mobility edges separating the MBL phase, which is nonergodic and nonthermal, from the delocalized phase, which is ergodic and thermal. The range of the delocalized regime increases with an increase in the strength of Γ , and eventually for Γ larger than ΓCP the entire many-body spectrum is delocalized. We show that the Renyi entropy is almost independent of the system size in the MBL phase while the delocalized phase shows extensive Renyi entropy. We further obtain the spin-glass transition curve in the energy density ɛ -Γ plane from the collapse of the eigenstate spin susceptibility. We demonstrate that in most of the parameter regime, the spin-glass transition occurs close to the MBL transition, indicating that the spin-glass phase is nonergodic and nonthermal while the paramagnetic phase is delocalized and thermal.

Scalar meson field and many-body forces. Chapter 23

International Nuclear Information System (INIS)

Nyman, E.M.

1979-01-01

In applications of field theory to the theory of the nuclear forces, one has frequently assumed that there is a scalar meson. It will then be responsible for most of the medium-range attraction between the nucleons. According to current ideas, however, it is possible to account for the medium-range attraction without an elementary sigma meson. This approach requires a careful treatment of the exchange of interacting pairs of π mesons, such as to include those ππ interactions which are responsible for the formation and decay of the sigma meson. Recently, the scalar field in the nuclear many-body problem has begun to receive more attention. There are two reasons for this change of philosophy. One reason is the discovery of neutron stars. In neutron stars, the nucleon number density can be much higher than in nuclei. One therefore wants to derive the equation of state from a relativistic many-body theory. This forces one to deal explicitly with a set of mesons, such that in the non-relativistic limit one recovers the one-boson-exchange potential. (Auth.)

Invariant subsets under compact quantum group actions

OpenAIRE

Huang, Huichi

2012-01-01

We investigate compact quantum group actions on unital $C^*$-algebras by analyzing invariant subsets and invariant states. In particular, we come up with the concept of compact quantum group orbits and use it to show that countable compact metrizable spaces with infinitely many points are not quantum homogeneous spaces.

Efficient numerical simulations of many-body localized systems

Energy Technology Data Exchange (ETDEWEB)

Pollmann, Frank [Max-Planck-Institut fuer Physik komplexer Systeme, 01187 Dresden (Germany); Khemani, Vedika; Sondhi, Shivaji [Physics Department, Princeton University, Princeton, NJ 08544 (United States)

2016-07-01

Many-body localization (MBL) occurs in isolated quantum systems when Anderson localization persists in the presence of finite interactions. To understand this phenomenon, the development of new, efficient numerical methods to find highly excited eigenstates is essential. We introduce a variant of the density-matrix renormalization group (DMRG) method that obtains individual highly excited eigenstates of MBL systems to machine precision accuracy at moderate-large disorder. This method explicitly takes advantage of the local spatial structure characterizing MBL eigenstates.

Assessing Many-Body Effects of Water Self-Ions. I: OH-(H2O) n Clusters.

Science.gov (United States)

Egan, Colin K; Paesani, Francesco

2018-04-10

The importance of many-body effects in the hydration of the hydroxide ion (OH - ) is investigated through a systematic analysis of the many-body expansion of the interaction energy carried out at the CCSD(T) level of theory, extrapolated to the complete basis set limit, for the low-lying isomers of OH - (H 2 O) n clusters, with n = 1-5. This is accomplished by partitioning individual fragments extracted from the whole clusters into "groups" that are classified by both the number of OH - and water molecules and the hydrogen bonding connectivity within each fragment. With the aid of the absolutely localized molecular orbital energy decomposition analysis (ALMO-EDA) method, this structure-based partitioning is found to largely correlate with the character of different many-body interactions, such as cooperative and anticooperative hydrogen bonding, within each fragment. This analysis emphasizes the importance of a many-body representation of inductive electrostatics and charge transfer in modeling OH - hydration. Furthermore, the rapid convergence of the many-body expansion of the interaction energy also suggests a rigorous path for the development of analytical potential energy functions capable of describing individual OH - -water many-body terms, with chemical accuracy. Finally, a comparison between the reference CCSD(T) many-body interaction terms with the corresponding values obtained with various exchange-correlation functionals demonstrates that range-separated, dispersion-corrected, hybrid functionals exhibit the highest accuracy, while GGA functionals, with or without dispersion corrections, are inadequate to describe OH - -water interactions.

Many-body optimization using an ab initio monte carlo method.

Science.gov (United States)

Haubein, Ned C; McMillan, Scott A; Broadbelt, Linda J

2003-01-01

Advances in computing power have made it possible to study solvated molecules using ab initio quantum chemistry. Inclusion of discrete solvent molecules is required to determine geometric information about solute/solvent clusters. Monte Carlo methods are well suited to finding minima in many-body systems, and ab initio methods are applicable to the widest range of systems. A first principles Monte Carlo (FPMC) method was developed to find minima in many-body systems, and emphasis was placed on implementing moves that increase the likelihood of finding minimum energy structures. Partial optimization and molecular interchange moves aid in finding minima and overcome the incomplete sampling that is unavoidable when using ab initio methods. FPMC was validated by studying the boron trifluoride-water system, and then the method was used to examine the methyl carbenium ion in water to demonstrate its application to solvation problems.

Many-Body Green Function of Degenerate Systems

International Nuclear Information System (INIS)

Brouder, Christian; Panati, Gianluca; Stoltz, Gabriel

2009-01-01

A rigorous nonperturbative adiabatic approximation of the evolution operator in the many-body physics of degenerate systems is derived. This approximation is used to solve the long-standing problem of the choice of the initial states of H 0 leading to eigenstates of H 0 +V for degenerate systems. These initial states are eigenstates of P 0 VP 0 , where P 0 is the projection onto a degenerate eigenspace of H 0 . This result is used to give the proper definition of the Green function, the statistical Green function and the nonequilibrium Green function of degenerate systems. The convergence of these Green functions is established.

Many-Body Energy Decomposition with Basis Set Superposition Error Corrections.

Science.gov (United States)

Mayer, István; Bakó, Imre

2017-05-09

The problem of performing many-body decompositions of energy is considered in the case when BSSE corrections are also performed. It is discussed that the two different schemes that have been proposed go back to the two different interpretations of the original Boys-Bernardi counterpoise correction scheme. It is argued that from the physical point of view the "hierarchical" scheme of Valiron and Mayer should be preferred and not the scheme recently discussed by Ouyang and Bettens, because it permits the energy of the individual monomers and all the two-body, three-body, etc. energy components to be free of unphysical dependence on the arrangement (basis functions) of other subsystems in the cluster.

A Symmetric Chaos-Based Image Cipher with an Improved Bit-Level Permutation Strategy

Directory of Open Access Journals (Sweden)

Chong Fu

2014-02-01

Full Text Available Very recently, several chaos-based image ciphers using a bit-level permutation have been suggested and shown promising results. Due to the diffusion effect introduced in the permutation stage, the workload of the time-consuming diffusion stage is reduced, and hence the performance of the cryptosystem is improved. In this paper, a symmetric chaos-based image cipher with a 3D cat map-based spatial bit-level permutation strategy is proposed. Compared with those recently proposed bit-level permutation methods, the diffusion effect of the new method is superior as the bits are shuffled among different bit-planes rather than within the same bit-plane. Moreover, the diffusion key stream extracted from hyperchaotic system is related to both the secret key and the plain image, which enhances the security against known/chosen plaintext attack. Extensive security analysis has been performed on the proposed scheme, including the most important ones like key space analysis, key sensitivity analysis, plaintext sensitivity analysis and various statistical analyses, which has demonstrated the satisfactory security of the proposed scheme

A novel chaos-based image encryption scheme with an efficient permutation-diffusion mechanism

Science.gov (United States)

Ye, Ruisong

2011-10-01

This paper proposes a novel chaos-based image encryption scheme with an efficient permutation-diffusion mechanism, in which permuting the positions of image pixels incorporates with changing the gray values of image pixels to confuse the relationship between cipher-image and plain-image. In the permutation process, a generalized Arnold map is utilized to generate one chaotic orbit used to get two index order sequences for the permutation of image pixel positions; in the diffusion process, a generalized Arnold map and a generalized Bernoulli shift map are employed to yield two pseudo-random gray value sequences for a two-way diffusion of gray values. The yielded gray value sequences are not only sensitive to the control parameters and initial conditions of the considered chaotic maps, but also strongly depend on the plain-image processed, therefore the proposed scheme can resist statistical attack, differential attack, known-plaintext as well as chosen-plaintext attack. Experimental results are carried out with detailed analysis to demonstrate that the proposed image encryption scheme possesses large key space to resist brute-force attack as well.

Introduction to modern methods of quantum many-body theory and their applications

CERN Document Server

Fantoni, Stefano; Krotscheck, Eckhard S

2002-01-01

This invaluable book contains pedagogical articles on the dominant nonstochastic methods of microscopic many-body theories - the methods of density functional theory, coupled cluster theory, and correlated basis functions - in their widest sense. Other articles introduce students to applications of these methods in front-line research, such as Bose-Einstein condensates, the nuclear many-body problem, and the dynamics of quantum liquids. These keynote articles are supplemented by experimental reviews on intimately connected topics that are of current relevance. The book addresses the striking l

Diagrammatic many-body perturbation expansion for atoms and molecules. Pt. 6

International Nuclear Information System (INIS)

Moncrieff, D.; Baker, D.J.; Wilson, S.

1989-01-01

The efficient evaluation of the second-order expression in the many-body perturbation theory expansion for the correlation energy on vector processing and parallel processing computers is discussed. It is argued that the linked diagram theorem not only leads to the well known theoretical advantages of the many-body perturbation theory approach which allows the calculation of correlation energies for large (i.e. extended molecules or species containing heavy atoms) systems but also decouples the many-electron problem allowing efficient implementation on parallel processing machines. Furthermore, the computation associated with each of the resulting subproblems is very well suited to vector processing machines. Timing tests are reported for the CRAY 1 and CDC Cyber 205 vector processors, for a 1 processor implementation on the CRAY X-MP/48 and the ETA-10E, and for a 4 processor implementation on the Cray X-MP/48. (orig.)

Computational Nuclear Quantum Many-Body Problem: The UNEDF Project

OpenAIRE

Bogner, Scott; Bulgac, Aurel; Carlson, Joseph A.; Engel, Jonathan; Fann, George; Furnstahl, Richard J.; Gandolfi, Stefano; Hagen, Gaute; Horoi, Mihai; Johnson, Calvin W.; Kortelainen, Markus; Lusk, Ewing; Maris, Pieter; Nam, Hai Ah; Navratil, Petr

2013-01-01

The UNEDF project was a large-scale collaborative effort that applied high-performance computing to the nuclear quantum many-body problem. UNEDF demonstrated that close associations among nuclear physicists, mathematicians, and computer scientists can lead to novel physics outcomes built on algorithmic innovations and computational developments. This review showcases a wide range of UNEDF science results to illustrate this interplay.

Many-body effects in the mesoscopic x-ray edge problem

International Nuclear Information System (INIS)

Hentschel, Martina; Roeder, Georg; Ullmo, Denis

2007-01-01

Many-body phenomena, a key interest in the investigation of bulk solid state systems, are studied here in the context of the x-ray edge problem for mesoscopic systems. We investigate the many-body effects associated with the sudden perturbation following the x-ray exciton of a core electron into the conduction band. For small systems with dimensions at the nanoscale we find considerable deviations from the well-understood metallic case where Anderson orthogonality catastrophe and the Mahan-Nozieres-DeDominicis response cause characteristic deviations of the photoabsorption cross section from the naive expectation. Whereas the K-edge is typically rounded in metallic systems, we find a slightly peaked K-edge in generic mesoscopic systems with chaotic-coherent electron dynamics. Thus the behavior of the photoabsorption cross section at threshold depends on the system size and is different for the metallic and the mesoscopic case. (author)

Many-body dynamics with cold atoms and molecules in optical lattices

International Nuclear Information System (INIS)

Schachenmayer, J.

2012-01-01

Systems of cold atoms or molecules, trapped in a periodic potential formed from standing waves of laser light, provide an experimental possibility to study strongly correlated many-body lattice models, which are traditionally used in condensed matter physics. Due to the relatively weak energy scales in these ''optical lattices'' (next-neighbor tunneling energies are typically on the order of tens of Hertz), the time-scales of the dynamics in these systems is relatively slow and can be observed in experiments. Furthermore, the microscopic parameters of the models can be very well controlled by lattice laser intensities and external fields. Thus, optical lattices provide an excellent framework to study many-body quantum non-equilibrium dynamics, which on the theoretical level is the topic of this thesis. This thesis contains a study of many-body dynamics in optical lattices for both idealized isolated models and realistic models with imperfections. It is centered around four main topics: The first two topics are studies of coherent many-body dynamics. This contains explicitly: (i) an analysis of the possibility to dynamically prepare crystalline states of Rydberg atoms or polar molecules by adiabatically tuning laser parameters; and (ii) a study of the collapses and revivals of the momentum-distribution of a Bose-Einstein condensate with a fixed number of atoms, which is suddenly loaded into a deep optical lattice. The third main topic is entanglement and specifically the dynamical growth of entanglement between portions of an optical lattice in quench experiments. A method to create and measure large-scale entanglement is presented in this thesis. The fourth main topic addresses classical noise. Specifically, a system of atoms in an optical lattice, which is created from lasers with intensity fluctuations, is analyzed in this work. The noisy evolution of many-body correlation functions is studied and a method to cancel this noise in a realistic experimental setup is

Exploring one-particle orbitals in large many-body localized systems

Science.gov (United States)

Villalonga, Benjamin; Yu, Xiongjie; Luitz, David J.; Clark, Bryan K.

2018-03-01

Strong disorder in interacting quantum systems can give rise to the phenomenon of many-body localization (MBL), which defies thermalization due to the formation of an extensive number of quasilocal integrals of motion. The one-particle operator content of these integrals of motion is related to the one-particle orbitals (OPOs) of the one-particle density matrix and shows a strong signature across the MBL transition as recently pointed out by Bera et al. [Phys. Rev. Lett. 115, 046603 (2015), 10.1103/PhysRevLett.115.046603; Ann. Phys. 529, 1600356 (2017), 10.1002/andp.201600356]. We study the properties of the OPOs of many-body eigenstates of an MBL system in one dimension. Using shift-and-invert MPS, a matrix product state method to target highly excited many-body eigenstates introduced previously [Phys. Rev. Lett. 118, 017201 (2017), 10.1103/PhysRevLett.118.017201], we are able to obtain accurate results for large systems of sizes up to L =64 . We find that the OPOs drawn from eigenstates at different energy densities have high overlap and their occupations are correlated with the energy of the eigenstates. Moreover, the standard deviation of the inverse participation ratio of these orbitals is maximal at the nose of the mobility edge. Also, the OPOs decay exponentially in real space, with a correlation length that increases at low disorder. In addition, we find that the probability distribution of the strength of the large-range coupling constants of the number operators generated by the OPOs approach a log-uniform distribution at strong disorder.

The mean field in many body quantum physics

International Nuclear Information System (INIS)

Llano, M. de

1984-01-01

As an introduction to the quantum problem of many bodies we present a panoramic view of the most elementary theories called mean field theories. They comprise: i) the fermions ideal gas theory which implies, in a simple manner, the stability of white dwarf stars and of neutron stars, ii) the Hartree-Fock approximation for thermodynamical systems which is presented here in the context of a liquid-crystal phase transition, and iii) the Thomas-Fermi theory which is applied to the total binding energy of neutral atoms. (author)

Relativistic many-body XMCD theory including core degenerate effects

Science.gov (United States)

Fujikawa, Takashi

2009-11-01

A many-body relativistic theory to analyze X-ray Magnetic Circular Dichroism (XMCD) spectra has been developed on the basis of relativistic quantum electrodynamic (QED) Keldysh Green's function approach. This theoretical framework enables us to handle relativistic many-body effects in terms of correlated nonrelativistic Green's function and relativistic correction operator Q, which naturally incorporates radiation field screening and other optical field effects in addition to electron-electron interactions. The former can describe the intensity ratio of L2/L3 which deviates from the statistical weight (branching ratio) 1/2. In addition to these effects, we consider the degenerate or nearly degenerate effects of core levels from which photoelectrons are excited. In XPS spectra, for example in Rh 3d sub level excitations, their peak shapes are quite different: This interesting behavior is explained by core-hole moving after the core excitation. We discuss similar problems in X-ray absorption spectra in particular excitation from deep 2p sub levels which are degenerate in each sub levels and nearly degenerate to each other in light elements: The hole left behind is not frozen there. We derive practical multiple scattering formulas which incorporate all those effects.

EXPLICIT SYMPLECTIC-LIKE INTEGRATORS WITH MIDPOINT PERMUTATIONS FOR SPINNING COMPACT BINARIES

Energy Technology Data Exchange (ETDEWEB)

Luo, Junjie; Wu, Xin; Huang, Guoqing [Department of Physics and Institute of Astronomy, Nanchang University, Nanchang 330031 (China); Liu, Fuyao, E-mail: xwu@ncu.edu.cn [School of Fundamental Studies, Shanghai University of Engineering Science, Shanghai 201620 (China)

2017-01-01

We refine the recently developed fourth-order extended phase space explicit symplectic-like methods for inseparable Hamiltonians using Yoshida’s triple product combined with a midpoint permuted map. The midpoint between the original variables and their corresponding extended variables at every integration step is readjusted as the initial values of the original variables and their corresponding extended ones at the next step integration. The triple-product construction is apparently superior to the composition of two triple products in computational efficiency. Above all, the new midpoint permutations are more effective in restraining the equality of the original variables and their corresponding extended ones at each integration step than the existing sequent permutations of momenta and coordinates. As a result, our new construction shares the benefit of implicit symplectic integrators in the conservation of the second post-Newtonian Hamiltonian of spinning compact binaries. Especially for the chaotic case, it can work well, but the existing sequent permuted algorithm cannot. When dissipative effects from the gravitational radiation reaction are included, the new symplectic-like method has a secular drift in the energy error of the dissipative system for the orbits that are regular in the absence of radiation, as an implicit symplectic integrator does. In spite of this, it is superior to the same-order implicit symplectic integrator in accuracy and efficiency. The new method is particularly useful in discussing the long-term evolution of inseparable Hamiltonian problems.

Weighted multiscale Rényi permutation entropy of nonlinear time series

Science.gov (United States)

Chen, Shijian; Shang, Pengjian; Wu, Yue

2018-04-01

In this paper, based on Rényi permutation entropy (RPE), which has been recently suggested as a relative measure of complexity in nonlinear systems, we propose multiscale Rényi permutation entropy (MRPE) and weighted multiscale Rényi permutation entropy (WMRPE) to quantify the complexity of nonlinear time series over multiple time scales. First, we apply MPRE and WMPRE to the synthetic data and make a comparison of modified methods and RPE. Meanwhile, the influence of the change of parameters is discussed. Besides, we interpret the necessity of considering not only multiscale but also weight by taking the amplitude into account. Then MRPE and WMRPE methods are employed to the closing prices of financial stock markets from different areas. By observing the curves of WMRPE and analyzing the common statistics, stock markets are divided into 4 groups: (1) DJI, S&P500, and HSI, (2) NASDAQ and FTSE100, (3) DAX40 and CAC40, and (4) ShangZheng and ShenCheng. Results show that the standard deviations of weighted methods are smaller, showing WMRPE is able to ensure the results more robust. Besides, WMPRE can provide abundant dynamical properties of complex systems, and demonstrate the intrinsic mechanism.

Optimal control of hybrid qubits: Implementing the quantum permutation algorithm

Science.gov (United States)

Rivera-Ruiz, C. M.; de Lima, E. F.; Fanchini, F. F.; Lopez-Richard, V.; Castelano, L. K.

2018-03-01

The optimal quantum control theory is employed to determine electric pulses capable of producing quantum gates with a fidelity higher than 0.9997, when noise is not taken into account. Particularly, these quantum gates were chosen to perform the permutation algorithm in hybrid qubits in double quantum dots (DQDs). The permutation algorithm is an oracle based quantum algorithm that solves the problem of the permutation parity faster than a classical algorithm without the necessity of entanglement between particles. The only requirement for achieving the speedup is the use of a one-particle quantum system with at least three levels. The high fidelity found in our results is closely related to the quantum speed limit, which is a measure of how fast a quantum state can be manipulated. Furthermore, we model charge noise by considering an average over the optimal field centered at different values of the reference detuning, which follows a Gaussian distribution. When the Gaussian spread is of the order of 5 μ eV (10% of the correct value), the fidelity is still higher than 0.95. Our scheme also can be used for the practical realization of different quantum algorithms in DQDs.

Multi-response permutation procedure as an alternative to the analysis of variance: an SPSS implementation.

Science.gov (United States)

Cai, Li

2006-02-01

A permutation test typically requires fewer assumptions than does a comparable parametric counterpart. The multi-response permutation procedure (MRPP) is a class of multivariate permutation tests of group difference useful for the analysis of experimental data. However, psychologists seldom make use of the MRPP in data analysis, in part because the MRPP is not implemented in popular statistical packages that psychologists use. A set of SPSS macros implementing the MRPP test is provided in this article. The use of the macros is illustrated by analyzing example data sets.

Body composition and military performance--many things to many people.

Science.gov (United States)

Friedl, Karl E

2012-07-01

Soldiers are expected to maintain the highest possible level of physical readiness because they must be ready to mobilize and perform their duties anywhere in the world at any time. The objective of Army body composition standards is to motivate physical training and good nutrition habits to ensure a high state of readiness. Establishment of enforceable and rational standards to support this objective has been challenging even at extremes of body size. Morbidly obese individuals are clearly not suited to military service, but very large muscular individuals may be superbly qualified for soldier performance demands. For this reason, large individuals are measured for body fat using a waist circumference-based equation (female soldiers are also measured for hip circumference). The main challenge comes in setting appropriate fat standards to support the full range of Army requirements. Military appearance ideals dictate the most stringent body fat standards, whereas health risk thresholds anchor the most liberal standards, and physical performance associations fall on a spectrum between these 2 poles. Standards should not exclude or penalize specialized performance capabilities such as endurance running or power lifting across a spectrum of body sizes and fat. The full integration of women into the military further complicates the issue because of sexually dimorphic characteristics that make gender-appropriate standards essential and where inappropriately stringent standards can compromise both health and performance of this segment of the force. Other associations with body composition such as stress effects on intraabdominal fat distribution patterns and metabolic implications of a fat reserve for survival in extreme environments are also relevant considerations. This is a review of the science that underpins the U.S. Army body composition standards.

Many-body localization transition: Schmidt gap, entanglement length, and scaling

Science.gov (United States)

Gray, Johnnie; Bose, Sougato; Bayat, Abolfazl

2018-05-01

Many-body localization has become an important phenomenon for illuminating a potential rift between nonequilibrium quantum systems and statistical mechanics. However, the nature of the transition between ergodic and localized phases in models displaying many-body localization is not yet well understood. Assuming that this is a continuous transition, analytic results show that the length scale should diverge with a critical exponent ν ≥2 in one-dimensional systems. Interestingly, this is in stark contrast with all exact numerical studies which find ν ˜1 . We introduce the Schmidt gap, new in this context, which scales near the transition with an exponent ν >2 compatible with the analytical bound. We attribute this to an insensitivity to certain finite-size fluctuations, which remain significant in other quantities at the sizes accessible to exact numerical methods. Additionally, we find that a physical manifestation of the diverging length scale is apparent in the entanglement length computed using the logarithmic negativity between disjoint blocks.

Many-body effects in X-ray photoemission spectroscopy and electronic properties of solids

International Nuclear Information System (INIS)

Kohiki, S.

1999-01-01

Photoemission from a solid is evidently a many-body process since the motion of each electron cannot be independent of the motions of other electrons. In this article we review the reported many-body effects in X-ray photoemission such as extra-atomic relaxation energy, charge transfer satellite and energy loss structure which are informative in relation to the characteristics of solids. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)

The use of many-body expansions and geometry optimizations in fragment-based methods.

Science.gov (United States)

Fedorov, Dmitri G; Asada, Naoya; Nakanishi, Isao; Kitaura, Kazuo

2014-09-16

Conspectus Chemists routinely work with complex molecular systems: solutions, biochemical molecules, and amorphous and composite materials provide some typical examples. The questions one often asks are what are the driving forces for a chemical phenomenon? How reasonable are our views of chemical systems in terms of subunits, such as functional groups and individual molecules? How can one quantify the difference in physicochemical properties of functional units found in a different chemical environment? Are various effects on functional units in molecular systems additive? Can they be represented by pairwise potentials? Are there effects that cannot be represented in a simple picture of pairwise interactions? How can we obtain quantitative values for these effects? Many of these questions can be formulated in the language of many-body effects. They quantify the properties of subunits (fragments), referred to as one-body properties, pairwise interactions (two-body properties), couplings of two-body interactions described by three-body properties, and so on. By introducing the notion of fragments in the framework of quantum chemistry, one obtains two immense benefits: (a) chemists can finally relate to quantum chemistry, which now speaks their language, by discussing chemically interesting subunits and their interactions and (b) calculations become much faster due to a reduced computational scaling. For instance, the somewhat academic sounding question of the importance of three-body effects in water clusters is actually another way of asking how two hydrogen bonds affect each other, when they involve three water molecules. One aspect of this is the many-body charge transfer (CT), because the charge transfers in the two hydrogen bonds are coupled to each other (not independent). In this work, we provide a generalized view on the use of many-body expansions in fragment-based methods, focusing on the general aspects of the property expansion and a contraction of a

PERMUTATION-BASED POLYMORPHIC STEGO-WATERMARKS FOR PROGRAM CODES

Directory of Open Access Journals (Sweden)

Denys Samoilenko

2016-06-01

Full Text Available Purpose: One of the most actual trends in program code protection is code marking. The problem consists in creation of some digital “watermarks” which allow distinguishing different copies of the same program codes. Such marks could be useful for authority protection, for code copies numbering, for program propagation monitoring, for information security proposes in client-server communication processes. Methods: We used the methods of digital steganography adopted for program codes as text objects. The same-shape symbols method was transformed to same-semantic element method due to codes features which makes them different from ordinary texts. We use dynamic principle of marks forming making codes similar to be polymorphic. Results: We examined the combinatorial capacity of permutations possible in program codes. As a result it was shown that the set of 5-7 polymorphic variables is suitable for the most modern network applications. Marks creation and restoration algorithms where proposed and discussed. The main algorithm is based on full and partial permutations in variables names and its declaration order. Algorithm for partial permutation enumeration was optimized for calculation complexity. PHP code fragments which realize the algorithms were listed. Discussion: Methodic proposed in the work allows distinguishing of each client-server connection. In a case if a clone of some network resource was found the methodic could give information about included marks and thereby data on IP, date and time, authentication information of client copied the resource. Usage of polymorphic stego-watermarks should improve information security indexes in network communications.

Local conservation laws and the structure of the many-body localized states.

Science.gov (United States)

Serbyn, Maksym; Papić, Z; Abanin, Dmitry A

2013-09-20

We construct a complete set of local integrals of motion that characterize the many-body localized (MBL) phase. Our approach relies on the assumption that local perturbations act locally on the eigenstates in the MBL phase, which is supported by numerical simulations of the random-field XXZ spin chain. We describe the structure of the eigenstates in the MBL phase and discuss the implications of local conservation laws for its nonequilibrium quantum dynamics. We argue that the many-body localization can be used to protect coherence in the system by suppressing relaxation between eigenstates with different local integrals of motion.

Patterns in Permutations and Words

CERN Document Server

Kitaev, Sergey

2011-01-01

There has been considerable interest recently in the subject of patterns in permutations and words, a new branch of combinatorics with its roots in the works of Rotem, Rogers, and Knuth in the 1970s. Consideration of the patterns in question has been extremely interesting from the combinatorial point of view, and it has proved to be a useful language in a variety of seemingly unrelated problems, including the theory of Kazhdan--Lusztig polynomials, singularities of Schubert varieties, interval orders, Chebyshev polynomials, models in statistical mechanics, and various sorting algorithms, inclu

Real-time trajectory analysis using stacked invariance methods

OpenAIRE

Kitts, B.

1998-01-01

Invariance methods are used widely in pattern recognition as a preprocessing stage before algorithms such as neural networks are applied to the problem. A pattern recognition system has to be able to recognise objects invariant to scale, translation, and rotation. Presumably the human eye implements some of these preprocessing transforms in making sense of incoming stimuli, for example, placing signals onto a log scale. This paper surveys many of the commonly used invariance methods, and asse...

Permutation Entropy: New Ideas and Challenges

Directory of Open Access Journals (Sweden)

Karsten Keller

2017-03-01

Full Text Available Over recent years, some new variants of Permutation entropy have been introduced and applied to EEG analysis, including a conditional variant and variants using some additional metric information or being based on entropies that are different from the Shannon entropy. In some situations, it is not completely clear what kind of information the new measures and their algorithmic implementations provide. We discuss the new developments and illustrate them for EEG data.

EPEPT: A web service for enhanced P-value estimation in permutation tests

Directory of Open Access Journals (Sweden)

Knijnenburg Theo A

2011-10-01

Full Text Available Abstract Background In computational biology, permutation tests have become a widely used tool to assess the statistical significance of an event under investigation. However, the common way of computing the P-value, which expresses the statistical significance, requires a very large number of permutations when small (and thus interesting P-values are to be accurately estimated. This is computationally expensive and often infeasible. Recently, we proposed an alternative estimator, which requires far fewer permutations compared to the standard empirical approach while still reliably estimating small P-values 1. Results The proposed P-value estimator has been enriched with additional functionalities and is made available to the general community through a public website and web service, called EPEPT. This means that the EPEPT routines can be accessed not only via a website, but also programmatically using any programming language that can interact with the web. Examples of web service clients in multiple programming languages can be downloaded. Additionally, EPEPT accepts data of various common experiment types used in computational biology. For these experiment types EPEPT first computes the permutation values and then performs the P-value estimation. Finally, the source code of EPEPT can be downloaded. Conclusions Different types of users, such as biologists, bioinformaticians and software engineers, can use the method in an appropriate and simple way. Availability http://informatics.systemsbiology.net/EPEPT/

Off-shell effects and consistency of many-body treatments of dense matter

International Nuclear Information System (INIS)

Krippa, Boris; Birse, Michael C.; McGovern, Judith A.; Walet, Niels R.

2003-01-01

Effective field theory requires all observables to be independent of the representation used for the quantum field operators. It means that off-shell properties of the interactions should not lead to any observable effects. We analyze this issue in the context of many-body approaches to nuclear matter, where it should be possible to shift the contributions of lowest order in purely off-shell two-body interactions into three-body forces. We show that none of the commonly used truncations of the two-body scattering amplitude such as the ladder, Brueckner-Hartree-Fock, or parquet approximations respect this requirement

Probing correlated quantum many-body systems at the single-particle level

Energy Technology Data Exchange (ETDEWEB)

Endres, Manuel

2013-02-27

The detection of correlation and response functions plays a crucial role in the experimental characterization of quantum many-body systems. In this thesis, we present novel techniques for the measurement of such functions at the single-particle level. Specifically, we show the single-atom- and single-site-resolved detection of an ultracold quantum gas in an optical lattice. The quantum gas is described by the Bose-Hubbard model, which features a zero temperature phase transition from a superfluid to a Mott-insulating state, a paradigm example of a quantum phase transition. We used the aforementioned detection techniques to study correlation and response properties across the superfluid-Mott-insulator transition. The single-atom sensitivity of our method is achieved by fluorescence detection of individual atoms with a high signal-to-noise ratio. A high-resolution objective collects the fluorescence light and yields in situ 'snapshots' of the quantum gas that allow for a single-site-resolved reconstruction of the atomic distribution. This allowed us to measure two-site and non-local correlation-functions across the superfluid-Mott-insulator transition. Non-local correlation functions are based on the information of an extended region of the system and play an important role for the characterization of low-dimensional quantum phases. While non-local correlation functions were so far only theoretical tools, our results show that they are actually experimentally accessible. Furthermore, we used a new thermometry scheme, based on the counting of individual thermal excitations, to measure the response of the system to lattice modulation. Using this method, we studied the excitation spectrum of the system across the two-dimensional superfluid-Mott-insulator transition. In particular, we detected a 'Higgs' amplitude mode in the strongly-interacting superfluid close to the transition point where the system is described by an effectively Lorentz-invariant

Probing correlated quantum many-body systems at the single-particle level

International Nuclear Information System (INIS)

Endres, Manuel

2013-01-01

The detection of correlation and response functions plays a crucial role in the experimental characterization of quantum many-body systems. In this thesis, we present novel techniques for the measurement of such functions at the single-particle level. Specifically, we show the single-atom- and single-site-resolved detection of an ultracold quantum gas in an optical lattice. The quantum gas is described by the Bose-Hubbard model, which features a zero temperature phase transition from a superfluid to a Mott-insulating state, a paradigm example of a quantum phase transition. We used the aforementioned detection techniques to study correlation and response properties across the superfluid-Mott-insulator transition. The single-atom sensitivity of our method is achieved by fluorescence detection of individual atoms with a high signal-to-noise ratio. A high-resolution objective collects the fluorescence light and yields in situ 'snapshots' of the quantum gas that allow for a single-site-resolved reconstruction of the atomic distribution. This allowed us to measure two-site and non-local correlation-functions across the superfluid-Mott-insulator transition. Non-local correlation functions are based on the information of an extended region of the system and play an important role for the characterization of low-dimensional quantum phases. While non-local correlation functions were so far only theoretical tools, our results show that they are actually experimentally accessible. Furthermore, we used a new thermometry scheme, based on the counting of individual thermal excitations, to measure the response of the system to lattice modulation. Using this method, we studied the excitation spectrum of the system across the two-dimensional superfluid-Mott-insulator transition. In particular, we detected a 'Higgs' amplitude mode in the strongly-interacting superfluid close to the transition point where the system is described by an effectively Lorentz-invariant low-energy theory

A Weak Quantum Blind Signature with Entanglement Permutation

Science.gov (United States)

Lou, Xiaoping; Chen, Zhigang; Guo, Ying

2015-09-01

Motivated by the permutation encryption algorithm, a weak quantum blind signature (QBS) scheme is proposed. It involves three participants, including the sender Alice, the signatory Bob and the trusted entity Charlie, in four phases, i.e., initializing phase, blinding phase, signing phase and verifying phase. In a small-scale quantum computation network, Alice blinds the message based on a quantum entanglement permutation encryption algorithm that embraces the chaotic position string. Bob signs the blinded message with private parameters shared beforehand while Charlie verifies the signature's validity and recovers the original message. Analysis shows that the proposed scheme achieves the secure blindness for the signer and traceability for the message owner with the aid of the authentic arbitrator who plays a crucial role when a dispute arises. In addition, the signature can neither be forged nor disavowed by the malicious attackers. It has a wide application to E-voting and E-payment system, etc.

Invariance Signatures: Characterizing contours by their departures from invariance

OpenAIRE

Squire, David; Caelli, Terry M.

1997-01-01

In this paper, a new invariant feature of two-dimensional contours is reported: the Invariance Signature. The Invariance Signature is a measure of the degree to which a contour is invariant under a variety of transformations, derived from the theory of Lie transformation groups. It is shown that the Invariance Signature is itself invariant under shift, rotation and scaling of the contour. Since it is derived from local properties of the contour, it is well-suited to a neural network implement...

Single-particle basis and translational invariance in microscopic nuclear calculations

International Nuclear Information System (INIS)

Ehfros, V.D.

1977-01-01

The approach to the few-body problem is considered which allows to use the simple single-particle basis without violation of the translation invariance. A method is proposed to solve the nuclear reaction problems in the single-particle basis. The method satisfies the Pauli principle and the translation invariance. Calculation of the matrix elements of operators is treated

Heuristic method for determining outgoing waves in many-body wave functions

International Nuclear Information System (INIS)

Redish, E.F.; Tandy, P.C.; L'Huillier, M.

1975-12-01

A new and simple method is proposed for determining the kinds of outgoing waves present in a given many-body wave function. Whether any particular wave function contains ''hidden'' rearrangement components can be determined. 1 figure

Many-body calculations with deuteron based single-particle bases and their associated natural orbits

Science.gov (United States)

Puddu, G.

2018-06-01

We use the recently introduced single-particle states obtained from localized deuteron wave-functions as a basis for nuclear many-body calculations. We show that energies can be substantially lowered if the natural orbits (NOs) obtained from this basis are used. We use this modified basis for {}10{{B}}, {}16{{O}} and {}24{{Mg}} employing the bare NNLOopt nucleon–nucleon interaction. The lowering of the energies increases with the mass. Although in principle NOs require a full scale preliminary many-body calculation, we found that an approximate preliminary many-body calculation, with a marginal increase in the computational cost, is sufficient. The use of natural orbits based on an harmonic oscillator basis leads to a much smaller lowering of the energies for a comparable computational cost.

All ternary permutation constraint satisfaction problems parameterized above average have kernels with quadratic numbers of variables

DEFF Research Database (Denmark)

Gutin, Gregory; Van Iersel, Leo; Mnich, Matthias

2010-01-01

A ternary Permutation-CSP is specified by a subset Π of the symmetric group S3. An instance of such a problem consists of a set of variables V and a multiset of constraints, which are ordered triples of distinct variables of V. The objective is to find a linear ordering α of V that maximizes...... the number of triples whose rearrangement (under α) follows a permutation in Π. We prove that all ternary Permutation-CSPs parameterized above average have kernels with quadratic numbers of variables....

A permutation test for the race model inequality

DEFF Research Database (Denmark)

Gondan, Matthias

2010-01-01

signals. Several statistical procedures have been used for testing the race model inequality. However, the commonly employed procedure does not control the Type I error. In this article a permutation test is described that keeps the Type I error at the desired level. Simulations show that the power...

Enhancement and sign change of magnetic correlations in a driven quantum many-body system

Science.gov (United States)

Görg, Frederik; Messer, Michael; Sandholzer, Kilian; Jotzu, Gregor; Desbuquois, Rémi; Esslinger, Tilman

2018-01-01

Periodic driving can be used to control the properties of a many-body state coherently and to realize phases that are not accessible in static systems. For example, exposing materials to intense laser pulses makes it possible to induce metal-insulator transitions, to control magnetic order and to generate transient superconducting behaviour well above the static transition temperature. However, pinning down the mechanisms underlying these phenomena is often difficult because the response of a material to irradiation is governed by complex, many-body dynamics. For static systems, extensive calculations have been performed to explain phenomena such as high-temperature superconductivity. Theoretical analyses of driven many-body Hamiltonians are more challenging, but approaches have now been developed, motivated by recent observations. Here we report an experimental quantum simulation in a periodically modulated hexagonal lattice and show that antiferromagnetic correlations in a fermionic many-body system can be reduced, enhanced or even switched to ferromagnetic correlations (sign reversal). We demonstrate that the description of the many-body system using an effective Floquet-Hamiltonian with a renormalized tunnelling energy remains valid in the high-frequency regime by comparing the results to measurements in an equivalent static lattice. For near-resonant driving, the enhancement and sign reversal of correlations is explained by a microscopic model of the system in which the particle tunnelling and magnetic exchange energies can be controlled independently. In combination with the observed sufficiently long lifetimes of the correlations in this system, periodic driving thus provides an alternative way of investigating unconventional pairing in strongly correlated systems experimentally.

Exactly solvable models in many-body theory

CERN Document Server

March, N H

2016-01-01

The book reviews several theoretical, mostly exactly solvable, models for selected systems in condensed states of matter, including the solid, liquid, and disordered states, and for systems of few or many bodies, both with boson, fermion, or anyon statistics. Some attention is devoted to models for quantum liquids, including superconductors and superfluids. Open problems in relativistic fields and quantum gravity are also briefly reviewed.The book ranges almost comprehensively, but concisely, across several fields of theoretical physics of matter at various degrees of correlation and at different energy scales, with relevance to molecular, solid-state, and liquid-state physics, as well as to phase transitions, particularly for quantum liquids. Mostly exactly solvable models are presented, with attention also to their numerical approximation and, of course, to their relevance for experiments.

Modified potentials in many-body perturbation theory

International Nuclear Information System (INIS)

Silver, D.M.; Bartlett, R.J.

1976-01-01

Many-body perturbation-theory calculations of the pair-correlation energy within the regime of various finite expansions in two-center Slater-type basis sets are performed using a wide variety of modified potentials for the determination of unoccupied orbitals. To achieve meaningful convergence, it appears that the perturbation series must be carried through third order, using shifted denominators to include contributions from various higher-order diagrams. Moreover, certain denominator shifts are found necessary to ensure that a negative-definite resolvent accompanies the perturbation scheme when an arbitrary modified potential is employed. Through third order with denominator shifts, well-behaved modified potentials are found to give results that are equivalent, within 1 kcal/mole, to those obtained for pair-correlation energies with the standard self-consistent-field-V/sup N/ potential

Relativistic many-body theory of atomic structures

International Nuclear Information System (INIS)

Cheng, K.T.

1983-01-01

The main objective of this program is to improve our understanding of the effect of relativity and electron correlations on atomic processes. Current efforts include hyperfine structure (hfs) studies using the multiconfiguration Dirac-Fock (MCDF) technique. Atomic hfs are known to be sensitive to relativity and electron correlations, and provide important tests of relativistic atomic many-body theories. Preliminary results on the hfs of the 4f 12 3 H ground state of 68 Er 167 are shown and are in good agreement with experiment. This shows that the MCDF technique can be an efficient and powerful method for atomic hfs studies. Further tests of this method are in progress. We are also studying the absorption spectra for Xe-like ions in the region of 4d → nf, epsilonf transitions

Many-body theory and Energy Density Functionals

Energy Technology Data Exchange (ETDEWEB)

Baldo, M. [INFN, Catania (Italy)

2016-07-15

In this paper a method is first presented to construct an Energy Density Functional on a microscopic basis. The approach is based on the Kohn-Sham method, where one introduces explicitly the Nuclear Matter Equation of State, which can be obtained by an accurate many-body calculation. In this way it connects the functional to the bare nucleon-nucleon interaction. It is shown that the resulting functional can be performing as the best Gogny force functional. In the second part of the paper it is shown how one can go beyond the mean-field level and the difficulty that can appear. The method is based on the particle-vibration coupling scheme and a formalism is presented that can handle the correct use of the vibrational degrees of freedom within a microscopic approach. (orig.)

SCOPES: steganography with compression using permutation search

Science.gov (United States)

Boorboor, Sahar; Zolfaghari, Behrouz; Mozafari, Saadat Pour

2011-10-01

LSB (Least Significant Bit) is a widely used method for image steganography, which hides the secret message as a bit stream in LSBs of pixel bytes in the cover image. This paper proposes a variant of LSB named SCOPES that encodes and compresses the secret message while being hidden through storing addresses instead of message bytes. Reducing the length of the stored message improves the storage capacity and makes the stego image visually less suspicious to the third party. The main idea behind the SCOPES approach is dividing the message into 3-character segments, seeking each segment in the cover image and storing the address of the position containing the segment instead of the segment itself. In this approach, every permutation of the 3 bytes (if found) can be stored along with some extra bits indicating the permutation. In some rare cases the segment may not be found in the image and this can cause the message to be expanded by some overhead bits2 instead of being compressed. But experimental results show that SCOPES performs overlay better than traditional LSB even in the worst cases.

Many-body problem in one-dimension

International Nuclear Information System (INIS)

Emery, V.J.

1979-11-01

This work attempts to give a qualitative feeling for the more important physical ideas involved with the study of many-body systems in one dimension, and considers a particular strong-coupling model. This model provides an excellent description of the chains of mercury ions in Hg/sub 3-delta/AsF 6 ; some of the predictions of the theory can be checked by x-ray and neutron diffraction. Much of the physics of nearly one-dimensional materials is concerned with understanding the possible types of phase transition that may take place, and establishing the conditions in which one or another will be predominant. The most significant feature of purely one-dimensional systems is the dominant effect of fluctuations. The paper is organized as follows: introduction; qualitative aspects of one-dimensional systems (general survey, mathematical model, qualitative discussion of strong coupling - strong attractive U, strong repulsive U, large V); strong coupling between parallel spins (independent spin systems, coupling between opposite spins); mercury chains; electrons with arbitrary coupling; boson representations of operators; and classical Coulomb gas

N=2 superconformal Newton-Hooke algebra and many-body mechanics

International Nuclear Information System (INIS)

Galajinsky, Anton

2009-01-01

A representation of the conformal Newton-Hooke algebra on a phase space of n particles in arbitrary dimension which interact with one another via a generic conformal potential and experience a universal cosmological repulsion or attraction is constructed. The minimal N=2 superconformal extension of the Newton-Hooke algebra and its dynamical realization in many-body mechanics are studied.

On nonequilibrium many-body systems III: nonlinear transport theory

International Nuclear Information System (INIS)

Luzzi, R.; Vasconcellos, A.R.; Algarte, A.C.S.

1986-01-01

A nonlinear transport theory for many-body systems arbitrarily away from equilibrium, based on the nonequilibrium statistical operator (NSO) method, is presented. Nonlinear transport equations for a basis set of dynamical quantities are derived using two equivalent treatments that may be considered far reaching generalizations of the Hilbert-Chapman-Enskog method and Mori's generalized Langevin equations method. The first case is considered in some detail and the general characteristics of the theory are discussed. (Author) [pt

Statistical Significance of the Contribution of Variables to the PCA Solution: An Alternative Permutation Strategy

Science.gov (United States)

Linting, Marielle; van Os, Bart Jan; Meulman, Jacqueline J.

2011-01-01

In this paper, the statistical significance of the contribution of variables to the principal components in principal components analysis (PCA) is assessed nonparametrically by the use of permutation tests. We compare a new strategy to a strategy used in previous research consisting of permuting the columns (variables) of a data matrix…

Many-body-localization: strong disorder perturbative approach for the local integrals of motion

Science.gov (United States)

Monthus, Cécile

2018-05-01

For random quantum spin models, the strong disorder perturbative expansion of the local integrals of motion around the real-spin operators is revisited. The emphasis is on the links with other properties of the many-body-localized phase, in particular the memory in the dynamics of the local magnetizations and the statistics of matrix elements of local operators in the eigenstate basis. Finally, this approach is applied to analyze the many-body-localization transition in a toy model studied previously from the point of view of the entanglement entropy.

Nonlinear field theories and non-Gaussian fluctuations for near-critical many-body systems

International Nuclear Information System (INIS)

Tuszynski, J.A.; Dixon, J.M.; Grundland, A.M.

1994-01-01

This review article outlines a number of efforts made over the past several decades to understand the physics of near critical many-body systems. Beginning with the phenomenological theories of Landau and Ginzburg the paper discusses the two main routes adopted in the past. The first approach is based on statistical calculations while the second investigates the underlying nonlinear field equations. In the last part of the paper we outline a generalisation of these methods which combines classical and quantum properties of the many-body systems studied. (orig.)

Testing for changes using permutations of U-statistics

Czech Academy of Sciences Publication Activity Database

Horvath, L.; Hušková, Marie

2005-01-01

Roč. 2005, č. 128 (2005), s. 351-371 ISSN 0378-3758 R&D Projects: GA ČR GA201/00/0769 Institutional research plan: CEZ:AV0Z10750506 Keywords : U-statistics * permutations * change-point * weighted approximation * Brownian bridge Subject RIV: BD - Theory of Information Impact factor: 0.481, year: 2005

The proceedings of the 9th international conference on recent progress in many-body theories

International Nuclear Information System (INIS)

Neilson, D.; Bishop, R. F.

1998-01-01

This inaugural volume in this new World Scientific Publications series, 'Advances in Quantum Many-Body Theory' records the invited and contributed papers given at the Ninth International Conference on Recent Progress in Many-Body Theories. This conference was held in the School of Physics at The University of New South Wales in Sydney in July, 1997. The conference was also the seventh in the University's series of Gordon Godfrey International Workshop on Theoretical Physics. The style and format of the conference followed the accepted pattern for the series, focusing on the development, refinement, and important applications of many-body methods. A major aim of the series has been to foster an exchange of ideas among physicists working in such diverse areas as nuclear and subnuclear physics, quantum chemistry, complex systems, quantum field theory, strongly correlated electronic systems, magnetism, quantum fluids and condensed matter physics. A special feature of this ninth conference was a session devoted to theories for many-electron systems in zero dimensions (quantum dots), one dimension (quantum wires) and two dimensions (electron layers). These new systems are now firmly established as fertile sources of novel and challenging many-body phenomena

A Comparison of Multiscale Permutation Entropy Measures in On-Line Depth of Anesthesia Monitoring.

Science.gov (United States)

Su, Cui; Liang, Zhenhu; Li, Xiaoli; Li, Duan; Li, Yongwang; Ursino, Mauro

2016-01-01

Multiscale permutation entropy (MSPE) is becoming an interesting tool to explore neurophysiological mechanisms in recent years. In this study, six MSPE measures were proposed for on-line depth of anesthesia (DoA) monitoring to quantify the anesthetic effect on the real-time EEG recordings. The performance of these measures in describing the transient characters of simulated neural populations and clinical anesthesia EEG were evaluated and compared. Six MSPE algorithms-derived from Shannon permutation entropy (SPE), Renyi permutation entropy (RPE) and Tsallis permutation entropy (TPE) combined with the decomposition procedures of coarse-graining (CG) method and moving average (MA) analysis-were studied. A thalamo-cortical neural mass model (TCNMM) was used to generate noise-free EEG under anesthesia to quantitatively assess the robustness of each MSPE measure against noise. Then, the clinical anesthesia EEG recordings from 20 patients were analyzed with these measures. To validate their effectiveness, the ability of six measures were compared in terms of tracking the dynamical changes in EEG data and the performance in state discrimination. The Pearson correlation coefficient (R) was used to assess the relationship among MSPE measures. CG-based MSPEs failed in on-line DoA monitoring at multiscale analysis. In on-line EEG analysis, the MA-based MSPE measures at 5 decomposed scales could track the transient changes of EEG recordings and statistically distinguish the awake state, unconsciousness and recovery of consciousness (RoC) state significantly. Compared to single-scale SPE and RPE, MSPEs had better anti-noise ability and MA-RPE at scale 5 performed best in this aspect. MA-TPE outperformed other measures with faster tracking speed of the loss of unconsciousness. MA-based multiscale permutation entropies have the potential for on-line anesthesia EEG analysis with its simple computation and sensitivity to drug effect changes. CG-based multiscale permutation

Permutational distribution of the log-rank statistic under random censorship with applications to carcinogenicity assays.

Science.gov (United States)

Heimann, G; Neuhaus, G

1998-03-01

In the random censorship model, the log-rank test is often used for comparing a control group with different dose groups. If the number of tumors is small, so-called exact methods are often applied for computing critical values from a permutational distribution. Two of these exact methods are discussed and shown to be incorrect. The correct permutational distribution is derived and studied with respect to its behavior under unequal censoring in the light of recent results proving that the permutational version and the unconditional version of the log-rank test are asymptotically equivalent even under unequal censoring. The log-rank test is studied by simulations of a realistic scenario from a bioassay with small numbers of tumors.

Permuting sparse rectangular matrices into block-diagonal form

Energy Technology Data Exchange (ETDEWEB)

Aykanat, Cevdet; Pinar, Ali; Catalyurek, Umit V.

2002-12-09

This work investigates the problem of permuting a sparse rectangular matrix into block diagonal form. Block diagonal form of a matrix grants an inherent parallelism for the solution of the deriving problem, as recently investigated in the context of mathematical programming, LU factorization and QR factorization. We propose graph and hypergraph models to represent the nonzero structure of a matrix, which reduce the permutation problem to those of graph partitioning by vertex separator and hypergraph partitioning, respectively. Besides proposing the models to represent sparse matrices and investigating related combinatorial problems, we provide a detailed survey of relevant literature to bridge the gap between different societies, investigate existing techniques for partitioning and propose new ones, and finally present a thorough empirical study of these techniques. Our experiments on a wide range of matrices, using state-of-the-art graph and hypergraph partitioning tools MeTiS and PaT oH, revealed that the proposed methods yield very effective solutions both in terms of solution quality and run time.

Multiscale Permutation Entropy Based Rolling Bearing Fault Diagnosis

Directory of Open Access Journals (Sweden)

Jinde Zheng

2014-01-01

Full Text Available A new rolling bearing fault diagnosis approach based on multiscale permutation entropy (MPE, Laplacian score (LS, and support vector machines (SVMs is proposed in this paper. Permutation entropy (PE was recently proposed and defined to measure the randomicity and detect dynamical changes of time series. However, for the complexity of mechanical systems, the randomicity and dynamic changes of the vibration signal will exist in different scales. Thus, the definition of MPE is introduced and employed to extract the nonlinear fault characteristics from the bearing vibration signal in different scales. Besides, the SVM is utilized to accomplish the fault feature classification to fulfill diagnostic procedure automatically. Meanwhile, in order to avoid a high dimension of features, the Laplacian score (LS is used to refine the feature vector by ranking the features according to their importance and correlations with the main fault information. Finally, the rolling bearing fault diagnosis method based on MPE, LS, and SVM is proposed and applied to the experimental data. The experimental data analysis results indicate that the proposed method could identify the fault categories effectively.

Comparison of electromagnetically induced transparency schemes in semiconductor quantum dot structures: Impact of many-body interactions

DEFF Research Database (Denmark)

Houmark-Nielsen, Jakob; Nielsen, Torben Roland; Mørk, Jesper

2009-01-01

an important impact on the slow light properties. In the case of the Lambda and V schemes, the minimum required coupling power to achieve slow light is significantly reduced by many-body interactions. V type schemes are found to be generally preferable due to a favorable redistribution of carriers in energy......We investigate the impact of many-body interactions on group-velocity slowdown achieved via electromagnetically induced transparency in quantum dots using three different coupling-probe schemes (ladder, V, and Lambda, respectively). We find that for all schemes many-body interactions have...

Model many-body Stoner Hamiltonian for binary FeCr alloys

Science.gov (United States)

Nguyen-Manh, D.; Dudarev, S. L.

2009-09-01

We derive a model tight-binding many-body d -electron Stoner Hamiltonian for FeCr binary alloys and investigate the sensitivity of its mean-field solutions to the choice of hopping integrals and the Stoner exchange parameters. By applying the local charge-neutrality condition within a self-consistent treatment we show that the negative enthalpy-of-mixing anomaly characterizing the alloy in the low chromium concentration limit is due entirely to the presence of the on-site exchange Stoner terms and that the occurrence of this anomaly is not specifically related to the choice of hopping integrals describing conventional chemical bonding between atoms in the alloy. The Bain transformation pathway computed, using the proposed model Hamiltonian, for the Fe15Cr alloy configuration is in excellent agreement with ab initio total-energy calculations. Our investigation also shows how the parameters of a tight-binding many-body model Hamiltonian for a magnetic alloy can be derived from the comparison of its mean-field solutions with other, more accurate, mean-field approximations (e.g., density-functional calculations), hence stimulating the development of large-scale computational algorithms for modeling radiation damage effects in magnetic alloys and steels.

Quasiparticle engineering and entanglement propagation in a quantum many-body system.

Science.gov (United States)

Jurcevic, P; Lanyon, B P; Hauke, P; Hempel, C; Zoller, P; Blatt, R; Roos, C F

2014-07-10

The key to explaining and controlling a range of quantum phenomena is to study how information propagates around many-body systems. Quantum dynamics can be described by particle-like carriers of information that emerge in the collective behaviour of the underlying system, the so-called quasiparticles. These elementary excitations are predicted to distribute quantum information in a fashion determined by the system's interactions. Here we report quasiparticle dynamics observed in a quantum many-body system of trapped atomic ions. First, we observe the entanglement distributed by quasiparticles as they trace out light-cone-like wavefronts. Second, using the ability to tune the interaction range in our system, we observe information propagation in an experimental regime where the effective-light-cone picture does not apply. Our results will enable experimental studies of a range of quantum phenomena, including transport, thermalization, localization and entanglement growth, and represent a first step towards a new quantum-optic regime of engineered quasiparticles with tunable nonlinear interactions.

Auger recombination in Dirac materials: A tangle of many-body effects

Science.gov (United States)

Alymov, Georgy; Vyurkov, Vladimir; Ryzhii, Victor; Satou, Akira; Svintsov, Dmitry

2018-05-01

The peculiar electron dispersion in Dirac materials makes lowest-order Auger processes prohibited or marginally prohibited by energy and momentum conservation laws. Thus, Auger recombination (AR) in these materials is very sensitive to many-body effects. We incorporate them at the level of the G W approximation into the nonequilibrium Green's functions approach to AR and study the role of dynamic screening, spectrum broadening, and renormalization in the case of weakly pumped undoped graphene. We find that incorrect treatment of many-body effects can lead to an order-of-magnitude error in the recombination rate. We show that the AR time depends weakly (sublinearly) on the background dielectric constant, which limits the possibility to control recombination by the choice of substrate. However, the AR time can be considerably prolonged by placing graphene under a metal gate or by introducing a band gap. With carrier cooling taken into account, our results comply with experiments on photoexcited graphene.

Permuted tRNA genes of Cyanidioschyzon merolae, the origin of the tRNA molecule and the root of the Eukarya domain.

Science.gov (United States)

Di Giulio, Massimo

2008-08-07

An evolutionary analysis is conducted on the permuted tRNA genes of Cyanidioschyzon merolae, in which the 5' half of the tRNA molecule is codified at the 3' end of the gene and its 3' half is codified at the 5' end. This analysis has shown that permuted genes cannot be considered as derived traits but seem to possess characteristics that suggest they are ancestral traits, i.e. they originated when tRNA molecule genes originated for the first time. In particular, if the hypothesis that permuted genes are a derived trait were true, then we should not have been able to observe that the most frequent class of permuted genes is that of the anticodon loop type, for the simple reason that this class would derive by random permutation from a class of non-permuted tRNA genes, which instead is the rarest. This would not explain the high frequency with which permuted tRNA genes with perfectly separate 5' and 3' halves were observed. Clearly the mechanism that produced this class of permuted genes would envisage the existence, in an advanced stage of evolution, of minigenes codifying for the 5' and 3' halves of tRNAs which were assembled in a permuted way at the origin of the tRNA molecule, thus producing a high frequency of permuted genes of the class here referred. Therefore, this evidence supports the hypothesis that the genes of the tRNA molecule were assembled by minigenes codifying for hairpin-like RNA molecules, as suggested by one model for the origin of tRNA [Di Giulio, M., 1992. On the origin of the transfer RNA molecule. J. Theor. Biol. 159, 199-214; Di Giulio, M., 1999. The non-monophyletic origin of tRNA molecule. J. Theor. Biol. 197, 403-414]. Moreover, the late assembly of the permuted genes of C. merolae, as well as their ancestrality, strengthens the hypothesis of the polyphyletic origins of these genes. Finally, on the basis of the uniqueness and the ancestrality of these permuted genes, I suggest that the root of the Eukarya domain is in the super

Infinity-Norm Permutation Covering Codes from Cyclic Groups

OpenAIRE

Karni, Ronen; Schwartz, Moshe

2017-01-01

We study covering codes of permutations with the $\\ell_\\infty$-metric. We provide a general code construction, which uses smaller building-block codes. We study cyclic transitive groups as building blocks, determining their exact covering radius, and showing linear-time algorithms for finding a covering codeword. We also bound the covering radius of relabeled cyclic transitive groups under conjugation.

CIME School on Quantum Many Body Systems

CERN Document Server

Rivasseau, Vincent; Solovej, Jan Philip; Spencer, Thomas

2012-01-01

The book is based on the lectures given at the CIME school "Quantum many body systems" held in the summer of 2010. It provides a tutorial introduction to recent advances in the mathematics of interacting systems, written by four leading experts in the field: V. Rivasseau illustrates the applications of constructive Quantum Field Theory to 2D interacting electrons and their relation to quantum gravity; R. Seiringer describes a proof of Bose-Einstein condensation in the Gross-Pitaevski limit and explains the effects of rotating traps and the emergence of lattices of quantized vortices; J.-P. Solovej gives an introduction to the theory of quantum Coulomb systems and to the functional analytic methods used to prove their thermodynamic stability; finally, T. Spencer explains the supersymmetric approach to Anderson localization and its relation to the theory of random matrices. All the lectures are characterized by their mathematical rigor combined with physical insights.

Resonating-group method for nuclear many-body problems

International Nuclear Information System (INIS)

Tang, Y.C.; LeMere, M.; Thompson, D.R.

1977-01-01

The resonating-group method is a microscopic method which uses fully antisymmetric wave functions, treats correctly the motion of the total center of mass, and takes cluster correlation into consideration. In this review, the formulation of this method is discussed for various nuclear many-body problems, and a complex-generator-coordinate technique which has been employed to evaluate matrix elements required in resonating-group calculations is described. Several illustrative examples of bound-state, scattering, and reaction calculations, which serve to demonstrate the usefulness of this method, are presented. Finally, by utilization of the results of these calculations, the role played by the Pauli principle in nuclear scattering and reaction processes is discussed. 21 figures, 2 tables, 185 references

The partition function of an interacting many body system

International Nuclear Information System (INIS)

Rummel, C.; Ankerhold, J.

2002-01-01

Based on the path integral approach the partition function of a many body system with separable two body interaction is calculated in the sense of a semiclassical approximation. The commonly used Gaussian type of approximation, known as the perturbed static path approximation (PSPA), breaks down near a crossover temperature due to instabilities of the classical mean field solution. It is shown how the PSPA is systematically improved within the crossover region by taking into account large non-Gaussian fluctuation and an approximation applicable down to very low temperatures is carried out. These findings are tested against exact results for the archetypical cases of a particle moving in a one dimensional double well and the exactly solvable Lipkin-Meshkov-Glick model. The extensions should have applications in finite systems at low temperatures as in nuclear physics and mesoscopic systems, e. g. for gap fluctuations in nano-scale superconducting devices previously studied within a PSPA type of approximation. (author)

Optimization and experimental realization of the quantum permutation algorithm

Science.gov (United States)

Yalçınkaya, I.; Gedik, Z.

2017-12-01

The quantum permutation algorithm provides computational speed-up over classical algorithms for determining the parity of a given cyclic permutation. For its n -qubit implementations, the number of required quantum gates scales quadratically with n due to the quantum Fourier transforms included. We show here for the n -qubit case that the algorithm can be simplified so that it requires only O (n ) quantum gates, which theoretically reduces the complexity of the implementation. To test our results experimentally, we utilize IBM's 5-qubit quantum processor to realize the algorithm by using the original and simplified recipes for the 2-qubit case. It turns out that the latter results in a significantly higher success probability which allows us to verify the algorithm more precisely than the previous experimental realizations. We also verify the algorithm for the first time for the 3-qubit case with a considerable success probability by taking the advantage of our simplified scheme.

Self-consistent RPA based on a many-body vacuum

International Nuclear Information System (INIS)

Jemaï, M.; Schuck, P.

2011-01-01

Self-Consistent RPA is extended in a way so that it is compatible with a variational ansatz for the ground-state wave function as a fermionic many-body vacuum. Employing the usual equation-of-motion technique, we arrive at extended RPA equations of the Self-Consistent RPA structure. In principle the Pauli principle is, therefore, fully respected. However, the correlation functions entering the RPA matrix can only be obtained from a systematic expansion in powers of some combinations of RPA amplitudes. We demonstrate for a model case that this expansion may converge rapidly.

Real-space decoupling transformation for quantum many-body systems.

Science.gov (United States)

Evenbly, G; Vidal, G

2014-06-06

We propose a real-space renormalization group method to explicitly decouple into independent components a many-body system that, as in the phenomenon of spin-charge separation, exhibits separation of degrees of freedom at low energies. Our approach produces a branching holographic description of such systems that opens the path to the efficient simulation of the most entangled phases of quantum matter, such as those whose ground state violates a boundary law for entanglement entropy. As in the coarse-graining transformation of Vidal [Phys. Rev. Lett. 99, 220405 (2007).

In-Medium Similarity Renormalization Group Approach to the Nuclear Many-Body Problem

Science.gov (United States)

Hergert, Heiko; Bogner, Scott K.; Lietz, Justin G.; Morris, Titus D.; Novario, Samuel J.; Parzuchowski, Nathan M.; Yuan, Fei

We present a pedagogical discussion of Similarity Renormalization Group (SRG) methods, in particular the In-Medium SRG (IMSRG) approach for solving the nuclear many-body problem. These methods use continuous unitary transformations to evolve the nuclear Hamiltonian to a desired shape. The IMSRG, in particular, is used to decouple the ground state from all excitations and solve the many-body Schrödinger equation. We discuss the IMSRG formalism as well as its numerical implementation, and use the method to study the pairing model and infinite neutron matter. We compare our results with those of Coupled cluster theory (Chap. 8), Configuration-Interaction Monte Carlo (Chap. 9), and the Self-Consistent Green's Function approach discussed in Chap. 11 The chapter concludes with an expanded overview of current research directions, and a look ahead at upcoming developments.

PREFACE: 17th International Conference on Recent Progress in Many-Body Theories (MBT17)

Science.gov (United States)

Reinholz, Heidi; Boronat, Jordi

2014-08-01

These are the proceedings of the XVII International Conference on Recent Progress in Many-Body Theories, which was held from 8-13 September 2013 in Rostock, Germany. The conference continued the triennial series initiated in Trieste in 1978 and was devoted to new developments in the field of many-body theories. The conference series encourages the exchange of ideas between physicists working in such diverse areas as nuclear physics, quantum chemistry, lattice Hamiltonians or quantum uids. Many-body theories are an integral part in different fields of theoretical physics such as condensed matter, nuclear matter and field theory. Phase transitions and macroscopic quantum effects such as magnetism, Bose-Einstein condensation, super uidity or superconductivity have been investigated within ultra-cold gases, finite systems or various nanomaterials. The conference series on Recent Progress in Many-Body Theories is devoted to foster the interaction and to cross-fertilize between different fields and to discuss future lines of research. The topics of the 17th meeting were Cluster Physics Cold Gases High Energy Density Matter and Intense Lasers Magnetism New Developments in Many-Body Techniques Nuclear Many-Body and Relativistic Theories Quantum Fluids and Solids Quantum Phase Transitions Topological Insulators and Low Dimensional Systems. 109 participants from 20 countries participated. 44 talks and 61 posters werde presented. As a particular highlight of the conference, The Eugene Feenberg Memorial Medal for outstanding results in the field of many-body theory and The Hermann Kümmel Early Achievement Award in Many-Body Physics for young scientists in that field were awarded. The Feenberg Medal went jointly to Patrick Lee (MIT, USA) for his fundamental contributions to condensed-matter theory, especially in regard to the quantum Hall effect, to universal conductance uctuations, and to the Kondo effect in quantum dots, and Douglas Scalapino (UC Santa Barbara, USA) for his

Relativistic many-body theory of atomic transitions. The relativistic equation-of-motion approach

International Nuclear Information System (INIS)

Huang, K.

1982-01-01

An equation-of-motion approach is used to develop the relativistic many-body theory of atomic transitions. The relativistic equations of motion for transition matrices are formulated with the use of techniques of quantum-field theory. To reduce the equations of motion to a tractable form which is appropriate for numerical calculations, a graphical method to resolve the complication arising from the antisymmetrization and angular-momentum coupling is employed. The relativistic equation-of-motion method allows an ab initio treatment of correlation and relativistic effects in both closed- and open-shell many-body systems. A special case of the present formulation reduces to the relativistic random-phase approximation

Relativistic many-body theory of atomic transitions: the relativistic equation-of-motion approach

International Nuclear Information System (INIS)

Huang, K.N.

1981-01-01

An equation-of-motion approach is used to develop the relativistic many-body theory of atomic transitions. The relativistic equations of motion for transition matrices are formulated using techniques of quantum field theory. To reduce the equation of motion to a tractable form which is appropriate for numerical calculations, a graphical method is employed to resolve the complication arising from the antisymmetrization and angular momentum coupling. The relativistic equation-of-motion method allows an ab initio treatment of correlation and relativistic effects in both closed- and open-shell many-body systems. A special case of the present formulation reduces to the relativistic random-phase approximation

Invariant subspaces

CERN Document Server

Radjavi, Heydar

2003-01-01

This broad survey spans a wealth of studies on invariant subspaces, focusing on operators on separable Hilbert space. Largely self-contained, it requires only a working knowledge of measure theory, complex analysis, and elementary functional analysis. Subjects include normal operators, analytic functions of operators, shift operators, examples of invariant subspace lattices, compact operators, and the existence of invariant and hyperinvariant subspaces. Additional chapters cover certain results on von Neumann algebras, transitive operator algebras, algebras associated with invariant subspaces,

Exact results for the many-body problem in one dimension with repulsive delta-function interaction

International Nuclear Information System (INIS)

Yang, C.N.

1983-01-01

The repulsive δ interaction problem in one dimension for N particles is reduced, through the use of Bethe's hypothesis, to an eigenvalue problem of matrices of the same sizes as the irreducible representations R of the permutation group S/sub N/. For some R's this eigenvalue problem itself is solved by a second use of Bethe's hypothesis, in a generalized form. In particular, the ground-state problem of spin-1/2 fermions is reduced to a generalized Fredholm equation

On the hierarchy of partially invariant submodels of differential equations

Energy Technology Data Exchange (ETDEWEB)

Golovin, Sergey V [Lavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk 630090 (Russian Federation)], E-mail: sergey@hydro.nsc.ru

2008-07-04

It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given.

On the hierarchy of partially invariant submodels of differential equations

Science.gov (United States)

Golovin, Sergey V.

2008-07-01

It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given.

On the hierarchy of partially invariant submodels of differential equations

International Nuclear Information System (INIS)

Golovin, Sergey V

2008-01-01

It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given

Measurement invariance versus selection invariance: Is fair selection possible?

NARCIS (Netherlands)

Borsboom, D.; Romeijn, J.W.; Wicherts, J.M.

2008-01-01

This article shows that measurement invariance (defined in terms of an invariant measurement model in different groups) is generally inconsistent with selection invariance (defined in terms of equal sensitivity and specificity across groups). In particular, when a unidimensional measurement

Measurement invariance versus selection invariance : Is fair selection possible?

NARCIS (Netherlands)

Borsboom, Denny; Romeijn, Jan-Willem; Wicherts, Jelte M.

This article shows that measurement invariance (defined in terms of an invariant measurement model in different groups) is generally inconsistent with selection invariance (defined in terms of equal sensitivity and specificity across groups). In particular, when a unidimensional measurement

Physics in one dimension: theoretical concepts for quantum many-body systems.

Science.gov (United States)

Schönhammer, K

2013-01-09

Various sophisticated approximation methods exist for the description of quantum many-body systems. It was realized early on that the theoretical description can simplify considerably in one-dimensional systems and various exact solutions exist. The focus in this introductory paper is on fermionic systems and the emergence of the Luttinger liquid concept.

Sampling solution traces for the problem of sorting permutations by signed reversals

Science.gov (United States)

2012-01-01

Background Traditional algorithms to solve the problem of sorting by signed reversals output just one optimal solution while the space of all optimal solutions can be huge. A so-called trace represents a group of solutions which share the same set of reversals that must be applied to sort the original permutation following a partial ordering. By using traces, we therefore can represent the set of optimal solutions in a more compact way. Algorithms for enumerating the complete set of traces of solutions were developed. However, due to their exponential complexity, their practical use is limited to small permutations. A partial enumeration of traces is a sampling of the complete set of traces and can be an alternative for the study of distinct evolutionary scenarios of big permutations. Ideally, the sampling should be done uniformly from the space of all optimal solutions. This is however conjectured to be ♯P-complete. Results We propose and evaluate three algorithms for producing a sampling of the complete set of traces that instead can be shown in practice to preserve some of the characteristics of the space of all solutions. The first algorithm (RA) performs the construction of traces through a random selection of reversals on the list of optimal 1-sequences. The second algorithm (DFALT) consists in a slight modification of an algorithm that performs the complete enumeration of traces. Finally, the third algorithm (SWA) is based on a sliding window strategy to improve the enumeration of traces. All proposed algorithms were able to enumerate traces for permutations with up to 200 elements. Conclusions We analysed the distribution of the enumerated traces with respect to their height and average reversal length. Various works indicate that the reversal length can be an important aspect in genome rearrangements. The algorithms RA and SWA show a tendency to lose traces with high average reversal length. Such traces are however rare, and qualitatively our results

How many invariant polynomials are needed to decide local unitary equivalence of qubit states?

International Nuclear Information System (INIS)

Maciążek, Tomasz; Oszmaniec, Michał; Sawicki, Adam

2013-01-01

Given L-qubit states with the fixed spectra of reduced one-qubit density matrices, we find a formula for the minimal number of invariant polynomials needed for solving local unitary (LU) equivalence problem, that is, problem of deciding if two states can be connected by local unitary operations. Interestingly, this number is not the same for every collection of the spectra. Some spectra require less polynomials to solve LU equivalence problem than others. The result is obtained using geometric methods, i.e., by calculating the dimensions of reduced spaces, stemming from the symplectic reduction procedure

Many-body delocalization with random vector potentials

Science.gov (United States)

Cheng, Chen; Mondaini, Rubem

In this talk we present the ergodic properties of excited states in a model of interacting fermions in quasi-one dimensional chains subjected to a random vector potential. In the non-interacting limit, we show that arbitrarily small values of this complex off-diagonal disorder triggers localization for the whole spectrum; the divergence of the localization length in the single particle basis is characterized by a critical exponent ν which depends on the energy density being investigated. However, when short-ranged interactions are included, the localization is lost and the system is ergodic regardless of the magnitude of disorder in finite chains. Our numerical results suggest a delocalization scheme for arbitrary small values of interactions. This finding indicates that the standard scenario of the many-body localization cannot be obtained in a model with random gauge fields. This research is financially supported by the National Natural Science Foundation of China (NSFC) (Grant Nos. U1530401 and 11674021). RM also acknowledges support from NSFC (Grant No. 11650110441).

Quantum many-body physics in a nutshell

CERN Document Server

Shuryak, Edward

2018-01-01

This book provides an essential introduction to the physics of quantum many-body systems, which are at the heart of atomic and nuclear physics, condensed matter, and particle physics. Unlike other textbooks on the subject, it covers topics across a broad range of physical fields―phenomena as well as theoretical tools―and does so in a simple and accessible way. Edward Shuryak begins with Feynman diagrams of the quantum and statistical mechanics of a particle―in these applications, the diagrams are easy to calculate and there are no divergencies. He discusses the renormalization group and illustrates its uses and covers systems such as weakly and strongly coupled Bose and Fermi gases, electron gas, nuclear matter, and quark-gluon plasmas. Phenomena include Bose condensation and superfluidity. Shuryak also looks at Cooper pairing and superconductivity for electrons in metals, liquid 3He, nuclear matter, and quark-gluon plasma. A recurring topic throughout is topological matter, ranging from ensembles of q...

Permutation entropy and statistical complexity in characterising low-aspect-ratio reversed-field pinch plasma

International Nuclear Information System (INIS)

Onchi, T; Fujisawa, A; Sanpei, A; Himura, H; Masamune, S

2017-01-01

Permutation entropy and statistical complexity are measures for complex time series. The Bandt–Pompe methodology evaluates probability distribution using permutation. The method is robust and effective to quantify information of time series data. Statistical complexity is the product of Jensen–Shannon divergence and permutation entropy. These physical parameters are introduced to analyse time series of emission and magnetic fluctuations in low-aspect-ratio reversed-field pinch (RFP) plasma. The observed time-series data aggregates in a region of the plane, the so-called C – H plane, determined by entropy versus complexity. The C – H plane is a representation space used for distinguishing periodic, chaos, stochastic and noisy processes of time series data. The characteristics of the emissions and magnetic fluctuation change under different RFP-plasma conditions. The statistical complexities of soft x-ray emissions and magnetic fluctuations depend on the relationships between reversal and pinch parameters. (paper)

Infrared and Raman Spectroscopy of Liquid Water through "First-Principles" Many-Body Molecular Dynamics.

Science.gov (United States)

Medders, Gregory R; Paesani, Francesco

2015-03-10

Vibrational spectroscopy is a powerful technique to probe the structure and dynamics of water. However, deriving an unambiguous molecular-level interpretation of the experimental spectral features remains a challenge due to the complexity of the underlying hydrogen-bonding network. In this contribution, we present an integrated theoretical and computational framework (named many-body molecular dynamics or MB-MD) that, by systematically removing uncertainties associated with existing approaches, enables a rigorous modeling of vibrational spectra of water from quantum dynamical simulations. Specifically, we extend approaches used to model the many-body expansion of interaction energies to develop many-body representations of the dipole moment and polarizability of water. The combination of these "first-principles" representations with centroid molecular dynamics simulations enables the simulation of infrared and Raman spectra of liquid water under ambient conditions that, without relying on any ad hoc parameters, are in good agreement with the corresponding experimental results. Importantly, since the many-body energy, dipole, and polarizability surfaces employed in the simulations are derived independently from accurate fits to correlated electronic structure data, MB-MD allows for a systematic analysis of the calculated spectra in terms of both electronic and dynamical contributions. The present analysis suggests that, while MB-MD correctly reproduces both the shifts and the shapes of the main spectroscopic features, an improved description of quantum dynamical effects possibly combined with a dissociable water potential may be necessary for a quantitative representation of the OH stretch band.

Dynamical stability of a many-body Kapitza pendulum

Energy Technology Data Exchange (ETDEWEB)

Citro, Roberta, E-mail: citro@sa.infn.it [Dipartimento di Fisica “E. R. Caianiello” and Spin-CNR, Universita’ degli Studi di Salerno, Via Giovanni Paolo II, I-84084 Fisciano (Italy); Dalla Torre, Emanuele G., E-mail: emanuele.dalla-torre@biu.ac.il [Department of Physics, Bar Ilan University, Ramat Gan 5290002 (Israel); Department of Physics, Harvard University, Cambridge, MA 02138 (United States); D’Alessio, Luca [Department of Physics, The Pennsylvania State University, University Park, PA 16802 (United States); Department of Physics, Boston University, Boston, MA 02215 (United States); Polkovnikov, Anatoli [Department of Physics, Boston University, Boston, MA 02215 (United States); Babadi, Mehrtash [Department of Physics, Harvard University, Cambridge, MA 02138 (United States); Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125 (United States); Oka, Takashi [Department of Applied Physics, University of Tokyo, Tokyo, 113-8656 (Japan); Demler, Eugene [Department of Physics, Harvard University, Cambridge, MA 02138 (United States)

2015-09-15

We consider a many-body generalization of the Kapitza pendulum: the periodically-driven sine–Gordon model. We show that this interacting system is dynamically stable to periodic drives with finite frequency and amplitude. This finding is in contrast to the common belief that periodically-driven unbounded interacting systems should always tend to an absorbing infinite-temperature state. The transition to an unstable absorbing state is described by a change in the sign of the kinetic term in the Floquet Hamiltonian and controlled by the short-wavelength degrees of freedom. We investigate the stability phase diagram through an analytic high-frequency expansion, a self-consistent variational approach, and a numeric semiclassical calculation. Classical and quantum experiments are proposed to verify the validity of our results.

Another New Solvable Many-Body Model of Goldfish Type

Directory of Open Access Journals (Sweden)

Francesco Calogero

2012-07-01

Full Text Available A new solvable many-body problem is identified. It is characterized by nonlinear Newtonian equations of motion (''acceleration equal force'' featuring one-body and two-body velocity-dependent forces ''of goldfish type'' which determine the motion ofan arbitrary number $N$ of unit-mass point-particles in a plane. The $N$ (generally complex values $z_{n}(t$ at time $t$ ofthe $N$ coordinates of these moving particles are given by the $N$eigenvalues of a time-dependent $Nimes N$ matrix $U(t$explicitly known in terms of the $2N$ initial data $z_{n}(0$and $dot{z}_{n}(0 $. This model comes in two dif/ferentvariants, one featuring 3 arbitrary coupling constants, the other only 2; for special values of these parameters all solutions are completely periodic with the same period independent of the initial data (''isochrony''; for other special values of these parameters this property holds up to corrections vanishing exponentially as $tightarrow infty$ (''asymptotic isochrony''. Other isochronous variants of these models are also reported. Alternative formulations, obtained by changing the dependent variables from the $N$ zeros of a monic polynomial of degree $N$ to its $N$ coefficients, are also exhibited. Some mathematical findings implied by some of these results - such as Diophantine properties of the zeros of certain polynomials - are outlined, but their analysis is postponed to a separate paper.

The many-body content of quantum gauge theories and its connection to mass generation mechanisms

International Nuclear Information System (INIS)

Natoli, C.R.; Palumbo, F.

1985-01-01

The aim of the paper is to get more knowledge about many-body systems and their properties, about many-body content of quantum gauge theories and its connection with mass generation mechanisms. The way to achieve this is to perform the galilean limit of the relativistic theory by sending the speed of light c to infinity. This limiting process exposes the low energy behaviour of the relativistic theory

A discriminative syntactic model for source permutation via tree transduction

NARCIS (Netherlands)

Khalilov, M.; Sima'an, K.; Wu, D.

2010-01-01

A major challenge in statistical machine translation is mitigating the word order differences between source and target strings. While reordering and lexical translation choices are often conducted in tandem, source string permutation prior to translation is attractive for studying reordering using

Students' Errors in Solving the Permutation and Combination Problems Based on Problem Solving Steps of Polya

Science.gov (United States)

Sukoriyanto; Nusantara, Toto; Subanji; Chandra, Tjang Daniel

2016-01-01

This article was written based on the results of a study evaluating students' errors in problem solving of permutation and combination in terms of problem solving steps according to Polya. Twenty-five students were asked to do four problems related to permutation and combination. The research results showed that the students still did a mistake in…

Computational nuclear quantum many-body problem: The UNEDF project

Science.gov (United States)

Bogner, S.; Bulgac, A.; Carlson, J.; Engel, J.; Fann, G.; Furnstahl, R. J.; Gandolfi, S.; Hagen, G.; Horoi, M.; Johnson, C.; Kortelainen, M.; Lusk, E.; Maris, P.; Nam, H.; Navratil, P.; Nazarewicz, W.; Ng, E.; Nobre, G. P. A.; Ormand, E.; Papenbrock, T.; Pei, J.; Pieper, S. C.; Quaglioni, S.; Roche, K. J.; Sarich, J.; Schunck, N.; Sosonkina, M.; Terasaki, J.; Thompson, I.; Vary, J. P.; Wild, S. M.

2013-10-01

The UNEDF project was a large-scale collaborative effort that applied high-performance computing to the nuclear quantum many-body problem. The primary focus of the project was on constructing, validating, and applying an optimized nuclear energy density functional, which entailed a wide range of pioneering developments in microscopic nuclear structure and reactions, algorithms, high-performance computing, and uncertainty quantification. UNEDF demonstrated that close associations among nuclear physicists, mathematicians, and computer scientists can lead to novel physics outcomes built on algorithmic innovations and computational developments. This review showcases a wide range of UNEDF science results to illustrate this interplay.

Many-Body Potentials For Binary Immiscible liquid Metal Alloys

International Nuclear Information System (INIS)

Karaguelle, H.

2004-01-01

The modified analytic embedded atom method (MAEAM) type many- body potentials have been constructed for three binary liquid immiscible alloy systems: Al-Pb, Ag-Ni, Ag- Cu. The MAEAM potential functions are fitted to both solid and liquid state properties for only liquid pure metals which consist the immiscible alloy. In order to test the reliability of the constructed MAEAM effective potentials, partial structure factors and pair distribution functions of these binary liquid metal alloys have been calculated using the thermodynamically self-consistent variational modified hypernetted chain (VMHNC) theory of liquids. A good agreement with the available experimental data for structure has

From Discrete Breathers to Many Body Localization and Flatbands

Science.gov (United States)

Flach, Sergej

Discrete breathers (DB) and intrinsic localized modes (ILM) are synonymic dynamical states on nonlinear lattices - periodic in time and localized in space, and widely observed in many applications. I will discuss the connections between DBs and many-body localization (MBL) and the properties of DBs on flatband networks. A dense quantized gas of strongly excited DBs can lead to a MBL phase in a variety of different lattice models. Its classical counterpart corresponds to a 'nonergodic metal' in the MBL language, or to a nonGibbsean selftrapped state in the language of nonlinear dynamics. Flatband networks are lattices with small amplitude waves exhibiting macroscopic degeneracy in their band structure due to local symmetries, destructive interference, compact localized eigenstates and horizontal flat bands. DBs can preserve the compactness of localization in the presence of nonlinearity with properly tuned internal phase relationships, making them promising tools for control of the phase coherence of waves. Also at New Zealand Institute of Advanced Study, Massey University, Auckland, New Zealand.

Psychometric evaluation and sex invariance of the Spanish version of the Body and Appearance Self-Conscious Emotions Scale.

Science.gov (United States)

Alcaraz-Ibáñez, Manuel; Sicilia, Alvaro

2018-06-01

This study examined the psychometric properties of a Spanish translation of the Body and Appearance Self-Conscious Emotions Scale (BASES; Castonguay et al., 2014) in a sample of university Spanish students. A total of 815 participants enrolled in two public universities located in Almería and Elche, Spain, completed the BASES along with measures of social physique anxiety and positive/negative affect. Exploratory and confirmatory factor analyses showed that one item failed to load clearly on the hypothesized factor (guilt). Once it was removed, results supported the hypothesized four-factor structure. Evidence of invariance of the four-factor structure across sex was obtained. Scores on the BASES showed adequate internal consistency and acceptable convergent validity. Compared to men, women reported significantly higher body and appearance-related guilt and shame, and significant lower authentic and hubristic pride. Preliminary evidence supporting the validity and reliability of the Spanish translation of the BASES is provided. Copyright © 2018 Elsevier Ltd. All rights reserved.

Convex bodies with many elliptic sections

OpenAIRE

Arelio, Isaac; Montejano, Luis

2014-01-01

{We show in this paper that two normal elliptic sections through every point of the boundary of a smooth convex body essentially characterize an ellipsoid and furthermore, that four different pairwise non-tangent elliptic sections through every point of the $C^2$-differentiable boundary of a convex body also essentially characterize an ellipsoid.

Determinant method and quantum simulations of many-body effects in a single impurity Anderson model

International Nuclear Information System (INIS)

Gubernatis, J.E.; Olson, T.; Scalapino, D.J.; Sugar, R.L.

1985-01-01

A short description is presented of a quantum Monte Carlo technique, often referred to as the determinant method, that has proved useful for simulating many-body effects in systems of interacting fermions at finite temperatures. Preliminary results using this technique on a single impurity Anderson model are reported. Examples of such many-body effects as local moment formation, Kondo behavior, and mixed valence phenomena found in the simulations are shown. 10 refs., 3 figs

A studentized permutation test for three-arm trials in the 'gold standard' design.

Science.gov (United States)

Mütze, Tobias; Konietschke, Frank; Munk, Axel; Friede, Tim

2017-03-15

The 'gold standard' design for three-arm trials refers to trials with an active control and a placebo control in addition to the experimental treatment group. This trial design is recommended when being ethically justifiable and it allows the simultaneous comparison of experimental treatment, active control, and placebo. Parametric testing methods have been studied plentifully over the past years. However, these methods often tend to be liberal or conservative when distributional assumptions are not met particularly with small sample sizes. In this article, we introduce a studentized permutation test for testing non-inferiority and superiority of the experimental treatment compared with the active control in three-arm trials in the 'gold standard' design. The performance of the studentized permutation test for finite sample sizes is assessed in a Monte Carlo simulation study under various parameter constellations. Emphasis is put on whether the studentized permutation test meets the target significance level. For comparison purposes, commonly used Wald-type tests, which do not make any distributional assumptions, are included in the simulation study. The simulation study shows that the presented studentized permutation test for assessing non-inferiority in three-arm trials in the 'gold standard' design outperforms its competitors, for instance the test based on a quasi-Poisson model, for count data. The methods discussed in this paper are implemented in the R package ThreeArmedTrials which is available on the comprehensive R archive network (CRAN). Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Magic informationally complete POVMs with permutations

Science.gov (United States)

Planat, Michel; Gedik, Zafer

2017-09-01

Eigenstates of permutation gates are either stabilizer states (for gates in the Pauli group) or magic states, thus allowing universal quantum computation (Planat, Rukhsan-Ul-Haq 2017 Adv. Math. Phys. 2017, 5287862 (doi:10.1155/2017/5287862)). We show in this paper that a subset of such magic states, when acting on the generalized Pauli group, define (asymmetric) informationally complete POVMs. Such informationally complete POVMs, investigated in dimensions 2-12, exhibit simple finite geometries in their projector products and, for dimensions 4 and 8 and 9, relate to two-qubit, three-qubit and two-qutrit contextuality.

Morphology of Laplacian growth processes and statistics of equivalent many-body systems

International Nuclear Information System (INIS)

Blumenfeld, R.

1994-01-01

The authors proposes a theory for the nonlinear evolution of two dimensional interfaces in Laplacian fields. The growing region is conformally mapped onto the unit disk, generating an equivalent many-body system whose dynamics and statistics are studied. The process is shown to be Hamiltonian, with the Hamiltonian being the imaginary part of the complex electrostatic potential. Surface effects are introduced through the Hamiltonian as an external field. An extension to a continuous density of particles is presented. The results are used to study the morphology of the interface using statistical mechanics for the many-body system. The distribution of the curvature and the moments of the growth probability along the interface are calculated exactly from the distribution of the particles. In the dilute limit, the distribution of the curvature is shown to develop algebraic tails, which may, for the first time, explain the origin of fractality in diffusion controlled processes

Brain Computation Is Organized via Power-of-Two-Based Permutation Logic

Science.gov (United States)

Xie, Kun; Fox, Grace E.; Liu, Jun; Lyu, Cheng; Lee, Jason C.; Kuang, Hui; Jacobs, Stephanie; Li, Meng; Liu, Tianming; Song, Sen; Tsien, Joe Z.

2016-01-01

There is considerable scientific interest in understanding how cell assemblies—the long-presumed computational motif—are organized so that the brain can generate intelligent cognition and flexible behavior. The Theory of Connectivity proposes that the origin of intelligence is rooted in a power-of-two-based permutation logic (N = 2i–1), producing specific-to-general cell-assembly architecture capable of generating specific perceptions and memories, as well as generalized knowledge and flexible actions. We show that this power-of-two-based permutation logic is widely used in cortical and subcortical circuits across animal species and is conserved for the processing of a variety of cognitive modalities including appetitive, emotional and social information. However, modulatory neurons, such as dopaminergic (DA) neurons, use a simpler logic despite their distinct subtypes. Interestingly, this specific-to-general permutation logic remained largely intact although NMDA receptors—the synaptic switch for learning and memory—were deleted throughout adulthood, suggesting that the logic is developmentally pre-configured. Moreover, this computational logic is implemented in the cortex via combining a random-connectivity strategy in superficial layers 2/3 with nonrandom organizations in deep layers 5/6. This randomness of layers 2/3 cliques—which preferentially encode specific and low-combinatorial features and project inter-cortically—is ideal for maximizing cross-modality novel pattern-extraction, pattern-discrimination and pattern-categorization using sparse code, consequently explaining why it requires hippocampal offline-consolidation. In contrast, the nonrandomness in layers 5/6—which consists of few specific cliques but a higher portion of more general cliques projecting mostly to subcortical systems—is ideal for feedback-control of motivation, emotion, consciousness and behaviors. These observations suggest that the brain’s basic computational

Accurate first principles calculation of many-body interactions

International Nuclear Information System (INIS)

Tawa, G.J.; Moskowitz, J.W.; Schmidt, K.E.

1991-01-01

This paper reports on the electronic structure Schrodinger equation that is solved for the van der Waals complexes spin-polarized H 2 and H 3 , and the closed-shell systems He 2 and He 3 by Monte Carlo methods. Two types of calculations are performed, variational Monte Carlo, which gives an upper bound to the eigenvalue of the Schrodinger equation, and Green's function Monte Carlo, which can solve the Schrodinger equation exactly within statistical sampling errors. The simulations are carried out on an ETA-10 supercomputer, and already existing computer codes were extensively modified to ensure highly efficient coding. A major component of the computations was the development of highly optimized many-electron wave functions. The results from the variational Monte Carlo simulations are reported for both the two- and three-body interaction energies

Many-body physics with alkaline-earth Rydberg lattices

Energy Technology Data Exchange (ETDEWEB)

Mukherjee, R; Nath, R; Pohl, T [Max Planck Institute for the Physics of Complex Systems, Noethnitzer Strasse 38, 01187 Dresden (Germany); Millen, J; Jones, M P A, E-mail: rick@pks.mpg.de [Department of Physics, Durham University, Durham DH1 3LE (United Kingdom)

2011-09-28

We explore the prospects for confining alkaline-earth Rydberg atoms in an optical lattice via optical dressing of the secondary core-valence electron. Focussing on the particular case of strontium, we identify experimentally accessible magic wavelengths for simultaneous trapping of ground and Rydberg states. A detailed analysis of relevant loss mechanisms shows that the overall lifetime of such a system is limited only by the spontaneous decay of the Rydberg state, and is not significantly affected by photoionization or autoionization. The van der Waals C{sub 6} coefficients for the Sr(5sns {sup 1}S{sub 0}) Rydberg series are calculated, and we find that the interactions are attractive. Finally we show that the combination of magic-wavelength lattices and attractive interactions could be exploited to generate many-body Greenberger-Horne-Zeilinger states.

Rank-based permutation approaches for non-parametric factorial designs.

Science.gov (United States)

Umlauft, Maria; Konietschke, Frank; Pauly, Markus

2017-11-01

Inference methods for null hypotheses formulated in terms of distribution functions in general non-parametric factorial designs are studied. The methods can be applied to continuous, ordinal or even ordered categorical data in a unified way, and are based only on ranks. In this set-up Wald-type statistics and ANOVA-type statistics are the current state of the art. The first method is asymptotically exact but a rather liberal statistical testing procedure for small to moderate sample size, while the latter is only an approximation which does not possess the correct asymptotic α level under the null. To bridge these gaps, a novel permutation approach is proposed which can be seen as a flexible generalization of the Kruskal-Wallis test to all kinds of factorial designs with independent observations. It is proven that the permutation principle is asymptotically correct while keeping its finite exactness property when data are exchangeable. The results of extensive simulation studies foster these theoretical findings. A real data set exemplifies its applicability. © 2017 The British Psychological Society.

Rolling Bearing Fault Diagnosis Based on ELCD Permutation Entropy and RVM

Directory of Open Access Journals (Sweden)

Jiang Xingmeng

2016-01-01

Full Text Available Aiming at the nonstationary characteristic of a gear fault vibration signal, a recognition method based on permutation entropy of ensemble local characteristic-scale decomposition (ELCD and relevance vector machine (RVM is proposed. First, the vibration signal was decomposed by ELCD; then a series of intrinsic scale components (ISCs were obtained. Second, according to the kurtosis of ISCs, principal ISCs were selected and then the permutation entropy of principal ISCs was calculated and they were combined into a feature vector. Finally, the feature vectors were input in RVM classifier to train and test and identify the type of rolling bearing faults. Experimental results show that this method can effectively diagnose four kinds of working condition, and the effect is better than local characteristic-scale decomposition (LCD method.

Petascale Many Body Methods for Complex Correlated Systems

Science.gov (United States)

Pruschke, Thomas

2012-02-01

Correlated systems constitute an important class of materials in modern condensed matter physics. Correlation among electrons are at the heart of all ordering phenomena and many intriguing novel aspects, such as quantum phase transitions or topological insulators, observed in a variety of compounds. Yet, theoretically describing these phenomena is still a formidable task, even if one restricts the models used to the smallest possible set of degrees of freedom. Here, modern computer architectures play an essential role, and the joint effort to devise efficient algorithms and implement them on state-of-the art hardware has become an extremely active field in condensed-matter research. To tackle this task single-handed is quite obviously not possible. The NSF-OISE funded PIRE collaboration ``Graduate Education and Research in Petascale Many Body Methods for Complex Correlated Systems'' is a successful initiative to bring together leading experts around the world to form a virtual international organization for addressing these emerging challenges and educate the next generation of computational condensed matter physicists. The collaboration includes research groups developing novel theoretical tools to reliably and systematically study correlated solids, experts in efficient computational algorithms needed to solve the emerging equations, and those able to use modern heterogeneous computer architectures to make then working tools for the growing community.

Tolerance of a knotted near infrared fluorescent protein to random circular permutation

Science.gov (United States)

Pandey, Naresh; Kuypers, Brianna E.; Nassif, Barbara; Thomas, Emily E.; Alnahhas, Razan N.; Segatori, Laura; Silberg, Jonathan J.

2016-01-01

Bacteriophytochrome photoreceptors (BphP) are knotted proteins that have been developed as near-infrared fluorescent protein (iRFP) reporters of gene expression. To explore how rearrangements in the peptides that interlace into the knot within the BphP photosensory core affect folding, we subjected iRFP to random circular permutation using an improved transposase mutagenesis strategy and screened for variants that fluoresce. We identified twenty seven circularly permuted iRFP that display biliverdin-dependent fluorescence in Escherichia coli. The variants with the brightest whole cell fluorescence initiated translation at residues near the domain linker and knot tails, although fluorescent variants were discovered that initiated translation within the PAS and GAF domains. Circularly permuted iRFP retained sufficient cofactor affinity to fluoresce in tissue culture without the addition of biliverdin, and one variant displayed enhanced fluorescence when expressed in bacteria and tissue culture. This variant displayed a similar quantum yield as iRFP, but exhibited increased resistance to chemical denaturation, suggesting that the observed signal increase arose from more efficient protein maturation. These results show how the contact order of a knotted BphP can be altered without disrupting chromophore binding and fluorescence, an important step towards the creation of near-infrared biosensors with expanded chemical-sensing functions for in vivo imaging. PMID:27304983

Equilibrium and nonequilibrium many-body perturbation theory: a unified framework based on the Martin-Schwinger hierarchy

International Nuclear Information System (INIS)

Van Leeuwen, Robert; Stefanucci, Gianluca

2013-01-01

We present a unified framework for equilibrium and nonequilibrium many-body perturbation theory. The most general nonequilibrium many-body theory valid for general initial states is based on a time-contour originally introduced by Konstantinov and Perel'. The various other well-known formalisms of Keldysh, Matsubara and the zero-temperature formalism are then derived as special cases that arise under different assumptions. We further present a single simple proof of Wick's theorem that is at the same time valid in all these flavors of many-body theory. It arises simply as a solution of the equations of the Martin-Schwinger hierarchy for the noninteracting many-particle Green's function with appropriate boundary conditions. We further discuss a generalized Wick theorem for general initial states on the Keldysh contour and derive how the formalisms based on the Keldysh and Konstantinov-Perel'-contours are related for the case of general initial states.

Neural network models: from biology to many - body phenomenology

International Nuclear Information System (INIS)

Clark, J.W.

1993-01-01

Theoretical work in neural networks has a strange feel for most physicists. In some cases the aspect of design becomes paramount. More comfortable ground at least for many body theorists may be found in realistic biological simulation, although the complexity of most problems is so awesome that incisive results will be hard won. It has also shown the impressive capabilities of artificial networks in pattern recognition and classification may be exploited to solve management problems in experimental physics and for discovery of radically new theoretical description of physical systems. This advance represents an important step towards the ultimate goal of neuro biological paradigm. (A.B.)

Density functional and many-body theories of Hydrogen plasmas

International Nuclear Information System (INIS)

Perrot, F.; Dharma-Wardana, M.W.C.

1983-11-01

This work is an attempt to go beyond the standard description of hot condensed matter using the well-known ''average atom model''. The first part describes a static model using ''Density functional theory'' to calculate self-consistent coupled electron and ion density profiles of the plasma not restricted to a single average atomic sphere. In a second part, the results are used as ingredients for a many-body approach to electronic properties: the one-particle Green-function self-energy is calculated, from which shifted levels, populations and level-widths are deduced. Results for the Hydrogen plasma are reported, with emphasis on the 1s bound state

Many-body dynamics of driven-dissipative Rydberg cavity polaritons

Science.gov (United States)

Pistorius, Tim; Fan, Jingtao; Weimer, Hendrik

2017-04-01

The usage of photons as long-range information carriers has greatly increased the interest in systems with nonlinear optical properties in recent years. The nonlinearity is easily achievable in Rydberg mediums through the strong van der Waals interaction which makes them one of the best candidates for such a system. Here, we propose a way to analyze the steady state solutions of a Rydberg medium in a cavity through the combination of the variational principle for open quantum systems and the P-distribution of the density matrix. To get a better understanding of the many-body-dynamics a transformation into the polariton picture is performed and investigated. Volkswagen Foundation, Deutsche Forschungsgemeinschaft.

Dynamics of many-body localization in the presence of particle loss

Science.gov (United States)

van Nieuwenburg, EPL; Yago Malo, J.; Daley, AJ; Fischer, MH

2018-01-01

At long times, residual couplings to the environment become relevant even in the most isolated experiments, a crucial difficulty for the study of fundamental aspects of many-body dynamics. A particular example is many-body localization in a cold-atom setting, where incoherent photon scattering introduces both dephasing and particle loss. Whereas dephasing has been studied in detail and is known to destroy localization already on the level of non-interacting particles, the effect of particle loss is less well understood. A difficulty arises due to the ‘non-local’ nature of the loss process, complicating standard numerical tools using matrix product decomposition. Utilizing symmetries of the Lindbladian dynamics, we investigate the particle loss on both the dynamics of observables, as well as the structure of the density matrix and the individual states. We find that particle loss in the presence of interactions leads to dissipation and a strong suppression of the (operator space) entanglement entropy. Our approach allows for the study of the interplay of dephasing and loss for pure and mixed initial states to long times, which is important for future experiments using controlled coupling of the environment.

Computational invariant theory

CERN Document Server

Derksen, Harm

2015-01-01

This book is about the computational aspects of invariant theory. Of central interest is the question how the invariant ring of a given group action can be calculated. Algorithms for this purpose form the main pillars around which the book is built. There are two introductory chapters, one on Gröbner basis methods and one on the basic concepts of invariant theory, which prepare the ground for the algorithms. Then algorithms for computing invariants of finite and reductive groups are discussed. Particular emphasis lies on interrelations between structural properties of invariant rings and computational methods. Finally, the book contains a chapter on applications of invariant theory, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision. The book is intended for postgraduate students as well as researchers in geometry, computer algebra, and, of course, invariant theory. The text is enriched with numerous explicit examples which illustrate the theory and should be ...

Nuclear collision theory with many-body correlations, 2

International Nuclear Information System (INIS)

Kurihara, Yukio.

1984-12-01

A nuclear collision theory, in which the many-body correlation induced by the strong short-ranged repulsion and medium-ranged attraction of the realistic NN interaction is explicitly included, is applied to the deuteron+deuteron elastic scattering at low energies. Pair correlation functions calculated by the present theory are very different from the Hackenbroich et al. 's one. They contain not only the short-ranged suppressive correlation, but also the medium-ranged enhancing correlation. The former changes the shape of the d-d potential from the wine-bottle one. And the latter makes the d-d potential much more attractive. This effect is necessary for reproducing a bump around thatesub(cm)=90 0 in the experimental elastic differential cross section. The phase shifts evaluated by the present theory are compared with those from the resonating-group method. (author)

Invariance as a Tool for Ontology of Information

Directory of Open Access Journals (Sweden)

Marcin J. Schroeder

2016-03-01

Full Text Available Attempts to answer questions regarding the ontological status of information are frequently based on the assumption that information should be placed within an already existing framework of concepts of established ontological statuses related to science, in particular to physics. However, many concepts of physics have undetermined or questionable ontological foundations. We can look for a solution in the recognition of the fundamental role of invariance with respect to a change of reference frame and to other transformations as a criterion for objective existence. The importance of invariance (symmetry as a criterion for a primary ontological status can be identified in the methodology of physics from its beginnings in the work of Galileo, to modern classifications of elementary particles. Thus, the study of the invariance of the theoretical description of information is proposed as the first step towards ontology of information. With the exception of only a few works among publications which set the paradigm of information studies, the issues of invariance were neglected. Orthodox analysis of information lacks conceptual framework for the study of invariance. The present paper shows how invariance can be formalized for the definition of information and, accompanying it, mathematical formalism proposed by the author in his earlier publications.

Relativistic Dirac-Fock and many-body perturbation calculations on He, He-like ions, Ne, and Ar

International Nuclear Information System (INIS)

Ishikawa, Y.

1990-01-01

Relativistic Dirac-Fock and diagrammatic many-body perturbation-theory calculations have been performed on He, several He-like ions, Ne, and Ar. The no-pair Dirac-Coulomb Hamiltonian is taken as the starting point. A solution of the Dirac-Fock equations is obtained by analytic expansion in basis sets of Gaussian-type functions. Many-body perturbation improvements of Coulomb correlation are done to third order

Ultracold atoms in optical lattices simulating quantum many-body systems

CERN Document Server

Lewenstein, Maciej; Ahufinger, Verònica

2012-01-01

Quantum computers, though not yet available on the market, will revolutionize the future of information processing. Quantum computers for special purposes like quantum simulators are already within reach. The physics of ultracold atoms, ions and molecules offer unprecedented possibilities of control of quantum many body systems and novel possibilities of applications to quantum information processing and quantum metrology. Particularly fascinating is the possibility of usingultracold atoms in lattices to simulate condensed matter or even high energy physics.This book provides a complete and co

Invariant submanifold flows

Energy Technology Data Exchange (ETDEWEB)

Olver, Peter J [School of Mathematics, University of Minnesota, Minneapolis, MN 55455 (United States)], E-mail: olver@math.umn.edu

2008-08-29

Given a Lie group acting on a manifold, our aim is to analyze the evolution of differential invariants under invariant submanifold flows. The constructions are based on the equivariant method of moving frames and the induced invariant variational bicomplex. Applications to integrable soliton dynamics, and to the evolution of differential invariant signatures, used in equivalence problems and object recognition and symmetry detection in images, are discussed.

Determining the parity of a permutation using an experimental NMR qutrit

International Nuclear Information System (INIS)

Dogra, Shruti; Arvind,; Dorai, Kavita

2014-01-01

We present the NMR implementation of a recently proposed quantum algorithm to find the parity of a permutation. In the usual qubit model of quantum computation, it is widely believed that computational speedup requires the presence of entanglement and thus cannot be achieved by a single qubit. On the other hand, a qutrit is qualitatively more quantum than a qubit because of the existence of quantum contextuality and a single qutrit can be used for computing. We use the deuterium nucleus oriented in a liquid crystal as the experimental qutrit. This is the first experimental exploitation of a single qutrit to carry out a computational task. - Highlights: • NMR implementation of a quantum algorithm to determine the parity of a permutation. • Algorithm implemented on a single qutrit. • Computational speedup achieved without quantum entanglement. • Single qutrit shows quantum contextuality

Permutation Entropy for Random Binary Sequences

Directory of Open Access Journals (Sweden)

Lingfeng Liu

2015-12-01

Full Text Available In this paper, we generalize the permutation entropy (PE measure to binary sequences, which is based on Shannon’s entropy, and theoretically analyze this measure for random binary sequences. We deduce the theoretical value of PE for random binary sequences, which can be used to measure the randomness of binary sequences. We also reveal the relationship between this PE measure with other randomness measures, such as Shannon’s entropy and Lempel–Ziv complexity. The results show that PE is consistent with these two measures. Furthermore, we use PE as one of the randomness measures to evaluate the randomness of chaotic binary sequences.

PREFACE: Advanced many-body and statistical methods in mesoscopic systems

Science.gov (United States)

Anghel, Dragos Victor; Sabin Delion, Doru; Sorin Paraoanu, Gheorghe

2012-02-01

It has increasingly been realized in recent times that the borders separating various subfields of physics are largely artificial. This is the case for nanoscale physics, physics of lower-dimensional systems and nuclear physics, where the advanced techniques of many-body theory developed in recent times could provide a unifying framework for these disciplines under the general name of mesoscopic physics. Other fields, such as quantum optics and quantum information, are increasingly using related methods. The 6-day conference 'Advanced many-body and statistical methods in mesoscopic systems' that took place in Constanta, Romania, between 27 June and 2 July 2011 was, we believe, a successful attempt at bridging an impressive list of topical research areas: foundations of quantum physics, equilibrium and non-equilibrium quantum statistics/fractional statistics, quantum transport, phases and phase transitions in mesoscopic systems/superfluidity and superconductivity, quantum electromechanical systems, quantum dissipation, dephasing, noise and decoherence, quantum information, spin systems and their dynamics, fundamental symmetries in mesoscopic systems, phase transitions, exactly solvable methods for mesoscopic systems, various extension of the random phase approximation, open quantum systems, clustering, decay and fission modes and systematic versus random behaviour of nuclear spectra. This event brought together participants from seventeen countries and five continents. Each of the participants brought considerable expertise in his/her field of research and, at the same time, was exposed to the newest results and methods coming from the other, seemingly remote, disciplines. The talks touched on subjects that are at the forefront of topical research areas and we hope that the resulting cross-fertilization of ideas will lead to new, interesting results from which everybody will benefit. We are grateful for the financial and organizational support from IFIN-HH, Ovidius

Many-body pairing in a two-dimensional Fermi gas

Energy Technology Data Exchange (ETDEWEB)

Neidig, Mathias

2017-05-24

This thesis reports on experiments conducted in a single layer, quasi two-dimensional, two-component ultracold Fermi gas in the strongly interacting regime. Ultracold gases can be used to simulate key aspects of more complicated systems like for example cuprates which show high-T{sub c} superconductivity. The momentum distribution of a sample of bosonic dimers in a quasi-2D square lattice geometry was measured to obtain the coherence properties. For shallow lattices, sharp peaks in the momentum distribution, indicating coherence, were observed at zero momentum as well as at positive and negative lattice momenta along each axis. For deeper lattices, heating impeded the ability to prepare a Mott-insulator. A spatially resolved radio-frequency spectroscopy was employed for a quasi-2D Fermi gas in the normal phase throughout the BEC-BCS crossover. The interaction induced energy shifts were measured in the strongly interacting region where they can be on the order of the Fermi energy and thus the local resolution is crucial. Furthermore, the onset of pairing in the strongly interacting region was measured as a function of temperature and it was shown that the fraction of free atoms decreases faster than expected from thermal non-interacting theory. At last, the pairing gap was measured using an imbalanced sample. On the BEC side it was found to be in very good agreement with two-body physics as expected. In the strongly interacting regime, however, a deviation from two-body physics indicates that here many-body effects play a role and thus further studies are required.

Workshop on Kadanoff-Baym Equations : Progress and Perspectives for Many-Body Physics

CERN Document Server

2000-01-01

Equilibrium and nonequilibrium properties of correlated many-body systems are of growing interest in many fields of physics, including condensed matter, dense plasmas, nuclear matter and particles. The most powerful and general method which applies equally to all these areas is given by quantum field theory.Written by the leading experts and understandable to non-specialists, this book provides an overview on the basic ideas and concepts of the method of nonequilibrium Green's functions. It is complemented by modern applications of the method to a variety of topics, such as optics and transpor

Permutation 2-groups I: structure and splitness

OpenAIRE

Elgueta, Josep

2013-01-01

By a 2-group we mean a groupoid equipped with a weakened group structure. It is called split when it is equivalent to the semidirect product of a discrete 2-group and a one-object 2-group. By a permutation 2-group we mean the 2-group $\\mathbb{S}ym(\\mathcal{G})$ of self-equivalences of a groupoid $\\mathcal{G}$ and natural isomorphisms between them, with the product given by composition of self-equivalences. These generalize the symmetric groups $\\mathsf{S}_n$, $n\\geq 1$, obtained when $\\mathca...

Neural network models: from biology to many - body phenomenology

International Nuclear Information System (INIS)

Clark, J.W.

1993-01-01

The current surge of research on practical side of neural networks and their utility in memory storage/recall, pattern recognition and classification is given in this article. The initial attraction of neural networks as dynamical and statistical system has been investigated. From the view of many-body theorist, the neurons may be thought of as particles, and the weighted connection between the units, as the interaction between these particles. Finally, the author has seen the impressive capabilities of artificial neural networks in pattern recognition and classification may be exploited to solve data management problems in experimental physics and the discovery of radically new theoretically description of physical problems and neural networks can be used in physics. (A.B.)

Theoretical approaches to many-body perturbation theory and the challenges

International Nuclear Information System (INIS)

Barrett, Bruce R

2005-01-01

A brief review of the history of many-body perturbation theory (MBPT) and its applications in nuclear physics is given. Problems regarding its application to nuclear-structure calculations are discussed and analysed. It is concluded that the usefulness of nuclear MBPT in terms of an expansion in the nuclear reaction matrix G for the calculation of effective interactions in shell-model investigations is severely challenged and restricted by the problems and uncertainties connected with this approach. New methods based on unitary transformation approaches have proven to be more accurate and reliable, particularly for light nuclei

Universality in driven-dissipative quantum many-body systems

International Nuclear Information System (INIS)

Sieberer, L.M.

2015-01-01

Recent experimental investigations of condensation phenomena in driven-dissipative quantum many-body systems raise the question of what kind of novel universal behavior can emerge under non-equilibrium conditions. We explore various aspects of universality in this context. Our results are of relevance for a variety of open quantum systems on the interface of quantum optics and condensed matter physics, ranging from exciton-polariton condensates to cold atomic gases. In Part I we characterize the dynamical critical behavior at the Bose-Einstein condensation phase transition in driven open quantum systems in three spatial dimensions. Although thermodynamic equilibrium conditions are emergent at low frequencies, the approach to this thermalized low-frequency regime is described by a critical exponent which is specific to the non-equilibrium transition, and places the latter beyond the standard classification of equilibrium dynamical critical behavior. Our theoretical approach is based on the functional renormalization group within the framework of Keldysh non-equilibrium field theory, which is equivalent to a microscopic description of the open system dynamics in terms of a many-body quantum master equation. Universal behavior in the coherence properties of driven-dissipative condensates in reduced dimensions is investigated in Part II. We show that driven two-dimensional Bose systems cannot exhibit algebraic order as in thermodynamic equilibrium, unless they are sufficiently anisotropic. However, we find evidence that even isotropic systems may have a finite superfluidity fraction. In one-dimensional systems, non-equilibrium conditions are traceable in the behavior of the autocorrelation function. We obtain these results by mapping the long-wavelength condensate dynamics onto the Kardar-Parisi-Zhang equation. In Part III we show that systems in thermodynamic equilibrium have a specific symmetry, which makes them distinct from generic driven open systems. The novel

On the basis of molecular orbitals for relativistic bound systems of many bodies

International Nuclear Information System (INIS)

Cook, A.H.

1987-09-01

The quasi-relativistic Hamiltonian for bound states of many bodies proposed in previous articles (Cook, 1986, 1987a) is shown to provide a basis for the molecular orbital scheme of constructing wavefunctions and calculating eigenenergies. (author). 5 refs

Classical and quantum simulations of many-body systems

International Nuclear Information System (INIS)

Murg, Valentin

2008-01-01

This thesis is devoted to recent developments in the fields of classical and quantum simulations of many-body systems. We describe new classical algorithms that overcome problems apparent in conventional renormalization group and Monte Carlo methods. These algorithms make possible the detailed study of finite temperature properties of 2-D classical and 1-D quantum systems, the investigation of ground states of 2-D frustrated or fermionic systems and the analysis of time evolutions of 2-D quantum systems. Furthermore, we propose new ''analog'' quantum simulators that are able to realize interesting models such as a Tonks-Girardeau gas or a frustrated spin-1/2 XY model on a trigonal lattice. These quantum simulators make use of optical lattices and trapped ions and are technically feasible. In fact, the Tonks-Girardeau gas has been realized experimentally and we provide a detailed comparison between the experimental data and the theoretical predictions. (orig.)

Experimental statistical signature of many-body quantum interference

Science.gov (United States)

Giordani, Taira; Flamini, Fulvio; Pompili, Matteo; Viggianiello, Niko; Spagnolo, Nicolò; Crespi, Andrea; Osellame, Roberto; Wiebe, Nathan; Walschaers, Mattia; Buchleitner, Andreas; Sciarrino, Fabio

2018-03-01

Multi-particle interference is an essential ingredient for fundamental quantum mechanics phenomena and for quantum information processing to provide a computational advantage, as recently emphasized by boson sampling experiments. Hence, developing a reliable and efficient technique to witness its presence is pivotal in achieving the practical implementation of quantum technologies. Here, we experimentally identify genuine many-body quantum interference via a recent efficient protocol, which exploits statistical signatures at the output of a multimode quantum device. We successfully apply the test to validate three-photon experiments in an integrated photonic circuit, providing an extensive analysis on the resources required to perform it. Moreover, drawing upon established techniques of machine learning, we show how such tools help to identify the—a priori unknown—optimal features to witness these signatures. Our results provide evidence on the efficacy and feasibility of the method, paving the way for its adoption in large-scale implementations.

Convergence and Consistency Analysis for A 3D Invariant-EKF SLAM

OpenAIRE

Zhang, Teng; Wu, Kanzhi; Song, Jingwei; Huang, Shoudong; Dissanayake, Gamini

2017-01-01

In this paper, we investigate the convergence and consistency properties of an Invariant-Extended Kalman Filter (RI-EKF) based Simultaneous Localization and Mapping (SLAM) algorithm. Basic convergence properties of this algorithm are proven. These proofs do not require the restrictive assumption that the Jacobians of the motion and observation models need to be evaluated at the ground truth. It is also shown that the output of RI-EKF is invariant under any stochastic rigid body transformation...

Hippocampal activation during face-name associative memory encoding: blocked versus permuted design

International Nuclear Information System (INIS)

De Vogelaere, Frederick; Vingerhoets, Guy; Santens, Patrick; Boon, Paul; Achten, Erik

2010-01-01

The contribution of the hippocampal subregions to episodic memory through the formation of new associations between previously unrelated items such as faces and names is established but remains under discussion. Block design studies in this area of research generally tend to show posterior hippocampal activation during encoding of novel associational material while event-related studies emphasize anterior hippocampal involvement. We used functional magnetic resonance imaging to assess the involvement of anterior and posterior hippocampus in the encoding of novel associational material compared to the viewing of previously seen associational material. We used two different experimental designs, a block design and a permuted block design, and applied it to the same associative memory task to perform valid statistical comparisons. Our results indicate that the permuted design was able to capture more anterior hippocampal activation compared to the block design, which emphasized more posterior hippocampal involvement. These differences were further investigated and attributed to a combination of the polymodal stimuli we used and the experimental design. Activation patterns during encoding in both designs occurred along the entire longitudinal axis of the hippocampus, but with different centers of gravity. The maximal activated voxel in the block design was situated in the posterior half of the hippocampus while in the permuted design this was located in the anterior half. (orig.)

Hippocampal activation during face-name associative memory encoding: blocked versus permuted design

Energy Technology Data Exchange (ETDEWEB)

De Vogelaere, Frederick; Vingerhoets, Guy [Ghent University, Laboratory for Neuropsychology, Department of Neurology, Ghent (Belgium); Santens, Patrick; Boon, Paul [Ghent University Hospital, Department of Neurology, Ghent (Belgium); Achten, Erik [Ghent University Hospital, Department of Radiology, Ghent (Belgium)

2010-01-15

The contribution of the hippocampal subregions to episodic memory through the formation of new associations between previously unrelated items such as faces and names is established but remains under discussion. Block design studies in this area of research generally tend to show posterior hippocampal activation during encoding of novel associational material while event-related studies emphasize anterior hippocampal involvement. We used functional magnetic resonance imaging to assess the involvement of anterior and posterior hippocampus in the encoding of novel associational material compared to the viewing of previously seen associational material. We used two different experimental designs, a block design and a permuted block design, and applied it to the same associative memory task to perform valid statistical comparisons. Our results indicate that the permuted design was able to capture more anterior hippocampal activation compared to the block design, which emphasized more posterior hippocampal involvement. These differences were further investigated and attributed to a combination of the polymodal stimuli we used and the experimental design. Activation patterns during encoding in both designs occurred along the entire longitudinal axis of the hippocampus, but with different centers of gravity. The maximal activated voxel in the block design was situated in the posterior half of the hippocampus while in the permuted design this was located in the anterior half. (orig.)

Tolerance of a Knotted Near-Infrared Fluorescent Protein to Random Circular Permutation.

Science.gov (United States)

Pandey, Naresh; Kuypers, Brianna E; Nassif, Barbara; Thomas, Emily E; Alnahhas, Razan N; Segatori, Laura; Silberg, Jonathan J

2016-07-12

Bacteriophytochrome photoreceptors (BphP) are knotted proteins that have been developed as near-infrared fluorescent protein (iRFP) reporters of gene expression. To explore how rearrangements in the peptides that interlace into the knot within the BphP photosensory core affect folding, we subjected iRFPs to random circular permutation using an improved transposase mutagenesis strategy and screened for variants that fluoresce. We identified 27 circularly permuted iRFPs that display biliverdin-dependent fluorescence in Escherichia coli. The variants with the brightest whole cell fluorescence initiated translation at residues near the domain linker and knot tails, although fluorescent variants that initiated translation within the PAS and GAF domains were discovered. Circularly permuted iRFPs retained sufficient cofactor affinity to fluoresce in tissue culture without the addition of biliverdin, and one variant displayed enhanced fluorescence when expressed in bacteria and tissue culture. This variant displayed a quantum yield similar to that of iRFPs but exhibited increased resistance to chemical denaturation, suggesting that the observed increase in the magnitude of the signal arose from more efficient protein maturation. These results show how the contact order of a knotted BphP can be altered without disrupting chromophore binding and fluorescence, an important step toward the creation of near-infrared biosensors with expanded chemical sensing functions for in vivo imaging.

Diversification of Protein Cage Structure Using Circularly Permuted Subunits.

Science.gov (United States)

Azuma, Yusuke; Herger, Michael; Hilvert, Donald

2018-01-17

Self-assembling protein cages are useful as nanoscale molecular containers for diverse applications in biotechnology and medicine. To expand the utility of such systems, there is considerable interest in customizing the structures of natural cage-forming proteins and designing new ones. Here we report that a circularly permuted variant of lumazine synthase, a cage-forming enzyme from Aquifex aeolicus (AaLS) affords versatile building blocks for the construction of nanocompartments that can be easily produced, tailored, and diversified. The topologically altered protein, cpAaLS, self-assembles into spherical and tubular cage structures with morphologies that can be controlled by the length of the linker connecting the native termini. Moreover, cpAaLS proteins integrate into wild-type and other engineered AaLS assemblies by coproduction in Escherichia coli to form patchwork cages. This coassembly strategy enables encapsulation of guest proteins in the lumen, modification of the exterior through genetic fusion, and tuning of the size and electrostatics of the compartments. This addition to the family of AaLS cages broadens the scope of this system for further applications and highlights the utility of circular permutation as a potentially general strategy for tailoring the properties of cage-forming proteins.

Many-body effects in transport through a quantum-dot cavity system

Science.gov (United States)

Dinu, I. V.; Moldoveanu, V.; Gartner, P.

2018-05-01

We theoretically describe electric transport through an optically active quantum dot embedded in a single-mode cavity, and coupled to source-drain particle reservoirs. The populations of various many-body configurations (e.g., excitons, trions, biexciton) and the photon-number occupancies are calculated from a master equation which is derived in the basis of dressed states. These take into account both the Coulomb and the light-matter interaction. The former is essential in the description of the transport, while for the latter we identify situations in which it can be neglected in the expression of tunneling rates. The fermionic nature of the particle reservoirs plays an important role in the argument. The master equation is numerically solved for the s -shell many-body configurations of disk-shaped quantum dots. If the cavity is tuned to the biexciton-exciton transition, the most efficient optical processes take place in a three-level Λ system. The alternative exciton-ground-state route is inhibited as nonresonant due to the biexciton binding energy. The steady-state current is analyzed as a function of the photon frequency and the coupling to the leads. An unexpected feature appears in its dependence on the cavity loss rate, which turns out to be nonmonotonic.

Transformative decision rules, permutability, and non-sequential framing of decision problems

NARCIS (Netherlands)

Peterson, M.B.

2004-01-01

The concept of transformative decision rules provides auseful tool for analyzing what is often referred to as the`framing', or `problem specification', or `editing' phase ofdecision making. In the present study we analyze a fundamentalaspect of transformative decision rules, viz. permutability. A

Multiple comparisons permutation test for image based data mining in radiotherapy

NARCIS (Netherlands)

Chen, Chun; Witte, Marnix; Heemsbergen, Wilma; van Herk, Marcel

2013-01-01

: Comparing incidental dose distributions (i.e. images) of patients with different outcomes is a straightforward way to explore dose-response hypotheses in radiotherapy. In this paper, we introduced a permutation test that compares images, such as dose distributions from radiotherapy, while tackling

One-dimensional classical many-body system having a normal thermal conductivity

International Nuclear Information System (INIS)

Casati, G.; Ford, J.; Vivaldi, F.; Visscher, W.M.

1984-01-01

By numerically computing orbits for a chaotic, one-dimensional, many-body system placed between two thermal reservoirs, we verify directly that its energy transport obeys the Fourier heat law and we determine its thermal conductivity K. The same value of K is independently obtained by use of the Green-Kubo formalism. These numerical studies verify that chaos is the essential ingredient of diffusive energy transport, and they validate the Green-Kubo formalism

Learning molecular energies using localized graph kernels

Science.gov (United States)

Ferré, Grégoire; Haut, Terry; Barros, Kipton

2017-03-01

Recent machine learning methods make it possible to model potential energy of atomic configurations with chemical-level accuracy (as calculated from ab initio calculations) and at speeds suitable for molecular dynamics simulation. Best performance is achieved when the known physical constraints are encoded in the machine learning models. For example, the atomic energy is invariant under global translations and rotations; it is also invariant to permutations of same-species atoms. Although simple to state, these symmetries are complicated to encode into machine learning algorithms. In this paper, we present a machine learning approach based on graph theory that naturally incorporates translation, rotation, and permutation symmetries. Specifically, we use a random walk graph kernel to measure the similarity of two adjacency matrices, each of which represents a local atomic environment. This Graph Approximated Energy (GRAPE) approach is flexible and admits many possible extensions. We benchmark a simple version of GRAPE by predicting atomization energies on a standard dataset of organic molecules.

Universality of many-body two-nucleon momentum distributions: Correlated nucleon spectral function of complex nuclei

Science.gov (United States)

Ciofi degli Atti, Claudio; Morita, Hiko

2017-12-01

Background: The nuclear spectral function is a fundamental quantity that describes the mean-field and short-range correlation dynamics of nucleons embedded in the nuclear medium; its knowledge is a prerequisite for the interpretation of various electroweak scattering processes off nuclear targets aimed at providing fundamental information on strong and weak interactions. Whereas in the case of the three-nucleon and, partly, the four-nucleon systems, the spectral function can be calculated ab initio within a nonrelativistic many-body Schroedinger approach, in the case of complex nuclei only models of the correlated, high-momentum part of the spectral function are available so far. Purpose: The purpose of this paper is to present a new approach such that the spectral function for a specific nucleus can be obtained from a reliable many-body calculation based upon realistic nucleon-nucleon interactions, thus avoiding approximations leading to adjustable parameters. Methods: The expectation value of the nuclear many-body Hamiltonian, containing realistic nucleon-nucleon interaction of the Argonne family, is evaluated variationally by a normalization-conserving linked-cluster expansion and the resulting many-body correlated wave functions are used to calculate the one-nucleon and the two-nucleon momentum distributions; by analyzing the high-momentum behavior of the latter, the spectral function can be expressed in terms of a transparent convolution formula involving the relative and center-of-mass (c.m.) momentum distributions in specific regions of removal energy E and momentum k . Results: It is found that as a consequence of the factorization of the many-body wave functions at short internucleon separations, the high-momentum behavior of the two-nucleon momentum distributions in A =3 ,4 ,12 ,16 ,40 nuclei factorizes, at proper values of the relative and c.m. momenta, into the c.m. and relative momentum distributions, with the latter exhibiting a universal A

A permutation-based multiple testing method for time-course microarray experiments

Directory of Open Access Journals (Sweden)

George Stephen L

2009-10-01

Full Text Available Abstract Background Time-course microarray experiments are widely used to study the temporal profiles of gene expression. Storey et al. (2005 developed a method for analyzing time-course microarray studies that can be applied to discovering genes whose expression trajectories change over time within a single biological group, or those that follow different time trajectories among multiple groups. They estimated the expression trajectories of each gene using natural cubic splines under the null (no time-course and alternative (time-course hypotheses, and used a goodness of fit test statistic to quantify the discrepancy. The null distribution of the statistic was approximated through a bootstrap method. Gene expression levels in microarray data are often complicatedly correlated. An accurate type I error control adjusting for multiple testing requires the joint null distribution of test statistics for a large number of genes. For this purpose, permutation methods have been widely used because of computational ease and their intuitive interpretation. Results In this paper, we propose a permutation-based multiple testing procedure based on the test statistic used by Storey et al. (2005. We also propose an efficient computation algorithm. Extensive simulations are conducted to investigate the performance of the permutation-based multiple testing procedure. The application of the proposed method is illustrated using the Caenorhabditis elegans dauer developmental data. Conclusion Our method is computationally efficient and applicable for identifying genes whose expression levels are time-dependent in a single biological group and for identifying the genes for which the time-profile depends on the group in a multi-group setting.

An Advanced Rotation Invariant Descriptor for SAR Image Registration

Directory of Open Access Journals (Sweden)

Yuming Xiang

2017-07-01

Full Text Available The Scale-Invariant Feature Transform (SIFT algorithm and its many variants have been widely used in Synthetic Aperture Radar (SAR image registration. The SIFT-like algorithms maintain rotation invariance by assigning a dominant orientation for each keypoint, while the calculation of dominant orientation is not robust due to the effect of speckle noise in SAR imagery. In this paper, we propose an advanced local descriptor for SAR image registration to achieve rotation invariance without assigning a dominant orientation. Based on the improved intensity orders, we first divide a circular neighborhood into several sub-regions. Second, rotation-invariant ratio orientation histograms of each sub-region are proposed by accumulating the ratio values of different directions in a rotation-invariant coordinate system. The proposed descriptor is composed of the concatenation of the histograms of each sub-region. In order to increase the distinctiveness of the proposed descriptor, multiple image neighborhoods are aggregated. Experimental results on several satellite SAR images have shown an improvement in the matching performance over other state-of-the-art algorithms.

Tensor models, Kronecker coefficients and permutation centralizer algebras

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Geloun, Joseph Ben; Ramgoolam, Sanjaye

2017-11-01

We show that the counting of observables and correlators for a 3-index tensor model are organized by the structure of a family of permutation centralizer algebras. These algebras are shown to be semi-simple and their Wedderburn-Artin decompositions into matrix blocks are given in terms of Clebsch-Gordan coefficients of symmetric groups. The matrix basis for the algebras also gives an orthogonal basis for the tensor observables which diagonalizes the Gaussian two-point functions. The centres of the algebras are associated with correlators which are expressible in terms of Kronecker coefficients (Clebsch-Gordan multiplicities of symmetric groups). The color-exchange symmetry present in the Gaussian model, as well as a large class of interacting models, is used to refine the description of the permutation centralizer algebras. This discussion is extended to a general number of colors d: it is used to prove the integrality of an infinite family of number sequences related to color-symmetrizations of colored graphs, and expressible in terms of symmetric group representation theory data. Generalizing a connection between matrix models and Belyi maps, correlators in Gaussian tensor models are interpreted in terms of covers of singular 2-complexes. There is an intriguing difference, between matrix and higher rank tensor models, in the computational complexity of superficially comparable correlators of observables parametrized by Young diagrams.

A discrete firefly meta-heuristic with local search for makespan minimization in permutation flow shop scheduling problems

Directory of Open Access Journals (Sweden)

Nader Ghaffari-Nasab

2010-07-01

Full Text Available During the past two decades, there have been increasing interests on permutation flow shop with different types of objective functions such as minimizing the makespan, the weighted mean flow-time etc. The permutation flow shop is formulated as a mixed integer programming and it is classified as NP-Hard problem. Therefore, a direct solution is not available and meta-heuristic approaches need to be used to find the near-optimal solutions. In this paper, we present a new discrete firefly meta-heuristic to minimize the makespan for the permutation flow shop scheduling problem. The results of implementation of the proposed method are compared with other existing ant colony optimization technique. The preliminary results indicate that the new proposed method performs better than the ant colony for some well known benchmark problems.

A method for generating permutation distribution of ranks in a k ...

African Journals Online (AJOL)

... in a combinatorial sense the distribution of the ranks is obtained via its generating function. The formulas are defined recursively to speed up computations using the computer algebra system Mathematica. Key words: Partitions, generating functions, combinatorics, permutation test, exact tests, computer algebra, k-sample, ...

Detecting many-body-localization lengths with cold atoms

Science.gov (United States)

Guo, Xuefei; Li, Xiaopeng

2018-03-01

Considering ultracold atoms in optical lattices, we propose experimental protocols to study many-body-localization (MBL) length and criticality in quench dynamics. Through numerical simulations with exact diagonalization, we show that in the MBL phase the perturbed density profile following a local quench remains exponentially localized in postquench dynamics. The size of this density profile after long-time-dynamics defines a localization length, which tends to diverge at the MBL-to-ergodic transition as we increase the system size. The determined localization transition point agrees with previous exact diagonalization calculations using other diagnostics. Our numerical results provide evidence for violation of the Harris-Chayes bound for the MBL criticality. The critical exponent ν can be extracted from our proposed dynamical procedure, which can then be used directly in experiments to determine whether the Harris-Chayes-bound holds for the MBL transition. These proposed protocols to detect localization criticality are justified by benchmarking to the well-established results for the noninteracting three-dimensional Anderson localization.

Classical and quantum simulations of many-body systems

Energy Technology Data Exchange (ETDEWEB)

Murg, Valentin

2008-04-07

This thesis is devoted to recent developments in the fields of classical and quantum simulations of many-body systems. We describe new classical algorithms that overcome problems apparent in conventional renormalization group and Monte Carlo methods. These algorithms make possible the detailed study of finite temperature properties of 2-D classical and 1-D quantum systems, the investigation of ground states of 2-D frustrated or fermionic systems and the analysis of time evolutions of 2-D quantum systems. Furthermore, we propose new 'analog' quantum simulators that are able to realize interesting models such as a Tonks-Girardeau gas or a frustrated spin-1/2 XY model on a trigonal lattice. These quantum simulators make use of optical lattices and trapped ions and are technically feasible. In fact, the Tonks-Girardeau gas has been realized experimentally and we provide a detailed comparison between the experimental data and the theoretical predictions. (orig.)

Possible Many-Body Localization in a Long-Lived Finite-Temperature Ultracold Quasineutral Molecular Plasma

Science.gov (United States)

Sous, John; Grant, Edward

2018-03-01

We argue that the quenched ultracold plasma presents an experimental platform for studying the quantum many-body physics of disordered systems in the long-time and finite energy-density limits. We consider an experiment that quenches a plasma of nitric oxide to an ultracold system of Rydberg molecules, ions, and electrons that exhibits a long-lived state of arrested relaxation. The qualitative features of this state fail to conform with classical models. Here, we develop a microscopic quantum description for the arrested phase based on an effective many-body spin Hamiltonian that includes both dipole-dipole and van der Waals interactions. This effective model appears to offer a way to envision the essential quantum disordered nonequilibrium physics of this system.

Method for the Direct Solve of the Many-Body Schrödinger Wave Equation

Science.gov (United States)

Jerke, Jonathan; Tymczak, C. J.; Poirier, Bill

We report on theoretical and computational developments towards a computationally efficient direct solve of the many-body Schrödinger wave equation for electronic systems. This methodology relies on two recent developments pioneered by the authors: 1) the development of a Cardinal Sine basis for electronic structure calculations; and 2) the development of a highly efficient and compact representation of multidimensional functions using the Canonical tensor rank representation developed by Belykin et. al. which we have adapted to electronic structure problems. We then show several relevant examples of the utility and accuracy of this methodology, scaling with system size, and relevant convergence issues of the methodology. Method for the Direct Solve of the Many-Body Schrödinger Wave Equation.

The closed time-path Green function formalism in many-body theory

International Nuclear Information System (INIS)

Guang-zhao Zhou; Zhao-bin Su; Bai-lin Hao; Lu Yu.

1983-09-01

The closed time-path Green function formalism, developed by our group during recent years, is briefly reviewed. The generating functional technique, the coupled equations for the order parameter and the elementary excitations as well as the systematic loop expansion are outlined. The applications to critical dynamics, quenched random systems, nonlinear response theory, superconductivity, laser system and quasi-one-dimensional conductors are described. The theoretical approach developed can be applied to both equilibrium and non-equilibrium many-body systems. (author)

Maximizing kinetic energy transfer in one-dimensional many-body collisions

International Nuclear Information System (INIS)

Ricardo, Bernard; Lee, Paul

2015-01-01

The main problem discussed in this paper involves a simple one-dimensional two-body collision, in which the problem can be extended into a chain of one-dimensional many-body collisions. The result is quite interesting, as it provides us with a thorough mathematical understanding that will help in designing a chain system for maximum energy transfer for a range of collision types. In this paper, we will show that there is a way to improve the kinetic energy transfer between two masses, and the idea can be applied recursively. However, this method only works for a certain range of collision types, which is indicated by a range of coefficients of restitution. Although the concept of momentum, elastic and inelastic collision, as well as Newton’s laws, are taught in junior college physics, especially in Singapore schools, students in this level are not expected to be able to do this problem quantitatively, as it requires rigorous mathematics, including calculus. Nevertheless, this paper provides nice analytical steps that address some common misconceptions in students’ way of thinking about one-dimensional collisions. (paper)

Maximizing kinetic energy transfer in one-dimensional many-body collisions

Science.gov (United States)

Ricardo, Bernard; Lee, Paul

2015-03-01

The main problem discussed in this paper involves a simple one-dimensional two-body collision, in which the problem can be extended into a chain of one-dimensional many-body collisions. The result is quite interesting, as it provides us with a thorough mathematical understanding that will help in designing a chain system for maximum energy transfer for a range of collision types. In this paper, we will show that there is a way to improve the kinetic energy transfer between two masses, and the idea can be applied recursively. However, this method only works for a certain range of collision types, which is indicated by a range of coefficients of restitution. Although the concept of momentum, elastic and inelastic collision, as well as Newton’s laws, are taught in junior college physics, especially in Singapore schools, students in this level are not expected to be able to do this problem quantitatively, as it requires rigorous mathematics, including calculus. Nevertheless, this paper provides nice analytical steps that address some common misconceptions in students’ way of thinking about one-dimensional collisions.

Permutation entropy based time series analysis: Equalities in the input signal can lead to false conclusions

Energy Technology Data Exchange (ETDEWEB)

Zunino, Luciano, E-mail: lucianoz@ciop.unlp.edu.ar [Centro de Investigaciones Ópticas (CONICET La Plata – CIC), C.C. 3, 1897 Gonnet (Argentina); Departamento de Ciencias Básicas, Facultad de Ingeniería, Universidad Nacional de La Plata (UNLP), 1900 La Plata (Argentina); Olivares, Felipe, E-mail: olivaresfe@gmail.com [Instituto de Física, Pontificia Universidad Católica de Valparaíso (PUCV), 23-40025 Valparaíso (Chile); Scholkmann, Felix, E-mail: Felix.Scholkmann@gmail.com [Research Office for Complex Physical and Biological Systems (ROCoS), Mutschellenstr. 179, 8038 Zurich (Switzerland); Biomedical Optics Research Laboratory, Department of Neonatology, University Hospital Zurich, University of Zurich, 8091 Zurich (Switzerland); Rosso, Osvaldo A., E-mail: oarosso@gmail.com [Instituto de Física, Universidade Federal de Alagoas (UFAL), BR 104 Norte km 97, 57072-970, Maceió, Alagoas (Brazil); Instituto Tecnológico de Buenos Aires (ITBA) and CONICET, C1106ACD, Av. Eduardo Madero 399, Ciudad Autónoma de Buenos Aires (Argentina); Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Av. Mons. Álvaro del Portillo 12.455, Las Condes, Santiago (Chile)

2017-06-15

A symbolic encoding scheme, based on the ordinal relation between the amplitude of neighboring values of a given data sequence, should be implemented before estimating the permutation entropy. Consequently, equalities in the analyzed signal, i.e. repeated equal values, deserve special attention and treatment. In this work, we carefully study the effect that the presence of equalities has on permutation entropy estimated values when these ties are symbolized, as it is commonly done, according to their order of appearance. On the one hand, the analysis of computer-generated time series is initially developed to understand the incidence of repeated values on permutation entropy estimations in controlled scenarios. The presence of temporal correlations is erroneously concluded when true pseudorandom time series with low amplitude resolutions are considered. On the other hand, the analysis of real-world data is included to illustrate how the presence of a significant number of equal values can give rise to false conclusions regarding the underlying temporal structures in practical contexts. - Highlights: • Impact of repeated values in a signal when estimating permutation entropy is studied. • Numerical and experimental tests are included for characterizing this limitation. • Non-negligible temporal correlations can be spuriously concluded by repeated values. • Data digitized with low amplitude resolutions could be especially affected. • Analysis with shuffled realizations can help to overcome this limitation.

Confidence intervals and hypothesis testing for the Permutation Entropy with an application to epilepsy

Science.gov (United States)

Traversaro, Francisco; O. Redelico, Francisco

2018-04-01

In nonlinear dynamics, and to a lesser extent in other fields, a widely used measure of complexity is the Permutation Entropy. But there is still no known method to determine the accuracy of this measure. There has been little research on the statistical properties of this quantity that characterize time series. The literature describes some resampling methods of quantities used in nonlinear dynamics - as the largest Lyapunov exponent - but these seems to fail. In this contribution, we propose a parametric bootstrap methodology using a symbolic representation of the time series to obtain the distribution of the Permutation Entropy estimator. We perform several time series simulations given by well-known stochastic processes: the 1/fα noise family, and show in each case that the proposed accuracy measure is as efficient as the one obtained by the frequentist approach of repeating the experiment. The complexity of brain electrical activity, measured by the Permutation Entropy, has been extensively used in epilepsy research for detection in dynamical changes in electroencephalogram (EEG) signal with no consideration of the variability of this complexity measure. An application of the parametric bootstrap methodology is used to compare normal and pre-ictal EEG signals.

Many-body strategies for multiqubit gates: Quantum control through Krawtchouk-chain dynamics

Science.gov (United States)

Groenland, Koen; Schoutens, Kareljan

2018-04-01

We propose a strategy for engineering multiqubit quantum gates. As a first step, it employs an eigengate to map states in the computational basis to eigenstates of a suitable many-body Hamiltonian. The second step employs resonant driving to enforce a transition between a single pair of eigenstates, leaving all others unchanged. The procedure is completed by mapping back to the computational basis. We demonstrate the strategy for the case of a linear array with an even number N of qubits, with specific X X +Y Y couplings between nearest neighbors. For this so-called Krawtchouk chain, a two-body driving term leads to the iSWAPN gate, which we numerically test for N =4 and 6.

A Flexible Computational Framework Using R and Map-Reduce for Permutation Tests of Massive Genetic Analysis of Complex Traits.

Science.gov (United States)

Mahjani, Behrang; Toor, Salman; Nettelblad, Carl; Holmgren, Sverker

2017-01-01

In quantitative trait locus (QTL) mapping significance of putative QTL is often determined using permutation testing. The computational needs to calculate the significance level are immense, 10 4 up to 10 8 or even more permutations can be needed. We have previously introduced the PruneDIRECT algorithm for multiple QTL scan with epistatic interactions. This algorithm has specific strengths for permutation testing. Here, we present a flexible, parallel computing framework for identifying multiple interacting QTL using the PruneDIRECT algorithm which uses the map-reduce model as implemented in Hadoop. The framework is implemented in R, a widely used software tool among geneticists. This enables users to rearrange algorithmic steps to adapt genetic models, search algorithms, and parallelization steps to their needs in a flexible way. Our work underlines the maturity of accessing distributed parallel computing for computationally demanding bioinformatics applications through building workflows within existing scientific environments. We investigate the PruneDIRECT algorithm, comparing its performance to exhaustive search and DIRECT algorithm using our framework on a public cloud resource. We find that PruneDIRECT is vastly superior for permutation testing, and perform 2 ×10 5 permutations for a 2D QTL problem in 15 hours, using 100 cloud processes. We show that our framework scales out almost linearly for a 3D QTL search.

Invariant and Absolute Invariant Means of Double Sequences

Directory of Open Access Journals (Sweden)

Abdullah Alotaibi

2012-01-01

Full Text Available We examine some properties of the invariant mean, define the concepts of strong σ-convergence and absolute σ-convergence for double sequences, and determine the associated sublinear functionals. We also define the absolute invariant mean through which the space of absolutely σ-convergent double sequences is characterized.

Semiclassical expansion of quantum characteristics for many-body potential scattering problem

International Nuclear Information System (INIS)

Krivoruchenko, M.I.; Fuchs, C.; Faessler, A.

2007-01-01

In quantum mechanics, systems can be described in phase space in terms of the Wigner function and the star-product operation. Quantum characteristics, which appear in the Heisenberg picture as the Weyl's symbols of operators of canonical coordinates and momenta, can be used to solve the evolution equations for symbols of other operators acting in the Hilbert space. To any fixed order in the Planck's constant, many-body potential scattering problem simplifies to a statistical-mechanical problem of computing an ensemble of quantum characteristics and their derivatives with respect to the initial canonical coordinates and momenta. The reduction to a system of ordinary differential equations pertains rigorously at any fixed order in ℎ. We present semiclassical expansion of quantum characteristics for many-body scattering problem and provide tools for calculation of average values of time-dependent physical observables and cross sections. The method of quantum characteristics admits the consistent incorporation of specific quantum effects, such as non-locality and coherence in propagation of particles, into the semiclassical transport models. We formulate the principle of stationary action for quantum Hamilton's equations and give quantum-mechanical extensions of the Liouville theorem on conservation of the phase-space volume and the Poincare theorem on conservation of 2p-forms. The lowest order quantum corrections to the Kepler periodic orbits are constructed. These corrections show the resonance behavior. (Abstract Copyright [2007], Wiley Periodicals, Inc.)

Quantum measurement-induced dynamics of many-body ultracold bosonic and fermionic systems in optical lattices

Science.gov (United States)

Mazzucchi, Gabriel; Kozlowski, Wojciech; Caballero-Benitez, Santiago F.; Elliott, Thomas J.; Mekhov, Igor B.

2016-02-01

Trapping ultracold atoms in optical lattices enabled numerous breakthroughs uniting several disciplines. Coupling these systems to quantized light leads to a plethora of new phenomena and has opened up a new field of study. Here we introduce an unusual additional source of competition in a many-body strongly correlated system: We prove that quantum backaction of global measurement is able to efficiently compete with intrinsic short-range dynamics of an atomic system. The competition becomes possible due to the ability to change the spatial profile of a global measurement at a microscopic scale comparable to the lattice period without the need of single site addressing. In coherence with a general physical concept, where new competitions typically lead to new phenomena, we demonstrate nontrivial dynamical effects such as large-scale multimode oscillations, long-range entanglement, and correlated tunneling, as well as selective suppression and enhancement of dynamical processes beyond the projective limit of the quantum Zeno effect. We demonstrate both the breakup and protection of strongly interacting fermion pairs by measurement. Such a quantum optical approach introduces into many-body physics novel processes, objects, and methods of quantum engineering, including the design of many-body entangled environments for open systems.

A permutation information theory tour through different interest rate maturities: the Libor case.

Science.gov (United States)

Bariviera, Aurelio Fernández; Guercio, María Belén; Martinez, Lisana B; Rosso, Osvaldo A

2015-12-13

This paper analyses Libor interest rates for seven different maturities and referred to operations in British pounds, euros, Swiss francs and Japanese yen, during the period 2001-2015. The analysis is performed by means of two quantifiers derived from information theory: the permutation Shannon entropy and the permutation Fisher information measure. An anomalous behaviour in the Libor is detected in all currencies except euros during the years 2006-2012. The stochastic switch is more severe in one, two and three months maturities. Given the special mechanism of Libor setting, we conjecture that the behaviour could have been produced by the manipulation that was uncovered by financial authorities. We argue that our methodology is pertinent as a market overseeing instrument. © 2015 The Author(s).

On nonequilibrium many-body systems. 1: The nonequilibrium statistical operator method

International Nuclear Information System (INIS)

Algarte, A.C.S.; Vasconcellos, A.R.; Luzzi, R.; Sampaio, A.J.C.

1985-01-01

The theoretical aspects involved in the treatment of many-body systems strongly departed from equilibrium are discussed. The nonequilibrium statistical operator (NSO) method is considered in detail. Using Jaynes' maximum entropy formalism complemented with an ad hoc hypothesis a nonequilibrium statistical operator is obtained. This approach introduces irreversibility from the outset and we recover statistical operators like those of Green-Mori and Zubarev as particular cases. The connection with Generalized Thermodynamics and the construction of nonlinear transport equations are briefly described. (Author) [pt

Permutation-symmetric three-particle hyper-spherical harmonics based on the S3⊗SO(3rot⊂O(2⊗SO(3rot⊂U(3⋊S2⊂O(6 subgroup chain

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Igor Salom

2017-07-01

Full Text Available We construct the three-body permutation symmetric hyperspherical harmonics to be used in the non-relativistic three-body Schrödinger equation in three spatial dimensions (3D. We label the state vectors according to the S3⊗SO(3rot⊂O(2⊗SO(3rot⊂U(3⋊S2⊂O(6 subgroup chain, where S3 is the three-body permutation group and S2 is its two element subgroup containing transposition of first two particles, O(2 is the “democracy transformation”, or “kinematic rotation” group for three particles; SO(3rot is the 3D rotation group, and U(3,O(6 are the usual Lie groups. We discuss the good quantum numbers implied by the above chain of algebras, as well as their relation to the S3 permutation properties of the harmonics, particularly in view of the SO(3rot⊂SU(3 degeneracy. We provide a definite, practically implementable algorithm for the calculation of harmonics with arbitrary finite integer values of the hyper angular momentum K, and show an explicit example of this construction in a specific case with degeneracy, as well as tables of K≤6 harmonics. All harmonics are expressed as homogeneous polynomials in the Jacobi vectors (λ,ρ with coefficients given as algebraic numbers unless the “operator method” is chosen for the lifting of the SO(3rot⊂SU(3 multiplicity and the dimension of the degenerate subspace is greater than four – in which case one must resort to numerical diagonalization; the latter condition is not met by any K≤15 harmonic, or by any L≤7 harmonic with arbitrary K. We also calculate a certain type of matrix elements (the Gaunt integrals of products of three harmonics in two ways: 1 by explicit evaluation of integrals and 2 by reduction to known SU(3 Clebsch–Gordan coefficients. In this way we complete the calculation of the ingredients sufficient for the solution to the quantum-mechanical three-body bound state problem.

Understanding the many-body expansion for large systems. III. Critical role of four-body terms, counterpoise corrections, and cutoffs

Science.gov (United States)

Liu, Kuan-Yu; Herbert, John M.

2017-10-01

Papers I and II in this series [R. M. Richard et al., J. Chem. Phys. 141, 014108 (2014); K. U. Lao et al., ibid. 144, 164105 (2016)] have attempted to shed light on precision and accuracy issues affecting the many-body expansion (MBE), which only manifest in larger systems and thus have received scant attention in the literature. Many-body counterpoise (CP) corrections are shown to accelerate convergence of the MBE, which otherwise suffers from a mismatch between how basis-set superposition error affects subsystem versus supersystem calculations. In water clusters ranging in size up to (H2O)37, four-body terms prove necessary to achieve accurate results for both total interaction energies and relative isomer energies, but the sheer number of tetramers makes the use of cutoff schemes essential. To predict relative energies of (H2O)20 isomers, two approximations based on a lower level of theory are introduced and an ONIOM-type procedure is found to be very well converged with respect to the appropriate MBE benchmark, namely, a CP-corrected supersystem calculation at the same level of theory. Results using an energy-based cutoff scheme suggest that if reasonable approximations to the subsystem energies are available (based on classical multipoles, say), then the number of requisite subsystem calculations can be reduced even more dramatically than when distance-based thresholds are employed. The end result is several accurate four-body methods that do not require charge embedding, and which are stable in large basis sets such as aug-cc-pVTZ that have sometimes proven problematic for fragment-based quantum chemistry methods. Even with aggressive thresholding, however, the four-body approach at the self-consistent field level still requires roughly ten times more processors to outmatch the performance of the corresponding supersystem calculation, in test cases involving 1500-1800 basis functions.

Understanding the many-body expansion for large systems. III. Critical role of four-body terms, counterpoise corrections, and cutoffs.

Science.gov (United States)

Liu, Kuan-Yu; Herbert, John M

2017-10-28

Papers I and II in this series [R. M. Richard et al., J. Chem. Phys. 141, 014108 (2014); K. U. Lao et al., ibid. 144, 164105 (2016)] have attempted to shed light on precision and accuracy issues affecting the many-body expansion (MBE), which only manifest in larger systems and thus have received scant attention in the literature. Many-body counterpoise (CP) corrections are shown to accelerate convergence of the MBE, which otherwise suffers from a mismatch between how basis-set superposition error affects subsystem versus supersystem calculations. In water clusters ranging in size up to (H 2 O) 37 , four-body terms prove necessary to achieve accurate results for both total interaction energies and relative isomer energies, but the sheer number of tetramers makes the use of cutoff schemes essential. To predict relative energies of (H 2 O) 20 isomers, two approximations based on a lower level of theory are introduced and an ONIOM-type procedure is found to be very well converged with respect to the appropriate MBE benchmark, namely, a CP-corrected supersystem calculation at the same level of theory. Results using an energy-based cutoff scheme suggest that if reasonable approximations to the subsystem energies are available (based on classical multipoles, say), then the number of requisite subsystem calculations can be reduced even more dramatically than when distance-based thresholds are employed. The end result is several accurate four-body methods that do not require charge embedding, and which are stable in large basis sets such as aug-cc-pVTZ that have sometimes proven problematic for fragment-based quantum chemistry methods. Even with aggressive thresholding, however, the four-body approach at the self-consistent field level still requires roughly ten times more processors to outmatch the performance of the corresponding supersystem calculation, in test cases involving 1500-1800 basis functions.

Comparative analysis of automotive paints by laser induced breakdown spectroscopy and nonparametric permutation tests

International Nuclear Information System (INIS)

McIntee, Erin; Viglino, Emilie; Rinke, Caitlin; Kumor, Stephanie; Ni Liqiang; Sigman, Michael E.

2010-01-01

Laser-induced breakdown spectroscopy (LIBS) has been investigated for the discrimination of automobile paint samples. Paint samples from automobiles of different makes, models, and years were collected and separated into sets based on the color, presence or absence of effect pigments and the number of paint layers. Twelve LIBS spectra were obtained for each paint sample, each an average of a five single shot 'drill down' spectra from consecutive laser ablations in the same spot on the sample. Analyses by a nonparametric permutation test and a parametric Wald test were performed to determine the extent of discrimination within each set of paint samples. The discrimination power and Type I error were assessed for each data analysis method. Conversion of the spectral intensity to a log-scale (base 10) resulted in a higher overall discrimination power while observing the same significance level. Working on the log-scale, the nonparametric permutation tests gave an overall 89.83% discrimination power with a size of Type I error being 4.44% at the nominal significance level of 5%. White paint samples, as a group, were the most difficult to differentiate with the power being only 86.56% followed by 95.83% for black paint samples. Parametric analysis of the data set produced lower discrimination (85.17%) with 3.33% Type I errors, which is not recommended for both theoretical and practical considerations. The nonparametric testing method is applicable across many analytical comparisons, with the specific application described here being the pairwise comparison of automotive paint samples.

The geometric Hopf invariant and surgery theory

CERN Document Server

Crabb, Michael

2017-01-01

Written by leading experts in the field, this monograph provides homotopy theoretic foundations for surgery theory on higher-dimensional manifolds. Presenting classical ideas in a modern framework, the authors carefully highlight how their results relate to (and generalize) existing results in the literature. The central result of the book expresses algebraic surgery theory in terms of the geometric Hopf invariant, a construction in stable homotopy theory which captures the double points of immersions. Many illustrative examples and applications of the abstract results are included in the book, making it of wide interest to topologists. Serving as a valuable reference, this work is aimed at graduate students and researchers interested in understanding how the algebraic and geometric topology fit together in the surgery theory of manifolds. It is the only book providing such a wide-ranging historical approach to the Hopf invariant, double points and surgery theory, with many results old and new. .

Invariant and semi-invariant probabilistic normed spaces

Energy Technology Data Exchange (ETDEWEB)

Ghaemi, M.B. [School of Mathematics Iran, University of Science and Technology, Narmak, Tehran (Iran, Islamic Republic of)], E-mail: mghaemi@iust.ac.ir; Lafuerza-Guillen, B. [Departamento de Estadistica y Matematica Aplicada, Universidad de Almeria, Almeria E-04120 (Spain)], E-mail: blafuerz@ual.es; Saiedinezhad, S. [School of Mathematics Iran, University of Science and Technology, Narmak, Tehran (Iran, Islamic Republic of)], E-mail: ssaiedinezhad@yahoo.com

2009-10-15

Probabilistic metric spaces were introduced by Karl Menger. Alsina, Schweizer and Sklar gave a general definition of probabilistic normed space based on the definition of Menger . We introduce the concept of semi-invariance among the PN spaces. In this paper we will find a sufficient condition for some PN spaces to be semi-invariant. We will show that PN spaces are normal spaces. Urysohn's lemma, and Tietze extension theorem for them are proved.

Many-body quantum simulation with Rydberg atoms and ions

International Nuclear Information System (INIS)

Mueller, M.

2010-01-01

This thesis presents my work that is located at the interface between the fields of atomic physics, quantum optics and quantum information. The work was performed at the Institute of Theoretical Physics of the University of Innsbruck and the Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences under the supervision of Prof. Peter Zoller. The main topic of this thesis is the investigation of new schemes for quantum simulation of interacting many-body systems. The thesis is divided into three parts, which cover my work on i) chains of trapped Rydberg ions ii) quantum information processing and simulation with Rydberg atoms and iii) quantum simulation with ground state ions. The first part of this thesis is concerned with the study of Rydberg ions trapped in a linear Paul trap. The properties of ionic Rydberg states in the presence of the static and time-dependent electric trapping fields are investigated. First it is analyzed under which conditions laser-excited Rydberg ions can be trapped in a stable configuration. Furthermore, it is shown that strong dipole-dipole interactions among the ions can be achieved by microwave dressing fields. These interactions can give rise to dynamics of Rydberg excitations through the ion crystal, which take place on a nanosecond timescale and can be described by effective spin-models. In addition, it is discussed how to achieve fast two-qubit entangling gates between pairs of Rydberg ions. In the second part of this thesis, novel possibilities of using neutral Rydberg atoms for quantum-information processing and quantum simulation are investigated. A new scheme for a multi-atom quantum gate is proposed and theoretically analyzed. This parallelized gate allows one to entangle a mesoscopic ensemble of atoms with a single control atom in a single step, with high fidelity and on a microsecond time scale. The operation relies on strong and long-ranged interactions between Rydberg atoms triggering a

Galileo-invariant theory of low energy pion-nucleus scattering

International Nuclear Information System (INIS)

Mach, R.

1980-01-01

Two classes of Galileo-invariant optical models are constructed for pion elastic scattering by nuclei. The first, the two-body model, has been obtained assuming that the pion-bound nucleon dynamics is determined by the pion-nucleon kinetic energy. In deriving the second model, the (A+1)-body dynamics has been taken into account. The technique of effective nucleon momenta maintains the nonlocal propagation of the pion-target nucleon subsystem through the nucleus in contrast with the standard static approximation

Quantum gases. Observation of many-body dynamics in long-range tunneling after a quantum quench.

Science.gov (United States)

Meinert, Florian; Mark, Manfred J; Kirilov, Emil; Lauber, Katharina; Weinmann, Philipp; Gröbner, Michael; Daley, Andrew J; Nägerl, Hanns-Christoph

2014-06-13

Quantum tunneling is at the heart of many low-temperature phenomena. In strongly correlated lattice systems, tunneling is responsible for inducing effective interactions, and long-range tunneling substantially alters many-body properties in and out of equilibrium. We observe resonantly enhanced long-range quantum tunneling in one-dimensional Mott-insulating Hubbard chains that are suddenly quenched into a tilted configuration. Higher-order tunneling processes over up to five lattice sites are observed as resonances in the number of doubly occupied sites when the tilt per site is tuned to integer fractions of the Mott gap. This forms a basis for a controlled study of many-body dynamics driven by higher-order tunneling and demonstrates that when some degrees of freedom are frozen out, phenomena that are driven by small-amplitude tunneling terms can still be observed. Copyright © 2014, American Association for the Advancement of Science.

Calculation of the hyperfine interaction using an effective-operator form of many-body theory

International Nuclear Information System (INIS)

Garpman, S.; Lindgren, I.; Lindgren, J.; Morrison, J.

1975-01-01

The effective-operator form of many-body theory is reviewed and applied to the calculation of the hyperfine structure. Numerical results are given for the 2p, 3p, and 4p excited states of Li and the 3p state of Na. This is the first complete calculation of the hyperfine structure using an effective-operator form of perturbation theory. As in the Brueckner-Goldstone form of many-body theory, the various terms in the perturbation expansion are represented by Feynman diagrams which correspond to basic physical processes. The angular part of the perturbation diagrams are evaluated by taking advantage of the formal analogy between the Feynman diagrams and the angular-momentum diagrams, introduced by Jucys et al. The radial part of the diagrams is calculated by solving one- and two-particle equations for the particular linear combination of excited states that contribute to the Feynman diagrams. In this way all second- and third-order effects are accurately evaluated without explicitly constructing the excited orbitals. For the 2p state of Li our results are in agreement with the calculations of Nesbet and of Hameed and Foley. However, our quadrupole calculation disagrees with the work of Das and co-workers. The many-body results for Li and Na are compared with semiempirical methods for evaluating the quadrupole moment from the hyperfine interaction, and a new quadrupole moment of 23 Na is given

Research of Planetary Gear Fault Diagnosis Based on Permutation Entropy of CEEMDAN and ANFIS

Directory of Open Access Journals (Sweden)

Moshen Kuai

2018-03-01

Full Text Available For planetary gear has the characteristics of small volume, light weight and large transmission ratio, it is widely used in high speed and high power mechanical system. Poor working conditions result in frequent failures of planetary gear. A method is proposed for diagnosing faults in planetary gear based on permutation entropy of Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN Adaptive Neuro-fuzzy Inference System (ANFIS in this paper. The original signal is decomposed into 6 intrinsic mode functions (IMF and residual components by CEEMDAN. Since the IMF contains the main characteristic information of planetary gear faults, time complexity of IMFs are reflected by permutation entropies to quantify the fault features. The permutation entropies of each IMF component are defined as the input of ANFIS, and its parameters and membership functions are adaptively adjusted according to training samples. Finally, the fuzzy inference rules are determined, and the optimal ANFIS is obtained. The overall recognition rate of the test sample used for ANFIS is 90%, and the recognition rate of gear with one missing tooth is relatively high. The recognition rates of different fault gears based on the method can also achieve better results. Therefore, the proposed method can be applied to planetary gear fault diagnosis effectively.

Research of Planetary Gear Fault Diagnosis Based on Permutation Entropy of CEEMDAN and ANFIS.

Science.gov (United States)

Kuai, Moshen; Cheng, Gang; Pang, Yusong; Li, Yong

2018-03-05

For planetary gear has the characteristics of small volume, light weight and large transmission ratio, it is widely used in high speed and high power mechanical system. Poor working conditions result in frequent failures of planetary gear. A method is proposed for diagnosing faults in planetary gear based on permutation entropy of Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) Adaptive Neuro-fuzzy Inference System (ANFIS) in this paper. The original signal is decomposed into 6 intrinsic mode functions (IMF) and residual components by CEEMDAN. Since the IMF contains the main characteristic information of planetary gear faults, time complexity of IMFs are reflected by permutation entropies to quantify the fault features. The permutation entropies of each IMF component are defined as the input of ANFIS, and its parameters and membership functions are adaptively adjusted according to training samples. Finally, the fuzzy inference rules are determined, and the optimal ANFIS is obtained. The overall recognition rate of the test sample used for ANFIS is 90%, and the recognition rate of gear with one missing tooth is relatively high. The recognition rates of different fault gears based on the method can also achieve better results. Therefore, the proposed method can be applied to planetary gear fault diagnosis effectively.

Canonical form of three-fermion pure-states with six single particle states

International Nuclear Information System (INIS)

Chen, Lin; Ž Ðoković, Dragomir; Grassl, Markus; Zeng, Bei

2014-01-01

We construct a canonical form for pure states in ∧ 3 (C 6 ), the three-fermion system with six single particle states, under local unitary (LU) transformations, i.e., the unitary group U(6). We also construct a minimal set of generators of the algebra of polynomial U(6)-invariants on ∧ 3 (C 6 ). It turns out that this algebra is isomorphic to the algebra of polynomial LU-invariants of three-qubits which are additionally invariant under qubit permutations. As a consequence of this surprising fact, we deduce that there is a one-to-one correspondence between the U(6)-orbits of pure three-fermion states in ∧ 3 (C 6 ) and the LU orbits of pure three-qubit states when qubit permutations are allowed. As an important byproduct, we obtain a new canonical form for pure three-qubit states under LU transformations U(2) × U(2) × U(2) (no qubit permutations allowed)

Rotationally invariant correlation filtering

International Nuclear Information System (INIS)

Schils, G.F.; Sweeney, D.W.

1985-01-01

A method is presented for analyzing and designing optical correlation filters that have tailored rotational invariance properties. The concept of a correlation of an image with a rotation of itself is introduced. A unified theory of rotation-invariant filtering is then formulated. The unified approach describes matched filters (with no rotation invariance) and circular-harmonic filters (with full rotation invariance) as special cases. The continuum of intermediate cases is described in terms of a cyclic convolution operation over angle. The angular filtering approach allows an exact choice for the continuous trade-off between loss of the correlation energy (or specificity regarding the image) and the amount of rotational invariance desired

Structures of two-dimensional three-body systems

International Nuclear Information System (INIS)

Ruan, W.Y.; Liu, Y.Y.; Bao, C.G.

1996-01-01

Features of the structure of L = 0 states of a two-dimensional three-body model system have been investigated. Three types of permutation symmetry of the spatial part, namely symmetric, antisymmetric, and mixed, have been considered. A comparison has been made between the two-dimensional system and the corresponding three-dimensional one. The effect of symmetry on microscopic structures is emphasized. (author)

Machine learning strategies for systems with invariance properties

Science.gov (United States)

Ling, Julia; Jones, Reese; Templeton, Jeremy

2016-08-01

In many scientific fields, empirical models are employed to facilitate computational simulations of engineering systems. For example, in fluid mechanics, empirical Reynolds stress closures enable computationally-efficient Reynolds Averaged Navier Stokes simulations. Likewise, in solid mechanics, constitutive relations between the stress and strain in a material are required in deformation analysis. Traditional methods for developing and tuning empirical models usually combine physical intuition with simple regression techniques on limited data sets. The rise of high performance computing has led to a growing availability of high fidelity simulation data. These data open up the possibility of using machine learning algorithms, such as random forests or neural networks, to develop more accurate and general empirical models. A key question when using data-driven algorithms to develop these empirical models is how domain knowledge should be incorporated into the machine learning process. This paper will specifically address physical systems that possess symmetry or invariance properties. Two different methods for teaching a machine learning model an invariance property are compared. In the first method, a basis of invariant inputs is constructed, and the machine learning model is trained upon this basis, thereby embedding the invariance into the model. In the second method, the algorithm is trained on multiple transformations of the raw input data until the model learns invariance to that transformation. Results are discussed for two case studies: one in turbulence modeling and one in crystal elasticity. It is shown that in both cases embedding the invariance property into the input features yields higher performance at significantly reduced computational training costs.

Information sets as permutation cycles for quadratic residue codes

Directory of Open Access Journals (Sweden)

Richard A. Jenson

1982-01-01

Full Text Available The two cases p=7 and p=23 are the only known cases where the automorphism group of the [p+1,   (p+1/2] extended binary quadratic residue code, O(p, properly contains PSL(2,p. These codes have some of their information sets represented as permutation cycles from Aut(Q(p. Analysis proves that all information sets of Q(7 are so represented but those of Q(23 are not.

Time-dependent restricted-active-space self-consistent-field theory for bosonic many-body systems

International Nuclear Information System (INIS)

Lévêque, Camille; Madsen, Lars Bojer

2017-01-01

We develop an ab initio time-dependent wavefunction based theory for the description of a many-body system of cold interacting bosons. Like the multi-configurational time-dependent Hartree method for bosons (MCTDHB), the theory is based on a configurational interaction Ansatz for the many-body wavefunction with time-dependent self-consistent-field orbitals. The theory generalizes the MCTDHB method by incorporating restrictions on the active space of the orbital excitations. The restrictions are specified based on the physical situation at hand. The equations of motion of this time-dependent restricted-active-space self-consistent-field (TD-RASSCF) theory are derived. The similarity between the formal development of the theory for bosons and fermions is discussed. The restrictions on the active space allow the theory to be evaluated under conditions where other wavefunction based methods due to exponential scaling in the numerical effort cannot, and to clearly identify the excitations that are important for an accurate description, significantly beyond the mean-field approach. For ground state calculations we find it to be important to allow a few particles to have the freedom to move in many orbitals, an insight facilitated by the flexibility of the restricted-active-space Ansatz . Moreover, we find that a high accuracy can be obtained by including only even excitations in the many-body self-consistent-field wavefunction. Time-dependent simulations of harmonically trapped bosons subject to a quenching of their noncontact interaction, show failure of the mean-field Gross-Pitaevskii approach within a fraction of a harmonic oscillation period. The TD-RASSCF theory remains accurate at much reduced computational cost compared to the MCTDHB method. Exploring the effect of changes of the restricted-active-space allows us to identify that even self-consistent-field excitations are mainly responsible for the accuracy of the method. (paper)

Structural analysis of papain-like NlpC/P60 superfamily enzymes with a circularly permuted topology reveals potential lipid binding sites.

Directory of Open Access Journals (Sweden)

Qingping Xu

Full Text Available NlpC/P60 superfamily papain-like enzymes play important roles in all kingdoms of life. Two members of this superfamily, LRAT-like and YaeF/YiiX-like families, were predicted to contain a catalytic domain that is circularly permuted such that the catalytic cysteine is located near the C-terminus, instead of at the N-terminus. These permuted enzymes are widespread in virus, pathogenic bacteria, and eukaryotes. We determined the crystal structure of a member of the YaeF/YiiX-like family from Bacillus cereus in complex with lysine. The structure, which adopts a ligand-induced, "closed" conformation, confirms the circular permutation of catalytic residues. A comparative analysis of other related protein structures within the NlpC/P60 superfamily is presented. Permutated NlpC/P60 enzymes contain a similar conserved core and arrangement of catalytic residues, including a Cys/His-containing triad and an additional conserved tyrosine. More surprisingly, permuted enzymes have a hydrophobic S1 binding pocket that is distinct from previously characterized enzymes in the family, indicative of novel substrate specificity. Further analysis of a structural homolog, YiiX (PDB 2if6 identified a fatty acid in the conserved hydrophobic pocket, thus providing additional insights into possible function of these novel enzymes.

New formalism for determining excitation spectra of many-body systems

International Nuclear Information System (INIS)

Saito, S.; Zhang, S.B.; Louie, S.G.; Cohen, M.L.

1990-01-01

We present a new general formalism for determining the excitation spectrum of interacting many-body systems. The basic assumption is that the number of the excitations is equal to the number of sites. Within this approximation, it is shown that the density-density response functions with two different pure-imaginary energies determine the excitation spectrum. The method is applied to the valence electrons of sodium clusters of differing sizes in the time-dependent local-density approximation (TDLDA). A jellium-sphere background model is used for the ion cores. The excitation spectra obtained in this way represent well the excitation spectra given by the full TDLDA calculation along the real energy axis. Important collective modes are reproduced very well

Properties of invariant modelling and invariant glueing of vector fields

International Nuclear Information System (INIS)

Petukhov, V.R.

1987-01-01

Invariant modelling and invariant glueing of both continuous (rates and accelerations) and descrete vector fields, gradient and divergence cases are considered. The following appendices are discussed: vector fields in crystals, crystal disclinations, topological charges and their fields

Graph Theory Meets Ab Initio Molecular Dynamics: Atomic Structures and Transformations at the Nanoscale

Science.gov (United States)

Pietrucci, Fabio; Andreoni, Wanda

2011-08-01

Social permutation invariant coordinates are introduced describing the bond network around a given atom. They originate from the largest eigenvalue and the corresponding eigenvector of the contact matrix, are invariant under permutation of identical atoms, and bear a clear signature of an order-disorder transition. Once combined with ab initio metadynamics, these coordinates are shown to be a powerful tool for the discovery of low-energy isomers of molecules and nanoclusters as well as for a blind exploration of isomerization, association, and dissociation reactions.

The mathematical description of resonances in many-body systems

International Nuclear Information System (INIS)

Orth, A.

1985-01-01

We introduce a characterization for quantum-mechanical resonance and use it in order to detect for certain distinct physical states an especially slow decay behaviour. We apply these results to a model of the quantum-mechanical many-body problem and obtain so a mathematical description of the Auger effect (self-ionization of atoms). The class of the interaction potentials admitted for our theory is compared with other theories on resonances extremely large. We establish differentiability conditions and conditions on the fading behaviour in the infinite. Especially the Coulomb potential and the Yukawa potential belong to our class but also non-spherical-symmetric and non-analytic potentials with a Coulomb-like singularity in the origin, two- to threefold differentiable which tend to zero at the infinite. In the introduction we discuss extensively also by means of some examples the problematics of the quantum-mechanical resonance. (orig.) [de

Stochastic evaluation of second-order many-body perturbation energies.

Science.gov (United States)

Willow, Soohaeng Yoo; Kim, Kwang S; Hirata, So

2012-11-28

With the aid of the Laplace transform, the canonical expression of the second-order many-body perturbation correction to an electronic energy is converted into the sum of two 13-dimensional integrals, the 12-dimensional parts of which are evaluated by Monte Carlo integration. Weight functions are identified that are analytically normalizable, are finite and non-negative everywhere, and share the same singularities as the integrands. They thus generate appropriate distributions of four-electron walkers via the Metropolis algorithm, yielding correlation energies of small molecules within a few mE(h) of the correct values after 10(8) Monte Carlo steps. This algorithm does away with the integral transformation as the hotspot of the usual algorithms, has a far superior size dependence of cost, does not suffer from the sign problem of some quantum Monte Carlo methods, and potentially easily parallelizable and extensible to other more complex electron-correlation theories.

Galileo-invariant theory of low energy pion-nucleus scattering. III

International Nuclear Information System (INIS)

Mach, R.

1983-01-01

Using two versions of the Galileo-invariant optical model, π - - 4 He elastic scattering cross sections were calculated in the energy interval 50 to 260 MeV. Level shifts and widths of several light π-mesoatoms were estimated in the Born approximation. Whereas the (A+1)-body model appears to be more suitable in the resonance region, the two-body model yields surprisingly good results for both the low-energy scattering and the characteristics of π-mesoatoms. (author)

Galileo-invariant theory of low energy pion-nucleus scattering. II

International Nuclear Information System (INIS)

Mach, R.

1983-01-01

Two classes of Galileo-invariant optical models are constructed for pion elastic scattering by nuclei. The former, the two-body model, was obtained assuming that the pion-bound nucleon dynamics is determined by the pion-nucleon kinetic energy. In deriving the latter model, the (A+1)-body dynamics was taken into account. The technique of effective nucleon momenta maintains the nonlocal propagation of the pion-target nucleon subsystem through the nucleus in contrast with the standard static approximation. (author)

Filtration of the classical knot concordance group and Casson-Gordon invariants

Science.gov (United States)

Kim, Taehee

2004-09-01

It is known that if every prime power branched cyclic cover of a knot in S(3) is a homology sphere, then the knot has vanishing Casson-Gordon invariants. We construct infinitely many examples of (topologically) non-slice knots in S(3) whose prime power branched cyclic covers are homology spheres. We show that these knots generate an infinite rank subgroup of scrf_{(1.0)}/scrf_{(1.5)} for which Casson-Gordon invariants vanish in Cochran-Orr-Teichner's filtration of the classical knot concordance group. As a corollary, it follows that Casson-Gordon invariants are not a complete set of obstructions to a second layer of Whitney disks.

Random walk generated by random permutations of {1, 2, 3, ..., n + 1}

International Nuclear Information System (INIS)

Oshanin, G; Voituriez, R

2004-01-01

We study properties of a non-Markovian random walk X (n) l , l = 0, 1, 2, ..., n, evolving in discrete time l on a one-dimensional lattice of integers, whose moves to the right or to the left are prescribed by the rise-and-descent sequences characterizing random permutations π of [n + 1] = {1, 2, 3, ..., n + 1}. We determine exactly the probability of finding the end-point X n = X (n) n of the trajectory of such a permutation-generated random walk (PGRW) at site X, and show that in the limit n → ∞ it converges to a normal distribution with a smaller, compared to the conventional Polya random walk, diffusion coefficient. We formulate, as well, an auxiliary stochastic process whose distribution is identical to the distribution of the intermediate points X (n) l , l < n, which enables us to obtain the probability measure of different excursions and to define the asymptotic distribution of the number of 'turns' of the PGRW trajectories

Generating All Permutations by Context-Free Grammars in Chomsky Normal Form

NARCIS (Netherlands)

Asveld, P.R.J.; Spoto, F.; Scollo, Giuseppe; Nijholt, Antinus

2003-01-01

Let $L_n$ be the finite language of all $n!$ strings that are permutations of $n$ different symbols ($n\\geq 1$). We consider context-free grammars $G_n$ in Chomsky normal form that generate $L_n$. In particular we study a few families $\\{G_n\\}_{n\\geq 1}$, satisfying $L(G_n)=L_n$ for $n\\geq 1$, with

Generating all permutations by context-free grammars in Chomsky normal form

NARCIS (Netherlands)

Asveld, P.R.J.

2006-01-01

Let $L_n$ be the finite language of all $n!$ strings that are permutations of $n$ different symbols ($n\\geq1$). We consider context-free grammars $G_n$ in Chomsky normal form that generate $L_n$. In particular we study a few families $\\{G_n\\}_{n\\geq1}$, satisfying $L(G_n)=L_n$ for $n\\geq1$, with

Generating All Permutations by Context-Free Grammars in Chomsky Normal Form

NARCIS (Netherlands)

Asveld, P.R.J.

2004-01-01

Let $L_n$ be the finite language of all $n!$ strings that are permutations of $n$ different symbols ($n\\geq 1$). We consider context-free grammars $G_n$ in Chomsky normal form that generate $L_n$. In particular we study a few families $\\{G_n\\}_{n\\geq1}$, satisfying $L(G_n)=L_n$ for $n\\geq 1$, with

Permutation importance: a corrected feature importance measure.

Science.gov (United States)

Altmann, André; Toloşi, Laura; Sander, Oliver; Lengauer, Thomas

2010-05-15

In life sciences, interpretability of machine learning models is as important as their prediction accuracy. Linear models are probably the most frequently used methods for assessing feature relevance, despite their relative inflexibility. However, in the past years effective estimators of feature relevance have been derived for highly complex or non-parametric models such as support vector machines and RandomForest (RF) models. Recently, it has been observed that RF models are biased in such a way that categorical variables with a large number of categories are preferred. In this work, we introduce a heuristic for normalizing feature importance measures that can correct the feature importance bias. The method is based on repeated permutations of the outcome vector for estimating the distribution of measured importance for each variable in a non-informative setting. The P-value of the observed importance provides a corrected measure of feature importance. We apply our method to simulated data and demonstrate that (i) non-informative predictors do not receive significant P-values, (ii) informative variables can successfully be recovered among non-informative variables and (iii) P-values computed with permutation importance (PIMP) are very helpful for deciding the significance of variables, and therefore improve model interpretability. Furthermore, PIMP was used to correct RF-based importance measures for two real-world case studies. We propose an improved RF model that uses the significant variables with respect to the PIMP measure and show that its prediction accuracy is superior to that of other existing models. R code for the method presented in this article is available at http://www.mpi-inf.mpg.de/ approximately altmann/download/PIMP.R CONTACT: altmann@mpi-inf.mpg.de, laura.tolosi@mpi-inf.mpg.de Supplementary data are available at Bioinformatics online.

Liouvillian propagator technique for perturbed wave functions, level shifts and broadenings of composite particles in a many-body medium

International Nuclear Information System (INIS)

Girardeau, M.D.; Oregon Univ., Eugene

1981-01-01

Many problems in several areas of physics and chemistry involve many-body systems of interacting composite particles, in regimes where their internal transitions and/or reactive collisions (breakup, recombination, rearrangement) are important. Standard many-body Green's function and quantum field theoretic techniques are not well adapted to such situations. I discuss generalized representations which allow application of standard techniques to more complicated systems of interacting composite particles and their constituents. (orig./HSI)

Gauge fixing, BRS invariance and Ward identities for randomly stirred flows

International Nuclear Information System (INIS)

Berera, Arjun; Hochberg, David

2009-01-01

The Galilean invariance of the Navier-Stokes equation is shown to be akin to a global gauge symmetry familiar from quantum field theory. This symmetry leads to a multiple counting of infinitely many inertial reference frames in the path integral approach to randomly stirred fluids. This problem is solved by fixing the gauge, i.e., singling out one reference frame. The gauge fixed theory has an underlying Becchi-Rouet-Stora (BRS) symmetry which leads to the Ward identity relating the exact inverse response and vertex functions. This identification of Galilean invariance as a gauge symmetry is explored in detail, for different gauge choices and by performing a rigorous examination of a discretized version of the theory. The Navier-Stokes equation is also invariant under arbitrary rectilinear frame accelerations, known as extended Galilean invariance (EGI). We gauge fix this extended symmetry and derive the generalized Ward identity that follows from the BRS invariance of the gauge-fixed theory. This new Ward identity reduces to the standard one in the limit of zero acceleration. This gauge-fixing approach unambiguously shows that Galilean invariance and EGI constrain only the zero mode of the vertex but none of the higher wavenumber modes.

Gauge fixing, BRS invariance and Ward identities for randomly stirred flows

Energy Technology Data Exchange (ETDEWEB)

Berera, Arjun [School of Physics and Astronomy, University of Edinburgh, Edinburgh, EH9 3JZ (United Kingdom)], E-mail: ab@ph.ed.ac.uk; Hochberg, David [Centro de Astrobiologia (CSIC-INTA), Ctra. Ajalvir Km. 4, 28850 Torrejon de Ardoz, Madrid (Spain)], E-mail: hochbergd@inta.es

2009-06-21

The Galilean invariance of the Navier-Stokes equation is shown to be akin to a global gauge symmetry familiar from quantum field theory. This symmetry leads to a multiple counting of infinitely many inertial reference frames in the path integral approach to randomly stirred fluids. This problem is solved by fixing the gauge, i.e., singling out one reference frame. The gauge fixed theory has an underlying Becchi-Rouet-Stora (BRS) symmetry which leads to the Ward identity relating the exact inverse response and vertex functions. This identification of Galilean invariance as a gauge symmetry is explored in detail, for different gauge choices and by performing a rigorous examination of a discretized version of the theory. The Navier-Stokes equation is also invariant under arbitrary rectilinear frame accelerations, known as extended Galilean invariance (EGI). We gauge fix this extended symmetry and derive the generalized Ward identity that follows from the BRS invariance of the gauge-fixed theory. This new Ward identity reduces to the standard one in the limit of zero acceleration. This gauge-fixing approach unambiguously shows that Galilean invariance and EGI constrain only the zero mode of the vertex but none of the higher wavenumber modes.

Invariants and labels for Lie-Poisson Systems

International Nuclear Information System (INIS)

Thiffeault, J.L.; Morrison, P.J.

1998-04-01

Reduction is a process that uses symmetry to lower the order of a Hamiltonian system. The new variables in the reduced picture are often not canonical: there are no clear variables representing positions and momenta, and the Poisson bracket obtained is not of the canonical type. Specifically, we give two examples that give rise to brackets of the noncanonical Lie-Poisson form: the rigid body and the two-dimensional ideal fluid. From these simple cases, we then use the semidirect product extension of algebras to describe more complex physical systems. The Casimir invariants in these systems are examined, and some are shown to be linked to the recovery of information about the configuration of the system. We discuss a case in which the extension is not a semidirect product, namely compressible reduced MHD, and find for this case that the Casimir invariants lend partial information about the configuration of the system

Successful attack on permutation-parity-machine-based neural cryptography.

Science.gov (United States)

Seoane, Luís F; Ruttor, Andreas

2012-02-01

An algorithm is presented which implements a probabilistic attack on the key-exchange protocol based on permutation parity machines. Instead of imitating the synchronization of the communicating partners, the strategy consists of a Monte Carlo method to sample the space of possible weights during inner rounds and an analytic approach to convey the extracted information from one outer round to the next one. The results show that the protocol under attack fails to synchronize faster than an eavesdropper using this algorithm.

On the hierarchy of partially invariant submodels of differential equations

OpenAIRE

Golovin, Sergey V.

2007-01-01

It is noticed, that partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PIS of the higher rank. This introduce a hierarchic structure in the set of all PISs of a given system of differential equations. By using this structure one can significantly decrease an amount of calculations required in enumeration of all PISs for a given system of partially differential equations. An equivalence of the two-step and the direct ...

Remarks on the E-invariant and the Casson invariant

International Nuclear Information System (INIS)

Seade, J.

1991-08-01

In this work a framed manifold means a pair (M,F) consisting of a closed C ∞ , stably parallelizable manifold M, together with a trivialization F of its stable tangent bundle. The purpose of this work is to understand and determine in higher dimensions the invariant h(M,F) appearing in connection with the Adams e-invariants. 28 refs

Three-body problem in d-dimensional space: Ground state, (quasi)-exact-solvability

Science.gov (United States)

Turbiner, Alexander V.; Miller, Willard; Escobar-Ruiz, M. A.

2018-02-01

As a straightforward generalization and extension of our previous paper [A. V. Turbiner et al., "Three-body problem in 3D space: Ground state, (quasi)-exact-solvability," J. Phys. A: Math. Theor. 50, 215201 (2017)], we study the aspects of the quantum and classical dynamics of a 3-body system with equal masses, each body with d degrees of freedom, with interaction depending only on mutual (relative) distances. The study is restricted to solutions in the space of relative motion which are functions of mutual (relative) distances only. It is shown that the ground state (and some other states) in the quantum case and the planar trajectories (which are in the interaction plane) in the classical case are of this type. The quantum (and classical) Hamiltonian for which these states are eigenfunctions is derived. It corresponds to a three-dimensional quantum particle moving in a curved space with special d-dimension-independent metric in a certain d-dependent singular potential, while at d = 1, it elegantly degenerates to a two-dimensional particle moving in flat space. It admits a description in terms of pure geometrical characteristics of the interaction triangle which is defined by the three relative distances. The kinetic energy of the system is d-independent; it has a hidden sl(4, R) Lie (Poisson) algebra structure, alternatively, the hidden algebra h(3) typical for the H3 Calogero model as in the d = 3 case. We find an exactly solvable three-body S3-permutationally invariant, generalized harmonic oscillator-type potential as well as a quasi-exactly solvable three-body sextic polynomial type potential with singular terms. For both models, an extra first order integral exists. For d = 1, the whole family of 3-body (two-dimensional) Calogero-Moser-Sutherland systems as well as the Tremblay-Turbiner-Winternitz model is reproduced. It is shown that a straightforward generalization of the 3-body (rational) Calogero model to d > 1 leads to two primitive quasi

Collective many-body dynamics in the vicinity of nuclear driplines

International Nuclear Information System (INIS)

Volya, Alexander; Zelevinsky, Vladimir

2007-01-01

The Continuum Shell Model is a powerful theoretical tool for analysis of many-body dynamics embedded in the continuum. Here we formulate the method and use an example of a realistic shell model calculation for oxygen isotopes to demonstrate the seamless transition from bound states to resonances and cross sections in continuum within the same framework. The coupled dynamics of intrinsic states and continuum is traced further to the regime of continuum dominance that implies the decay width collectivization and onset of super-radiance. The coexistence and interplay of internal collective motion, such as giant resonances, and decay are of particular interest. Schematic and realistic calculations illustrate changes in the strength distribution and the natural appearance of the so-called pygmy mode

Invariants of generalized Lie algebras

International Nuclear Information System (INIS)

Agrawala, V.K.

1981-01-01

Invariants and invariant multilinear forms are defined for generalized Lie algebras with arbitrary grading and commutation factor. Explicit constructions of invariants and vector operators are given by contracting invariant forms with basic elements of the generalized Lie algebra. The use of the matrix of a linear map between graded vector spaces is emphasized. With the help of this matrix, the concept of graded trace of a linear operator is introduced, which is a rich source of multilinear forms of degree zero. To illustrate the use of invariants, a characteristic identity similar to that of Green is derived and a few Racah coefficients are evaluated in terms of invariants

Loop corrections and other many-body effects in relativistic field theories

International Nuclear Information System (INIS)

Ainsworth, T.L.; Brown, G.E.; Prakash, M.; Weise, W.

1988-01-01

Incorporation of effective masses into negative energy states (nucleon loop corrections) gives rise to repulsive many-body forces, as has been known for some time. Rather than renormalizing away the three- and four-body terms, we introduce medium corrections into the effective σ-exchange, which roughly cancel the nucleon loop terms for densities ρ ≅ ρ nm , where ρ nm is nuclear matter density. Going to higher densities, the repulsive contributions tend to saturate whereas the attractive ones keep on growing in magnitude. The latter is achieved through use of a density-dependent effective mass for the σ-particle, m σ = m σ (ρ), such that m σ (ρ) decreases with increasing density. Such a behavior is seen e.g. in the Nambu-Jona-Lasinio model. It is argued that a smooth transition to chiral restoration implies a similar behavior. The resulting nuclear equation of state is, because of the self-consistency in the problem, immensely insensitive to changes in the mass or coupling constant of the σ-particle. (orig.)

Ab Initio Many-Body Calculations Of Nucleon-Nucleus Scattering

Energy Technology Data Exchange (ETDEWEB)

Quaglioni, S; Navratil, P

2008-12-17

We develop a new ab initio many-body approach capable of describing simultaneously both bound and scattering states in light nuclei, by combining the resonating-group method with the use of realistic interactions, and a microscopic and consistent description of the nucleon clusters. This approach preserves translational symmetry and Pauli principle. We outline technical details and present phase shift results for neutron scattering on {sup 3}H, {sup 4}He and {sup 10}Be and proton scattering on {sup 3,4}He, using realistic nucleon-nucleon (NN) potentials. Our A = 4 scattering results are compared to earlier ab initio calculations. We find that the CD-Bonn NN potential in particular provides an excellent description of nucleon-{sup 4}He S-wave phase shifts. We demonstrate that a proper treatment of the coupling to the n-{sup 10}Be continuum is successful in explaining the parity-inverted ground state in {sup 11}Be.

Refined composite multiscale weighted-permutation entropy of financial time series

Science.gov (United States)

Zhang, Yongping; Shang, Pengjian

2018-04-01

For quantifying the complexity of nonlinear systems, multiscale weighted-permutation entropy (MWPE) has recently been proposed. MWPE has incorporated amplitude information and been applied to account for the multiple inherent dynamics of time series. However, MWPE may be unreliable, because its estimated values show large fluctuation for slight variation of the data locations, and a significant distinction only for the different length of time series. Therefore, we propose the refined composite multiscale weighted-permutation entropy (RCMWPE). By comparing the RCMWPE results with other methods' results on both synthetic data and financial time series, RCMWPE method shows not only the advantages inherited from MWPE but also lower sensitivity to the data locations, more stable and much less dependent on the length of time series. Moreover, we present and discuss the results of RCMWPE method on the daily price return series from Asian and European stock markets. There are significant differences between Asian markets and European markets, and the entropy values of Hang Seng Index (HSI) are close to but higher than those of European markets. The reliability of the proposed RCMWPE method has been supported by simulations on generated and real data. It could be applied to a variety of fields to quantify the complexity of the systems over multiple scales more accurately.

Symmetric periodic orbits near a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2

International Nuclear Information System (INIS)

Corbera, Montserrat; Llibre, Jaume; Perez-Chavela, Ernesto

2006-01-01

In this paper we consider vector fields in R 3 that are invariant under a suitable symmetry and that possess a 'generalized heteroclinic loop' L formed by two singular points (e + and e - ) and their invariant manifolds: one of dimension 2 (a sphere minus the points e + and e - ) and one of dimension 1 (the open diameter of the sphere having endpoints e + and e - ). In particular, we analyse the dynamics of the vector field near the heteroclinic loop L by means of a convenient Poincar? map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in R 3 , and the second one is the charged rhomboidal four-body problem

On density of the Vassiliev invariants

DEFF Research Database (Denmark)

Røgen, Peter

1999-01-01

The main result is that the Vassiliev invariants are dense in the set of numeric knot invariants if and only if they separate knots.Keywords: Knots, Vassiliev invariants, separation, density, torus knots......The main result is that the Vassiliev invariants are dense in the set of numeric knot invariants if and only if they separate knots.Keywords: Knots, Vassiliev invariants, separation, density, torus knots...

On non-permutation solutions to some two machine flow shop scheduling problems

NARCIS (Netherlands)

V. Strusevich (Vitaly); P.J. Zwaneveld (Peter)

1994-01-01

textabstractIn this paper, we study two versions of the two machine flow shop scheduling problem, where schedule length is to be minimized. First, we consider the two machine flow shop with setup, processing, and removal times separated. It is shown that an optimal solution need not be a permutation

Multivariate Multi-Scale Permutation Entropy for Complexity Analysis of Alzheimer’s Disease EEG

Directory of Open Access Journals (Sweden)

Isabella Palamara

2012-07-01

Full Text Available An original multivariate multi-scale methodology for assessing the complexity of physiological signals is proposed. The technique is able to incorporate the simultaneous analysis of multi-channel data as a unique block within a multi-scale framework. The basic complexity measure is done by using Permutation Entropy, a methodology for time series processing based on ordinal analysis. Permutation Entropy is conceptually simple, structurally robust to noise and artifacts, computationally very fast, which is relevant for designing portable diagnostics. Since time series derived from biological systems show structures on multiple spatial-temporal scales, the proposed technique can be useful for other types of biomedical signal analysis. In this work, the possibility of distinguish among the brain states related to Alzheimer’s disease patients and Mild Cognitive Impaired subjects from normal healthy elderly is checked on a real, although quite limited, experimental database.

Beautiful Models: 70 Years of Exactly Solved Quantum Many-Body Problems

International Nuclear Information System (INIS)

Batchelor, M T

2005-01-01

A key element of theoretical physics is the conceptualisation of physical phenomena in terms of models, which are then investigated by the tools at hand. For quantum many-body systems, some models can be exactly solved, i.e., their physical properties can be calculated in an exact fashion. There is often a deep underlying reason why this can be done-the theory of integrability-which manifests itself in many guises. In Beautiful models, Bill Sutherland looks at exactly solved models in quantum many-body systems, a well established field dating back to Bethe's 1931 exact solution of the spin-1/2 Heisenberg chain. This field is enjoying a renaissance due to the ongoing and striking experimental advances in low-dimensional quantum physics, which includes the manufacture of quasi one-dimensional quantum gases. Apart from the intrinsic beauty of the subject material, Beautiful Models is written by a pioneering master of the field. Sutherland has aimed to provide a broad textbook style introduction to the subject for graduate students and interested non-experts. An important point here is the 'language' of the book. In Sutherland's words, the subject of exactly solved models 'belongs to the realm of mathematical physics-too mathematical to be 'respectable' physics, yet not rigorous enough to be 'real' mathematics. ...there are perennial attempts to translate this body of work into either respectable physics or real mathematics; this is not that sort of book.' Rather, Sutherland discusses the models and their solutions in terms of their 'intrinisic' language, which is largely as found in the physics literature. The book begins with a helpful overview of the contents and then moves on to the foundation material, which is the chapter on integrability and non-diffraction. As is shown, these two concepts go hand in hand. The topics covered in later chapters include models with δ-function potentials, the Heisenberg spin chain, the Hubbard model, exchange models, the Calogero

Beautiful Models: 70 Years of Exactly Solved Quantum Many-Body Problems

Energy Technology Data Exchange (ETDEWEB)

Batchelor, M T [Department of Theoretical Physics, RSPSE and Department of Mathematics, MSI, Australian National University, Canberra ACT 0200 (Australia)

2005-04-08

A key element of theoretical physics is the conceptualisation of physical phenomena in terms of models, which are then investigated by the tools at hand. For quantum many-body systems, some models can be exactly solved, i.e., their physical properties can be calculated in an exact fashion. There is often a deep underlying reason why this can be done-the theory of integrability-which manifests itself in many guises. In Beautiful models, Bill Sutherland looks at exactly solved models in quantum many-body systems, a well established field dating back to Bethe's 1931 exact solution of the spin-1/2 Heisenberg chain. This field is enjoying a renaissance due to the ongoing and striking experimental advances in low-dimensional quantum physics, which includes the manufacture of quasi one-dimensional quantum gases. Apart from the intrinsic beauty of the subject material, Beautiful Models is written by a pioneering master of the field. Sutherland has aimed to provide a broad textbook style introduction to the subject for graduate students and interested non-experts. An important point here is the 'language' of the book. In Sutherland's words, the subject of exactly solved models 'belongs to the realm of mathematical physics-too mathematical to be 'respectable' physics, yet not rigorous enough to be 'real' mathematics. ...there are perennial attempts to translate this body of work into either respectable physics or real mathematics; this is not that sort of book.' Rather, Sutherland discusses the models and their solutions in terms of their 'intrinisic' language, which is largely as found in the physics literature. The book begins with a helpful overview of the contents and then moves on to the foundation material, which is the chapter on integrability and non-diffraction. As is shown, these two concepts go hand in hand. The topics covered in later chapters include models with {delta}-function potentials, the

Invariant exchange perturbation theory for multicenter systems and its application to the calculation of magnetic chains in manganites

International Nuclear Information System (INIS)

Orlenko, E. V.; Ershova, E. V.; Orlenko, F. E.

2013-01-01

The formalism of exchange perturbation theory is presented with regard to the general principles of constructing an antisymmetric vector with the use of the Young diagrams and tableaux in which the coordinate and spin parts are not separated. The form of the energy and wave function corrections coincides with earlier obtained expressions, which are reduced in the present paper to a simpler form of a symmetry-adapted perturbation operator, which preserves all intercenter exchange contributions. The exchange perturbation theory (EPT) formalism itself is presented in the standard form of invariant perturbation theory that takes into account intercenter electron permutations between overlapping nonorthogonal states. As an example of application of the formalism of invariant perturbation theory, we consider the magnetic properties of perovskite manganites La 1/3 Ca 2/3 MnO 3 that are associated with the charge and spin ordering in magnetic chains of manganese. We try to interpret the experimental results obtained from the study of the effect of doping the above alloys by the model of superexchange interaction in manganite chains that is constructed on the basis of the exchange perturbation theory (EPT) formalism. The model proposed makes it possible to carry out a quantitative analysis of the effect of substitution of manganese atoms by doping elements with different electron configurations on the electronic structure and short-range order in a magnetic chain of manganites

Rotation of quantum impurities in the presence of a many-body environment

Science.gov (United States)

Lemeshko, Mikhail; Schmidt, Richard

2015-05-01

Pioneered by the seminal works of Wigner and Racah, the quantum theory of angular momentum evolved into a powerful machinery, commonly used to classify the states of isolated quantum systems and perturbations to their structure due to electromagnetic or crystalline fields. In ``realistic'' experiments, however, quantum systems are almost inevitably coupled to a many-particle environment and a field of elementary excitations associated with it, which is capable of fundamentally altering the physics of the system. We present the first systematic treatment of quantum rotation coupled to a many-particle environment. By using a series of canonical transformations on a generic microscopic Hamiltonian, we single out the conserved quantities of the problem. Using a variational ansatz accounting for an infinite number of many-body excitations, we characterize the spectrum of angular momentum eigenstates and identify the regions of instability, accompanied by emission of angular Cerenkov radiation. The developed technique can be applied to a wide range of systems described by the angular momentum algebra, from Rydberg atoms immersed into BEC's, to cold molecules solvated in helium droplets, to ultracold molecular ions.

Identifying the closeness of eigenstates in quantum many-body systems

International Nuclear Information System (INIS)

Li Hai-bin; Yang Yang; Wang Pei; Wang Xiao-guang

2017-01-01

We propose a quantity called modulus fidelity to measure the closeness of two quantum pure states. We use it to investigate the closeness of eigenstates in one-dimensional hard-core bosons. When the system is integrable, eigenstates close to their neighbor or not, which leads to a large fluctuation in the distribution of modulus fidelity. When the system becomes chaos, the fluctuation is reduced dramatically, which indicates all eigenstates become close to each other. It is also found that two kind of closeness, i.e., closeness of eigenstates and closeness of eigenvalues, are not correlated at integrability but correlated at chaos. We also propose that the closeness of eigenstates is the underlying mechanism of eigenstate thermalization hypothesis (ETH) which explains the thermalization in quantum many-body systems. (paper)

Cohomological invariants in Galois cohomology

CERN Document Server

Garibaldi, Skip; Serre, Jean Pierre

2003-01-01

This volume is concerned with algebraic invariants, such as the Stiefel-Whitney classes of quadratic forms (with values in Galois cohomology mod 2) and the trace form of �tale algebras (with values in the Witt ring). The invariants are analogues for Galois cohomology of the characteristic classes of topology. Historically, one of the first examples of cohomological invariants of the type considered here was the Hasse-Witt invariant of quadratic forms. The first part classifies such invariants in several cases. A principal tool is the notion of versal torsor, which is an analogue of the universal bundle in topology. The second part gives Rost's determination of the invariants of G-torsors with values in H^3(\\mathbb{Q}/\\mathbb{Z}(2)), when G is a semisimple, simply connected, linear group. This part gives detailed proofs of the existence and basic properties of the Rost invariant. This is the first time that most of this material appears in print.

Analysis of crude oil markets with improved multiscale weighted permutation entropy

Science.gov (United States)

Niu, Hongli; Wang, Jun; Liu, Cheng

2018-03-01

Entropy measures are recently extensively used to study the complexity property in nonlinear systems. Weighted permutation entropy (WPE) can overcome the ignorance of the amplitude information of time series compared with PE and shows a distinctive ability to extract complexity information from data having abrupt changes in magnitude. Improved (or sometimes called composite) multi-scale (MS) method possesses the advantage of reducing errors and improving the accuracy when applied to evaluate multiscale entropy values of not enough long time series. In this paper, we combine the merits of WPE and improved MS to propose the improved multiscale weighted permutation entropy (IMWPE) method for complexity investigation of a time series. Then it is validated effective through artificial data: white noise and 1 / f noise, and real market data of Brent and Daqing crude oil. Meanwhile, the complexity properties of crude oil markets are explored respectively of return series, volatility series with multiple exponents and EEMD-produced intrinsic mode functions (IMFs) which represent different frequency components of return series. Moreover, the instantaneous amplitude and frequency of Brent and Daqing crude oil are analyzed by the Hilbert transform utilized to each IMF.

Cosmological disformal invariance

Energy Technology Data Exchange (ETDEWEB)

Domènech, Guillem; Sasaki, Misao [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan); Naruko, Atsushi, E-mail: guillem.domenech@yukawa.kyoto-u.ac.jp, E-mail: naruko@th.phys.titech.ac.jp, E-mail: misao@yukawa.kyoto-u.ac.jp [Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551 (Japan)

2015-10-01

The invariance of physical observables under disformal transformations is considered. It is known that conformal transformations leave physical observables invariant. However, whether it is true for disformal transformations is still an open question. In this paper, it is shown that a pure disformal transformation without any conformal factor is equivalent to rescaling the time coordinate. Since this rescaling applies equally to all the physical quantities, physics must be invariant under a disformal transformation, that is, neither causal structure, propagation speed nor any other property of the fields are affected by a disformal transformation itself. This fact is presented at the action level for gravitational and matter fields and it is illustrated with some examples of observable quantities. We also find the physical invariance for cosmological perturbations at linear and high orders in perturbation, extending previous studies. Finally, a comparison with Horndeski and beyond Horndeski theories under a disformal transformation is made.

From optics to superconductivity. Many body effects in transition metal dichalcogenides

Energy Technology Data Exchange (ETDEWEB)

Roesner, Malte; Schoenhoff, Gunnar; Wehling, Tim [Institute for Theoretical Physics, University of Bremen (Germany); Bremen Center for Computational Material Sciences, University of Bremen (Germany); Steinhoff, Alexander; Jahnke, Frank; Gies, Christopher [Institute for Theoretical Physics, University of Bremen (Germany); Haas, Stephan [Department of Physics and Astronomy, University of Southern California, Los Angeles, CA (United States)

2015-07-01

We discuss many body effects in MoS{sub 2} ranging from optical properties to the emergence superconductivity (SC) and charge density wave phases (CDW). Combining ab-initio theory and semiconductor Bloch equations we show that excited carriers cause a redshift of the excitonic ground-state absorption line, while higher excitonic lines disappear successively due to a huge Coulomb-induced band gap shrinkage of more than 500 meV and concomitant exciton binding-energy reductions. Upon strong charge doping, we observe a succession of semiconducting, metallic, SC, and CDW regimes. Both, the SC and the CDW instabilities trace back to a Kohn anomaly and related softening of Brillouin zone boundary phonons.

Donaldson invariants in algebraic geometry

International Nuclear Information System (INIS)

Goettsche, L.

2000-01-01

In these lectures I want to give an introduction to the relation of Donaldson invariants with algebraic geometry: Donaldson invariants are differentiable invariants of smooth compact 4-manifolds X, defined via moduli spaces of anti-self-dual connections. If X is an algebraic surface, then these moduli spaces can for a suitable choice of the metric be identified with moduli spaces of stable vector bundles on X. This can be used to compute Donaldson invariants via methods of algebraic geometry and has led to a lot of activity on moduli spaces of vector bundles and coherent sheaves on algebraic surfaces. We will first recall the definition of the Donaldson invariants via gauge theory. Then we will show the relation between moduli spaces of anti-self-dual connections and moduli spaces of vector bundles on algebraic surfaces, and how this makes it possible to compute Donaldson invariants via algebraic geometry methods. Finally we concentrate on the case that the number b + of positive eigenvalues of the intersection form on the second homology of the 4-manifold is 1. In this case the Donaldson invariants depend on the metric (or in the algebraic geometric case on the polarization) via a system of walls and chambers. We will study the change of the invariants under wall-crossing, and use this in particular to compute the Donaldson invariants of rational algebraic surfaces. (author)

Controllability of symmetric spin networks

Science.gov (United States)

Albertini, Francesca; D'Alessandro, Domenico

2018-05-01

We consider a network of n spin 1/2 systems which are pairwise interacting via Ising interaction and are controlled by the same electro-magnetic control field. Such a system presents symmetries since the Hamiltonian is unchanged if we permute two spins. This prevents full (operator) controllability, in that not every unitary evolution can be obtained. We prove however that controllability is verified if we restrict ourselves to unitary evolutions which preserve the above permutation invariance. For low dimensional cases, n = 2 and n = 3, we provide an analysis of the Lie group of available evolutions and give explicit control laws to transfer between two arbitrary permutation invariant states. This class of states includes highly entangled states such as Greenberger-Horne-Zeilinger (GHZ) states and W states, which are of interest in quantum information.

Self-consistent many-body perturbation theory in range-separated density-functional theory

DEFF Research Database (Denmark)

Fromager, Emmanuel; Jensen, Hans Jørgen Aagaard

2008-01-01

effects adequately which, on the other hand, can be described by many-body perturbation theory MBPT. It is therefore of interest to develop a hybrid model which combines the best of both the MBPT and DFT approaches. This can be achieved by splitting the two-electron interaction into long-range and short...

Moment invariants for particle beams

International Nuclear Information System (INIS)

Lysenko, W.P.; Overley, M.S.

1988-01-01

The rms emittance is a certain function of second moments in 2-D phase space. It is preserved for linear uncoupled (1-D) motion. In this paper, the authors present new functions of moments that are invariants for coupled motion. These invariants were computed symbolically using a computer algebra system. Possible applications for these invariants are discussed. Also, approximate moment invariants for nonlinear motion are presented

Brain computation is organized via power-of-two-based permutation logic

Directory of Open Access Journals (Sweden)

Kun Xie

2016-11-01

Full Text Available There is considerable scientific interest in understanding how cell assemblies - the long-presumed computational motif - are organized so that the brain can generate cognitive behavior. The Theory of Connectivity proposes that the origin of intelligence is rooted in a power-of-two-based permutation logic (N=2i–1, giving rise to the specific-to-general cell-assembly organization capable of generating specific perceptions and memories, as well as generalized knowledge and flexible actions. We show that this power-of-two-based computational logic is widely used in cortical and subcortical circuits across animal species and is conserved for the processing of a variety of cognitive modalities including appetitive, emotional and social cognitions. However, modulatory neurons, such as dopaminergic neurons, use a simpler logic despite their distinct subtypes. Interestingly, this specific-to-general permutation logic remained largely intact despite the NMDA receptors – the synaptic switch for learning and memory – were deleted throughout adulthood, suggesting that it is likely developmentally pre-configured. Moreover, this logic is implemented in the cortex vertically via combining a random-connectivity strategy in superficial layers 2/3 with nonrandom organizations in deep layers 5/6. This randomness of layers 2/3 cliques – which preferentially encode specific and low-combinatorial features and project inter-cortically – is ideal for maximizing cross-modality novel pattern-extraction, pattern-discrimination, and pattern-categorization using sparse code, consequently explaining why it requires hippocampal offline-consolidation. In contrast, the non-randomness in layers 5/6 - which consists of few specific cliques but a higher portion of more general cliques projecting mostly to subcortical systems – is ideal for robust feedback-control of motivation, emotion, consciousness, and behaviors. These observations suggest that the brain’s basic

Feedback-Driven Dynamic Invariant Discovery

Science.gov (United States)

Zhang, Lingming; Yang, Guowei; Rungta, Neha S.; Person, Suzette; Khurshid, Sarfraz

2014-01-01

Program invariants can help software developers identify program properties that must be preserved as the software evolves, however, formulating correct invariants can be challenging. In this work, we introduce iDiscovery, a technique which leverages symbolic execution to improve the quality of dynamically discovered invariants computed by Daikon. Candidate invariants generated by Daikon are synthesized into assertions and instrumented onto the program. The instrumented code is executed symbolically to generate new test cases that are fed back to Daikon to help further re ne the set of candidate invariants. This feedback loop is executed until a x-point is reached. To mitigate the cost of symbolic execution, we present optimizations to prune the symbolic state space and to reduce the complexity of the generated path conditions. We also leverage recent advances in constraint solution reuse techniques to avoid computing results for the same constraints across iterations. Experimental results show that iDiscovery converges to a set of higher quality invariants compared to the initial set of candidate invariants in a small number of iterations.

Exploring excited eigenstates of many-body systems using the functional renormalization group

Science.gov (United States)

Klöckner, Christian; Kennes, Dante Marvin; Karrasch, Christoph

2018-05-01

We introduce approximate, functional renormalization group based schemes to obtain correlation functions in pure excited eigenstates of large fermionic many-body systems at arbitrary energies. The algorithms are thoroughly benchmarked and their strengths and shortcomings are documented using a one-dimensional interacting tight-binding chain as a prototypical testbed. We study two "toy applications" from the world of Luttinger liquid physics: the survival of power laws in lowly excited states as well as the spectral function of high-energy "block" excitations, which feature several single-particle Fermi edges.

Ordered kinematic endpoints for 5-body cascade decays

Energy Technology Data Exchange (ETDEWEB)

Klimek, Matthew D. [Theory Group, Department of Physics and Texas Cosmology Center,University of Texas at Austin, 2515 Speedway, Stop C1608, Austin, TX, 78712 (United States)

2016-12-23

We present expressions for the kinematic endpoints of 5-body cascade decay chains proceeding through all possible combinations of 2-body and 3-body decays, with one stable invisible particle in the final decay stage. When an invariant mass can be formed in multiple ways by choosing different final state particles from a common vertex, we introduce techniques for finding the sub-leading endpoints for all indistinguishable versions of the invariant mass. In contrast to short decay chains, where sub-leading endpoints are linearly related to the leading endpoints, we find that in 5-body decays, they provide additional independent constraints on the mass spectrum.

Relating measurement invariance, cross-level invariance, and multilevel reliability

OpenAIRE

Jak, S.; Jorgensen, T.D.

2017-01-01

Data often have a nested, multilevel structure, for example when data are collected from children in classrooms. This kind of data complicate the evaluation of reliability and measurement invariance, because several properties can be evaluated at both the individual level and the cluster level, as well as across levels. For example, cross-level invariance implies equal factor loadings across levels, which is needed to give latent variables at the two levels a similar interpretation. Reliabili...

Communication: Random phase approximation renormalized many-body perturbation theory

International Nuclear Information System (INIS)

Bates, Jefferson E.; Furche, Filipp

2013-01-01

We derive a renormalized many-body perturbation theory (MBPT) starting from the random phase approximation (RPA). This RPA-renormalized perturbation theory extends the scope of single-reference MBPT methods to small-gap systems without significantly increasing the computational cost. The leading correction to RPA, termed the approximate exchange kernel (AXK), substantially improves upon RPA atomization energies and ionization potentials without affecting other properties such as barrier heights where RPA is already accurate. Thus, AXK is more balanced than second-order screened exchange [A. Grüneis et al., J. Chem. Phys. 131, 154115 (2009)], which tends to overcorrect RPA for systems with stronger static correlation. Similarly, AXK avoids the divergence of second-order Møller-Plesset (MP2) theory for small gap systems and delivers a much more consistent performance than MP2 across the periodic table at comparable cost. RPA+AXK thus is an accurate, non-empirical, and robust tool to assess and improve semi-local density functional theory for a wide range of systems previously inaccessible to first-principles electronic structure calculations

Nuclear many-body problem with repulsive hard core interactions

Energy Technology Data Exchange (ETDEWEB)

Haddad, L M

1965-07-01

The nuclear many-body problem is considered using the perturbation-theoretic approach of Brueckner and collaborators. This approach is outlined with particular attention paid to the graphical representation of the terms in the perturbation expansion. The problem is transformed to centre-of-mass coordinates in configuration space and difficulties involved in ordinary methods of solution of the resulting equation are discussed. A new technique, the 'reference spectrum method', devised by Bethe, Brandow and Petschek in an attempt to simplify the numerical work in presented. The basic equations are derived in this approximation and considering the repulsive hard core part of the interaction only, the effective mass is calculated at high momentum (using the same energy spectrum for both 'particle' and 'hole' states). The result of 0.87m is in agreement with that of Bethe et al. A more complete treatment using the reference spectrum method in introduced and a self-consistent set of equations is established for the reference spectrum parameters again for the case of hard core repulsions. (author)

Many body effects in nuclear matter QCD sum rules

Science.gov (United States)

Drukarev, E. G.; Ryskin, M. G.; Sadovnikova, V. A.

2017-12-01

We calculate the single-particle nucleon characteristics in symmetric nuclear matter with inclusion of the 3N and 4N interactions. We calculated the contribution of the 3N interactions earlier, now we add that of the 4N ones. The contribution of the 4N forces to nucleon self energies is expressed in terms of the nonlocal scalar condensate (d = 3) and of the configurations of the vector-scalar and the scalar-scalar quark condensates (d = 6) in which two diquark operators act on two different nucleons of the matter.These four-quark condensates are obtained in the model-independent way. The density dependence of the nucleon effective mass, of the vector self energy and of the single-particle potential energy are obtained. We traced the dependence of the nucleon characteristics on the actual value of the pion-nucleon sigma term. We obtained also the nucleon characteristics in terms of the quasifree nucleons, with the noninteracting nucleons surrounded by their pion clouds as the starting point. This approach leads to strict hierarchy of the many body forces.

Many-body theory of effective mass in degenerate semiconductors

Science.gov (United States)

Tripathi, G. S.; Shadangi, S. K.

2018-03-01

We derive the many-body theory of the effective mass in the effective mass representation (EMR). In the EMR, we need to solve the equation of motion of an electron in the presence of electron-electron interactions, where the wavefunction is expanded over a complete set of Luttinger-Kohn wavefunctions. We use the Luttinger-Ward thermodynamic potential and the Green’s function perturbation to derive an expression for the band effective mass by taking into account the electron-electron interactions. Both quasi-particle and the correlation contributions are considered. We show that had we considered only the quasi-particle contribution, we would have missed important cancellations. Thus the correlated motion of electrons has important effects in the renormalization of the effective mass. Considering the exchange self-energy in the band model, we derive a tractable expression for the band effective mass. We apply the theory to n-type degenerate semiconductors, PbTe and SnTe, and analyze the impact of the theory on the anisotropic effective mass of the conduction bands in these systems.

Foliated vector fields, the Godbillon-Vey invariant and the invariant I(F)

International Nuclear Information System (INIS)

Banyaga, A.; Landa, Alain Musesa

2004-03-01

We prove that if the invariant I(F) constructed in 'An invariant of contact structures and transversally oriented foliations', Ann. Global Analysis and Geom. 14(1996) 427-441 (A. Banyaga), through the Lie algebra of infinitesimal automorphisms of transversally oriented foliations F is trivial, then the Godbillon-Vey invariant GV (F) of F is also trivial, but that the converse is not true. For codimension one foliations, the restrictions I τ , (F) of I(F) to the Lie subalgebra of vector fields tangent to the leaves is the Reeb class R(F) of F. We also prove that if there exists a foliated vector field which is everywhere transverse to a codimension one foliation, then the Reeb class R(F) is trivial, hence so is the GV(F) invariant. (author)

Amplitude-aware permutation entropy: Illustration in spike detection and signal segmentation.

Science.gov (United States)

Azami, Hamed; Escudero, Javier

2016-05-01

Signal segmentation and spike detection are two important biomedical signal processing applications. Often, non-stationary signals must be segmented into piece-wise stationary epochs or spikes need to be found among a background of noise before being further analyzed. Permutation entropy (PE) has been proposed to evaluate the irregularity of a time series. PE is conceptually simple, structurally robust to artifacts, and computationally fast. It has been extensively used in many applications, but it has two key shortcomings. First, when a signal is symbolized using the Bandt-Pompe procedure, only the order of the amplitude values is considered and information regarding the amplitudes is discarded. Second, in the PE, the effect of equal amplitude values in each embedded vector is not addressed. To address these issues, we propose a new entropy measure based on PE: the amplitude-aware permutation entropy (AAPE). AAPE is sensitive to the changes in the amplitude, in addition to the frequency, of the signals thanks to it being more flexible than the classical PE in the quantification of the signal motifs. To demonstrate how the AAPE method can enhance the quality of the signal segmentation and spike detection, a set of synthetic and realistic synthetic neuronal signals, electroencephalograms and neuronal data are processed. We compare the performance of AAPE in these problems against state-of-the-art approaches and evaluate the significance of the differences with a repeated ANOVA with post hoc Tukey's test. In signal segmentation, the accuracy of AAPE-based method is higher than conventional segmentation methods. AAPE also leads to more robust results in the presence of noise. The spike detection results show that AAPE can detect spikes well, even when presented with single-sample spikes, unlike PE. For multi-sample spikes, the changes in AAPE are larger than in PE. We introduce a new entropy metric, AAPE, that enables us to consider amplitude information in the

Index of French nuclear literature: IBM 360 programmes for preparing the permuted index of French titles

International Nuclear Information System (INIS)

Chonez, Nicole

1968-12-01

This report contains the assembly list, the flow chart and some comments about each of the IBM 360 assembler language programmes used for preparing one of the subject indexes contained in the bibliographical bulletin entitled: 'Index de la Litterature nucleaire francaise'; this bulletin has been produced by the French C.E.A. since 1968. Only the processing phases from the magnetic tape file of the bibliographical references, assumed correct, to the printing out of the permuted index obtained with the French titles of the documents on the tape are considered here. This permuted index has the peculiarity of automatically regrouping synonyms and certain grammatical variations of the words. (author) [fr

Torsional Topological Invariants (and their relevance for real life)

CERN Document Server

Chandia, O; Chandia, Osvaldo; Zanelli, Jorge

1997-01-01

The existence of topological invariants analogous to Chern/Pontryagin classes for a standard $SO(D)$ or SU(N) connection, but constructed out of the torsion tensor, is discussed. These invariants exhibit many of the features of the Chern/Pontryagin invariants: they can be expressed as integrals over the manifold of local densities and take integer values on compact spaces without boundary; their spectrum is determined by the homotopy groups determined by the connection bundle but depend also on the bundle of local orthonormal frames on the tangent space of the manifold. It is shown that in spacetimes with nonvanishing torsion there can occur topologically stable configurations associated with the frame bundle which are independent of the curvature. Explicit examples of topologically stable configurations carrying nonvanishing instanton number in four and eight dimensions are given, and they can be conjectured to exist in dimension $4k$. It is also shown that the chiral anomaly in a spacetime with torsion rece...

Atoms as many-body systems

International Nuclear Information System (INIS)

Amusia, M.Ya.

1995-01-01

The author presents this article in the volume, dedicated to the 70th birthday of Academician S. T. Belyaev. He has known him personally since 1961 and admires his profound contributions to the theory of Bose-liquids, to the theory of superconductivity of atomic nuclei and some other important scientific works. Belyaev is well known also as an organizer of science and education. For years he was, and is still the Chairman of the Synchrotron Radiation Commission of the Russian Academy of Science, a body which was established long ago to promote construction of high intensity light sources, and technological as well as scientific research using this light. One of the important directions of this study is investigation of photoabsorbtion by multielectron atoms in order to obtain information about their structure

Performance Optimization of Tensor Contraction Expressions for Many Body Methods in Quantum Chemistry

International Nuclear Information System (INIS)

Hartono, Albert; Lu, Qingda; Henretty, Thomas; Krishnamoorthy, Sriram; Zhang, Huaijian; Baumgartner, Gerald; Bernholdt, David E.; Nooijen, Marcel; Pitzer, Russell M.; Ramanujam, J.; Sadayappan, Ponnuswamy

2009-01-01

Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the coupled cluster method. This paper addresses two complementary aspects of performance optimization of such tensor contraction expressions. Transformations using algebraic properties of commutativity and associativity can be used to significantly decrease the number of arithmetic operations required for evaluation of these expressions. The identification of common subexpressions among a set of tensor contraction expressions can result in a reduction of the total number of operations required to evaluate the tensor contractions. The first part of the paper describes an effective algorithm for operation minimization with common subexpression identification and demonstrates its effectiveness on tensor contraction expressions for coupled cluster equations. The second part of the paper highlights the importance of data layout transformation in the optimization of tensor contraction computations on modern processors. A number of considerations such as minimization of cache misses and utilization of multimedia vector instructions are discussed. A library for efficient index permutation of multi-dimensional tensors is described and experimental performance data is provided that demonstrates its effectiveness.

Performance Optimization of Tensor Contraction Expressions for Many Body Methods in Quantum Chemistry

International Nuclear Information System (INIS)

Krishnamoorthy, Sriram; Bernholdt, David E.; Pitzer, R.M.; Sadayappan, Ponnuswamy

2009-01-01

Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the coupled cluster method. This paper addresses two complementary aspects of performance optimization of such tensor contraction expressions. Transformations using algebraic properties of commutativity and associativity can be used to significantly decrease the number of arithmetic operations required for evaluation of these expressions. The identification of common subexpressions among a set of tensor contraction expressions can result in a reduction of the total number of operations required to evaluate the tensor contractions. The first part of the paper describes an effective algorithm for operation minimization with common subexpression identification and demonstrates its effectiveness on tensor contraction expressions for coupled cluster equations. The second part of the paper highlights the importance of data layout transformation in the optimization of tensor contraction computations on modern processors. A number of considerations, such as minimization of cache misses and utilization of multimedia vector instructions, are discussed. A library for efficient index permutation of multidimensional tensors is described, and experimental performance data is provided that demonstrates its effectiveness.

Link invariants from finite Coxeter racks

OpenAIRE

Nelson, Sam; Wieghard, Ryan

2008-01-01

We study Coxeter racks over $\\mathbb{Z}_n$ and the knot and link invariants they define. We exploit the module structure of these racks to enhance the rack counting invariants and give examples showing that these enhanced invariants are stronger than the unenhanced rack counting invariants.

Evidence for several dipolar quasi-invariants in liquid crystals

Science.gov (United States)

Bonin, C. J.; González, C. E.; Segnorile, H. H.; Zamar, R. C.

2013-10-01

The quasi-equilibrium states of an observed quantum system involve as many constants of motion as the dimension of the operator basis which spans the blocks of all the degenerate eigenvalues of the Hamiltonian that drives the system dynamics, however, the possibility of observing such quasi-invariants in solid-like spin systems in Nuclear Magnetic Resonance (NMR) is not a strictly exact prediction. The aim of this work is to provide experimental evidence of several quasi-invariants, in the proton NMR of small spin clusters, like nematic liquid crystal molecules, in which the use of thermodynamic arguments is not justified. We explore the spin states prepared with the Jeener-Broekaert pulse sequence by analyzing the time-domain signals yielded by this sequence as a function of the preparation times, in a variety of dipolar networks, solids, and liquid crystals. We observe that the signals can be explained with two dipolar quasi-invariants only within a range of short preparation times, however at longer times liquid crystal signals show an echo-like behaviour whose description requires assuming more quasi-invariants. We study the multiple quantum coherence content of such signals on a basis orthogonal to the z-basis and see that such states involve a significant number of correlated spins. Therefore, we show that the NMR signals within the whole preparation time-scale can only be reconstructed by assuming the occurrence of multiple quasi-invariants which we experimentally isolate.

Rotation-invariant neural pattern recognition system with application to coin recognition.

Science.gov (United States)

Fukumi, M; Omatu, S; Takeda, F; Kosaka, T

1992-01-01

In pattern recognition, it is often necessary to deal with problems to classify a transformed pattern. A neural pattern recognition system which is insensitive to rotation of input pattern by various degrees is proposed. The system consists of a fixed invariance network with many slabs and a trainable multilayered network. The system was used in a rotation-invariant coin recognition problem to distinguish between a 500 yen coin and a 500 won coin. The results show that the approach works well for variable rotation pattern recognition.

Filtration of the classical knot concordance group and Casson-Gordon invariants

OpenAIRE

Kim, Taehee

2002-01-01

It is known that if any prime power branched cyclic cover of a knot in the 3-sphere is a homology sphere, then the knot has vanishing Casson-Gordon invariants. We construct infinitely many examples of (topologically) non-slice knots in the 3-sphere whose prime power branched cyclic covers are homology spheres. We show that these knots generate an infinite rank subgroup of F_(1.0)/F_(1.5) for which Casson-Gordon invariants vanish in Cochran-Orr-Teichner's filtration of the classical knot conco...

Many-body physics using cold atoms

Science.gov (United States)

Sundar, Bhuvanesh

Advances in experiments on dilute ultracold atomic gases have given us access to highly tunable quantum systems. In particular, there have been substantial improvements in achieving different kinds of interaction between atoms. As a result, utracold atomic gases oer an ideal platform to simulate many-body phenomena in condensed matter physics, and engineer other novel phenomena that are a result of the exotic interactions produced between atoms. In this dissertation, I present a series of studies that explore the physics of dilute ultracold atomic gases in different settings. In each setting, I explore a different form of the inter-particle interaction. Motivated by experiments which induce artificial spin-orbit coupling for cold fermions, I explore this system in my first project. In this project, I propose a method to perform universal quantum computation using the excitations of interacting spin-orbit coupled fermions, in which effective p-wave interactions lead to the formation of a topological superfluid. Motivated by experiments which explore the physics of exotic interactions between atoms trapped inside optical cavities, I explore this system in a second project. I calculate the phase diagram of lattice bosons trapped in an optical cavity, where the cavity modes mediates effective global range checkerboard interactions between the atoms. I compare this phase diagram with one that was recently measured experimentally. In two other projects, I explore quantum simulation of condensed matter phenomena due to spin-dependent interactions between particles. I propose a method to produce tunable spin-dependent interactions between atoms, using an optical Feshbach resonance. In one project, I use these spin-dependent interactions in an ultracold Bose-Fermi system, and propose a method to produce the Kondo model. I propose an experiment to directly observe the Kondo effect in this system. In another project, I propose using lattice bosons with a large hyperfine spin

Tokunaga self-similarity arises naturally from time invariance

Science.gov (United States)

Kovchegov, Yevgeniy; Zaliapin, Ilya

2018-04-01

The Tokunaga condition is an algebraic rule that provides a detailed description of the branching structure in a self-similar tree. Despite a solid empirical validation and practical convenience, the Tokunaga condition lacks a theoretical justification. Such a justification is suggested in this work. We define a geometric branching process G (s ) that generates self-similar rooted trees. The main result establishes the equivalence between the invariance of G (s ) with respect to a time shift and a one-parametric version of the Tokunaga condition. In the parameter region where the process satisfies the Tokunaga condition (and hence is time invariant), G (s ) enjoys many of the symmetries observed in a critical binary Galton-Watson branching process and reproduces the latter for a particular parameter value.

Many-Body Quantum Spin Dynamics with Monte Carlo Trajectories on a Discrete Phase Space

Directory of Open Access Journals (Sweden)

J. Schachenmayer

2015-02-01

Full Text Available Interacting spin systems are of fundamental relevance in different areas of physics, as well as in quantum information science and biology. These spin models represent the simplest, yet not fully understood, manifestation of quantum many-body systems. An important outstanding problem is the efficient numerical computation of dynamics in large spin systems. Here, we propose a new semiclassical method to study many-body spin dynamics in generic spin lattice models. The method is based on a discrete Monte Carlo sampling in phase space in the framework of the so-called truncated Wigner approximation. Comparisons with analytical and numerically exact calculations demonstrate the power of the technique. They show that it correctly reproduces the dynamics of one- and two-point correlations and spin squeezing at short times, thus capturing entanglement. Our results open the possibility to study the quantum dynamics accessible to recent experiments in regimes where other numerical methods are inapplicable.

Relativistic many-body theory of high density matter

International Nuclear Information System (INIS)

Chin, S.A.

1977-01-01

A fully relativistic quantum many-body theory is applied to the study of high-density matter. The latter is identified with the zero-temperature ground state of a system of interacting baryons. In accordance with the observed short-range repulsive and long-range attractive character of the nucleon--nucleon force, baryons are described as interacting with each other via a massive scalar and a massive vector meson exchange. In the Hartree approximation, the theory yields the same result as the mean-field theory, but with additional vacuum fluctuation corrections. The resultant equation of state for neutron matter is used to determine properties of neutron stars. The relativistic exchange energy, its corresponding single-particle excitation spectrum, and its effect on the neutron matter equation of state, are calculated. The correlation energy from summing the set of ring diagrams is derived directly from the energy-momentum tensor, with renormalization carried out by adding counterterms to the original Lagrangian and subtracting purely vacuum expectation values. Terms of order g 4 lng 2 are explicitly given. Effects of scalar-vector mixing are discussed. Collective modes corresponding to macroscopic density fluctuation are investigated. Two basic modes are found, a plasma-like mode and zero sound, with the latter dominant at high density. The stability and damping of these modes are studied. Last, the effect of vacuum polarization in high-density matter is examined

Gibbs Measures of Nonlinear Schrödinger Equations as Limits of Many-Body Quantum States in Dimensions {d ≤slant 3}

Science.gov (United States)

Fröhlich, Jürg; Knowles, Antti; Schlein, Benjamin; Sohinger, Vedran

2017-12-01

We prove that Gibbs measures of nonlinear Schrödinger equations arise as high-temperature limits of thermal states in many-body quantum mechanics. Our results hold for defocusing interactions in dimensions {d =1,2,3}. The many-body quantum thermal states that we consider are the grand canonical ensemble for d = 1 and an appropriate modification of the grand canonical ensemble for {d =2,3}. In dimensions d = 2, 3, the Gibbs measures are supported on singular distributions, and a renormalization of the chemical potential is necessary. On the many-body quantum side, the need for renormalization is manifested by a rapid growth of the number of particles. We relate the original many-body quantum problem to a renormalized version obtained by solving a counterterm problem. Our proof is based on ideas from field theory, using a perturbative expansion in the interaction, organized by using a diagrammatic representation, and on Borel resummation of the resulting series.

Rotation Invariance Neural Network

OpenAIRE

Li, Shiyuan

2017-01-01

Rotation invariance and translation invariance have great values in image recognition tasks. In this paper, we bring a new architecture in convolutional neural network (CNN) named cyclic convolutional layer to achieve rotation invariance in 2-D symbol recognition. We can also get the position and orientation of the 2-D symbol by the network to achieve detection purpose for multiple non-overlap target. Last but not least, this architecture can achieve one-shot learning in some cases using thos...

Permutation entropy with vector embedding delays

Science.gov (United States)

Little, Douglas J.; Kane, Deb M.

2017-12-01

Permutation entropy (PE) is a statistic used widely for the detection of structure within a time series. Embedding delay times at which the PE is reduced are characteristic timescales for which such structure exists. Here, a generalized scheme is investigated where embedding delays are represented by vectors rather than scalars, permitting PE to be calculated over a (D -1 ) -dimensional space, where D is the embedding dimension. This scheme is applied to numerically generated noise, sine wave and logistic map series, and experimental data sets taken from a vertical-cavity surface emitting laser exhibiting temporally localized pulse structures within the round-trip time of the laser cavity. Results are visualized as PE maps as a function of embedding delay, with low PE values indicating combinations of embedding delays where correlation structure is present. It is demonstrated that vector embedding delays enable identification of structure that is ambiguous or masked, when the embedding delay is constrained to scalar form.

Multiscale permutation entropy analysis of electrocardiogram

Science.gov (United States)

Liu, Tiebing; Yao, Wenpo; Wu, Min; Shi, Zhaorong; Wang, Jun; Ning, Xinbao

2017-04-01

To make a comprehensive nonlinear analysis to ECG, multiscale permutation entropy (MPE) was applied to ECG characteristics extraction to make a comprehensive nonlinear analysis of ECG. Three kinds of ECG from PhysioNet database, congestive heart failure (CHF) patients, healthy young and elderly subjects, are applied in this paper. We set embedding dimension to 4 and adjust scale factor from 2 to 100 with a step size of 2, and compare MPE with multiscale entropy (MSE). As increase of scale factor, MPE complexity of the three ECG signals are showing first-decrease and last-increase trends. When scale factor is between 10 and 32, complexities of the three ECG had biggest difference, entropy of the elderly is 0.146 less than the CHF patients and 0.025 larger than the healthy young in average, in line with normal physiological characteristics. Test results showed that MPE can effectively apply in ECG nonlinear analysis, and can effectively distinguish different ECG signals.

Many-body perturbation theory using the density-functional concept: beyond the GW approximation

OpenAIRE

Bruneval, Fabien; Sottile, Francesco; Olevano, Valerio; Del Sole, Rodolfo; Reining, Lucia

2005-01-01

We propose an alternative formulation of Many-Body Perturbation Theory that uses the density-functional concept. Instead of the usual four-point integral equation for the polarizability, we obtain a two-point one, that leads to excellent optical absorption and energy loss spectra. The corresponding three-point vertex function and self-energy are then simply calculated via an integration, for any level of approximation. Moreover, we show the direct impact of this formulation on the time-depend...

Lorentz invariance with an invariant energy scale.

Science.gov (United States)

Magueijo, João; Smolin, Lee

2002-05-13

We propose a modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einstein's theory at low energies. This is accomplished by a nonlinear modification of the action of the Lorentz group on momentum space, generated by adding a dilatation to each boost in such a way that the Planck energy remains invariant. The associated algebra has unmodified structure constants. We also discuss the resulting modifications of field theory and suggest a modification of the equivalence principle which determines how the new theory is embedded in general relativity.

Permutation flow-shop scheduling problem to optimize a quadratic objective function

Science.gov (United States)

Ren, Tao; Zhao, Peng; Zhang, Da; Liu, Bingqian; Yuan, Huawei; Bai, Danyu

2017-09-01

A flow-shop scheduling model enables appropriate sequencing for each job and for processing on a set of machines in compliance with identical processing orders. The objective is to achieve a feasible schedule for optimizing a given criterion. Permutation is a special setting of the model in which the processing order of the jobs on the machines is identical for each subsequent step of processing. This article addresses the permutation flow-shop scheduling problem to minimize the criterion of total weighted quadratic completion time. With a probability hypothesis, the asymptotic optimality of the weighted shortest processing time schedule under a consistency condition (WSPT-CC) is proven for sufficiently large-scale problems. However, the worst case performance ratio of the WSPT-CC schedule is the square of the number of machines in certain situations. A discrete differential evolution algorithm, where a new crossover method with multiple-point insertion is used to improve the final outcome, is presented to obtain high-quality solutions for moderate-scale problems. A sequence-independent lower bound is designed for pruning in a branch-and-bound algorithm for small-scale problems. A set of random experiments demonstrates the performance of the lower bound and the effectiveness of the proposed algorithms.

Proceedings of the fifth symposium on simulation of hadronic many-body system

Energy Technology Data Exchange (ETDEWEB)

Chiba, Satoshi; Maruyama, Toshiki [eds.

1998-07-01

The fifth symposium on Simulation of Hadronic Many-Body System, organized by the Research Group for Hadron Transport Theory, Advanced Science Research Center, was held at Tokai Research Establishment of JAERI on March 3 and 4, 1998. The symposium was devoted for discussion and presentation of research results on light- and heavy-ion induced nuclear reactions in terms of microscopic simulation method, while wide variety of other topics were also presented such as nuclear structure, properties of nuclear matter and high-energy multi-fragmentation experiments. The 17 of the presented papers are indexed individually. (J.P.N.)

Preparing and probing many-body correlated systems in a Quantum Gas Microscope by engineering arbitrary landscape potentials

Science.gov (United States)

Rispoli, Matthew; Lukin, Alexander; Ma, Ruichao; Preiss, Philipp; Tai, M. Eric; Islam, Rajibul; Greiner, Markus

2015-05-01

Ultracold atoms in optical lattices provide a versatile tool box for observing the emergence of strongly correlated physics in quantum systems. Dynamic control of optical potentials on the single-site level allows us to prepare and probe many-body quantum states through local Hamiltonian engineering. We achieve these high precision levels of optical control through spatial light modulation with a DMD (digital micro-mirror device). This allows for both arbitrary beam shaping and aberration compensation in our imaging system to produce high fidelity optical potentials. We use these techniques to control state initialization, Hamiltonian dynamics, and measurement in experiments investigating low-dimensional many-body physics - from one-dimensional correlated quantum walks to characterizing entanglement.

MCPerm: a Monte Carlo permutation method for accurately correcting the multiple testing in a meta-analysis of genetic association studies.

Directory of Open Access Journals (Sweden)

Yongshuai Jiang

Full Text Available Traditional permutation (TradPerm tests are usually considered the gold standard for multiple testing corrections. However, they can be difficult to complete for the meta-analyses of genetic association studies based on multiple single nucleotide polymorphism loci as they depend on individual-level genotype and phenotype data to perform random shuffles, which are not easy to obtain. Most meta-analyses have therefore been performed using summary statistics from previously published studies. To carry out a permutation using only genotype counts without changing the size of the TradPerm P-value, we developed a Monte Carlo permutation (MCPerm method. First, for each study included in the meta-analysis, we used a two-step hypergeometric distribution to generate a random number of genotypes in cases and controls. We then carried out a meta-analysis using these random genotype data. Finally, we obtained the corrected permutation P-value of the meta-analysis by repeating the entire process N times. We used five real datasets and five simulation datasets to evaluate the MCPerm method and our results showed the following: (1 MCPerm requires only the summary statistics of the genotype, without the need for individual-level data; (2 Genotype counts generated by our two-step hypergeometric distributions had the same distributions as genotype counts generated by shuffling; (3 MCPerm had almost exactly the same permutation P-values as TradPerm (r = 0.999; P<2.2e-16; (4 The calculation speed of MCPerm is much faster than that of TradPerm. In summary, MCPerm appears to be a viable alternative to TradPerm, and we have developed it as a freely available R package at CRAN: http://cran.r-project.org/web/packages/MCPerm/index.html.

The Dynamical Invariant of Open Quantum System

OpenAIRE

Wu, S. L.; Zhang, X. Y.; Yi, X. X.

2015-01-01

The dynamical invariant, whose expectation value is constant, is generalized to open quantum system. The evolution equation of dynamical invariant (the dynamical invariant condition) is presented for Markovian dynamics. Different with the dynamical invariant for the closed quantum system, the evolution of the dynamical invariant for the open quantum system is no longer unitary, and the eigenvalues of it are time-dependent. Since any hermitian operator fulfilling dynamical invariant condition ...

Synthesizing Modular Invariants for Synchronous Code

Directory of Open Access Journals (Sweden)

Pierre-Loic Garoche

2014-12-01

Full Text Available In this paper, we explore different techniques to synthesize modular invariants for synchronous code encoded as Horn clauses. Modular invariants are a set of formulas that characterizes the validity of predicates. They are very useful for different aspects of analysis, synthesis, testing and program transformation. We describe two techniques to generate modular invariants for code written in the synchronous dataflow language Lustre. The first technique directly encodes the synchronous code in a modular fashion. While in the second technique, we synthesize modular invariants starting from a monolithic invariant. Both techniques, take advantage of analysis techniques based on property-directed reachability. We also describe a technique to minimize the synthesized invariants.

Hidden scale invariance of metals

DEFF Research Database (Denmark)

Hummel, Felix; Kresse, Georg; Dyre, Jeppe C.

2015-01-01

Density functional theory (DFT) calculations of 58 liquid elements at their triple point show that most metals exhibit near proportionality between the thermal fluctuations of the virial and the potential energy in the isochoric ensemble. This demonstrates a general “hidden” scale invariance...... of metals making the condensed part of the thermodynamic phase diagram effectively one dimensional with respect to structure and dynamics. DFT computed density scaling exponents, related to the Grüneisen parameter, are in good agreement with experimental values for the 16 elements where reliable data were...... available. Hidden scale invariance is demonstrated in detail for magnesium by showing invariance of structure and dynamics. Computed melting curves of period three metals follow curves with invariance (isomorphs). The experimental structure factor of magnesium is predicted by assuming scale invariant...

Relativistic two-body forces in many-body systems

International Nuclear Information System (INIS)

Namyslowski, J.M.

1979-01-01

For the fully off-shell extension in the relativistic dynamics, based on a covariant light-front field theory, we define the relative momenta and their proper angular variables such that -1 < cos theta/sub α/ < 1. In terms of these variables and the timelike total momenta we write explicitly the Weinberg interaction, corresponding to the exchange of a spinless particle of mass μ. The total momentum dependence and the cluster decomposition property of the Weinberg interaction are presented in detail, together with its energy dependence and other nonlocal features. In the nonrelativistic limit we recover the Yukawa interaction, while for the finite masses the Weinberg interaction is a product of the Yukawa interaction and a form factor. The Weinberg two-body force goes to zero at large energies and is truly nonlocal, in spite of the fact that the underlying field theory has a local Lagrangian