WorldWideScience

Sample records for quantum statistical model

  1. Statistical transmutation in doped quantum dimer models.

    Science.gov (United States)

    Lamas, C A; Ralko, A; Cabra, D C; Poilblanc, D; Pujol, P

    2012-07-06

    We prove a "statistical transmutation" symmetry of doped quantum dimer models on the square, triangular, and kagome lattices: the energy spectrum is invariant under a simultaneous change of statistics (i.e., bosonic into fermionic or vice versa) of the holes and of the signs of all the dimer resonance loops. This exact transformation enables us to define the duality equivalence between doped quantum dimer Hamiltonians and provides the analytic framework to analyze dynamical statistical transmutations. We investigate numerically the doping of the triangular quantum dimer model with special focus on the topological Z(2) dimer liquid. Doping leads to four (instead of two for the square lattice) inequivalent families of Hamiltonians. Competition between phase separation, superfluidity, supersolidity, and fermionic phases is investigated in the four families.

  2. Current algebra, statistical mechanics and quantum models

    Science.gov (United States)

    Vilela Mendes, R.

    2017-11-01

    Results obtained in the past for free boson systems at zero and nonzero temperatures are revisited to clarify the physical meaning of current algebra reducible functionals which are associated to systems with density fluctuations, leading to observable effects on phase transitions. To use current algebra as a tool for the formulation of quantum statistical mechanics amounts to the construction of unitary representations of diffeomorphism groups. Two mathematical equivalent procedures exist for this purpose. One searches for quasi-invariant measures on configuration spaces, the other for a cyclic vector in Hilbert space. Here, one argues that the second approach is closer to the physical intuition when modelling complex systems. An example of application of the current algebra methodology to the pairing phenomenon in two-dimensional fermion systems is discussed.

  3. Quantum statistical model for hot dense matter

    International Nuclear Information System (INIS)

    Rukhsana Kouser; Tasneem, G.; Saleem Shahzad, M.; Shafiq-ur-Rehman; Nasim, M.H.; Amjad Ali

    2015-01-01

    In solving numerous applied problems, one needs to know the equation of state, photon absorption coefficient and opacity of substances employed. We present a code for absorption coefficient and opacity calculation based on quantum statistical model. A self-consistent method for the calculation of potential is used. By solving Schrödinger equation with self-consistent potential we find energy spectrum of quantum mechanical system and corresponding wave functions. In addition we find mean occupation numbers of electron states and average charge state of the substance studied. The main processes of interaction of radiation with matter included in our opacity calculation are photon absorption in spectral lines (Bound-bound), photoionization (Bound-free), inverse bremsstrahlung (Free-free), Compton and Thomson scattering. Bound-bound line shape function has contribution from natural, Doppler, fine structure, collisional and stark broadening. To illustrate the main features of the code and its capabilities, calculation of average charge state, absorption coefficient, Rosseland and Planck mean and group opacities of aluminum and iron are presented. Results are satisfactorily compared with the published data. (authors)

  4. Carrier Statistics and Quantum Capacitance Models of Graphene Nanoscroll

    Directory of Open Access Journals (Sweden)

    M. Khaledian

    2014-01-01

    schematic perfect scroll-like Archimedes spiral. The DOS model was derived at first, while it was later applied to compute the carrier concentration and quantum capacitance model. Furthermore, the carrier concentration and quantum capacitance were modeled for both degenerate and nondegenerate regimes, along with examining the effect of structural parameters and chirality number on the density of state and carrier concentration. Latterly, the temperature effect on the quantum capacitance was studied too.

  5. On quantum statistical inference

    NARCIS (Netherlands)

    Barndorff-Nielsen, O.E.; Gill, R.D.; Jupp, P.E.

    2003-01-01

    Interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially, in step with dramatic new developments in experimental techniques for studying small quantum systems. Furthermore, developments in the theory of quantum measurements have

  6. Generalized quantum statistics

    International Nuclear Information System (INIS)

    Chou, C.

    1992-01-01

    In the paper, a non-anyonic generalization of quantum statistics is presented, in which Fermi-Dirac statistics (FDS) and Bose-Einstein statistics (BES) appear as two special cases. The new quantum statistics, which is characterized by the dimension of its single particle Fock space, contains three consistent parts, namely the generalized bilinear quantization, the generalized quantum mechanical description and the corresponding statistical mechanics

  7. A statistical model of structure functions and quantum chromodynamics

    International Nuclear Information System (INIS)

    Mac, E.; Ugaz, E.; Universidad Nacional de Ingenieria, Lima

    1989-01-01

    We consider a model for the x-dependence of the quark distributions in the proton. Within the context of simple statistical assumptions, we obtain the parton densities in the infinite momentum frame. In a second step lowest order QCD corrections are incorporated to these distributions. Crude, but reasonable, agreement with experiment is found for the F 2 , valence and q, anti q distributions for x> or approx.0.2. (orig.)

  8. Fractional statistics and quantum theory

    CERN Document Server

    Khare, Avinash

    1997-01-01

    This book explains the subtleties of quantum statistical mechanics in lower dimensions and their possible ramifications in quantum theory. The discussion is at a pedagogical level and is addressed to both graduate students and advanced research workers with a reasonable background in quantum and statistical mechanics. The main emphasis will be on explaining new concepts. Topics in the first part of the book includes the flux tube model of anyons, the braid group and quantum and statistical mechanics of noninteracting anyon gas. The second part of the book provides a detailed discussion about f

  9. Generalized interpolative quantum statistics

    International Nuclear Information System (INIS)

    Ramanathan, R.

    1992-01-01

    A generalized interpolative quantum statistics is presented by conjecturing a certain reordering of phase space due to the presence of possible exotic objects other than bosons and fermions. Such an interpolation achieved through a Bose-counting strategy predicts the existence of an infinite quantum Boltzmann-Gibbs statistics akin to the one discovered by Greenberg recently

  10. On quantum statistical inference

    NARCIS (Netherlands)

    Barndorff-Nielsen, O.E.; Gill, R.D.; Jupp, P.E.

    2001-01-01

    Recent developments in the mathematical foundations of quantum mechanics have brought the theory closer to that of classical probability and statistics. On the other hand, the unique character of quantum physics sets many of the questions addressed apart from those met classically in stochastics.

  11. On quantum statistical inference

    DEFF Research Database (Denmark)

    Barndorff-Nielsen, Ole Eiler; Gill, Richard D.; Jupp, Peter E.

    Recent developments in the mathematical foundations of quantum mechanics have brought the theory closer to that of classical probability and statistics. On the other hand, the unique character of quantum physics sets many of the questions addressed apart from those met classically in stochastics....... Furthermore, concurrent advances in experimental techniques and in the theory of quantum computation have led to a strong interest in questions of quantum information, in particular in the sense of the amount of information about unknown parameters in given observational data or accessible through various...

  12. The Generalized Quantum Statistics

    OpenAIRE

    Hwang, WonYoung; Ji, Jeong-Young; Hong, Jongbae

    1999-01-01

    The concept of wavefunction reduction should be introduced to standard quantum mechanics in any physical processes where effective reduction of wavefunction occurs, as well as in the measurement processes. When the overlap is negligible, each particle obey Maxwell-Boltzmann statistics even if the particles are in principle described by totally symmetrized wavefunction [P.R.Holland, The Quantum Theory of Motion, Cambridge Unversity Press, 1993, p293]. We generalize the conjecture. That is, par...

  13. Beyond quantum microcanonical statistics

    International Nuclear Information System (INIS)

    Fresch, Barbara; Moro, Giorgio J.

    2011-01-01

    Descriptions of molecular systems usually refer to two distinct theoretical frameworks. On the one hand the quantum pure state, i.e., the wavefunction, of an isolated system is determined to calculate molecular properties and their time evolution according to the unitary Schroedinger equation. On the other hand a mixed state, i.e., a statistical density matrix, is the standard formalism to account for thermal equilibrium, as postulated in the microcanonical quantum statistics. In the present paper an alternative treatment relying on a statistical analysis of the possible wavefunctions of an isolated system is presented. In analogy with the classical ergodic theory, the time evolution of the wavefunction determines the probability distribution in the phase space pertaining to an isolated system. However, this alone cannot account for a well defined thermodynamical description of the system in the macroscopic limit, unless a suitable probability distribution for the quantum constants of motion is introduced. We present a workable formalism assuring the emergence of typical values of thermodynamic functions, such as the internal energy and the entropy, in the large size limit of the system. This allows the identification of macroscopic properties independently of the specific realization of the quantum state. A description of material systems in agreement with equilibrium thermodynamics is then derived without constraints on the physical constituents and interactions of the system. Furthermore, the canonical statistics is recovered in all generality for the reduced density matrix of a subsystem.

  14. Quantum statistical model of nuclear multifragmentation in the canonical ensemble method

    International Nuclear Information System (INIS)

    Toneev, V.D.; Ploszajczak, M.; Parvant, A.S.; Toneev, V.D.; Parvant, A.S.

    1999-01-01

    A quantum statistical model of nuclear multifragmentation is proposed. The recurrence equation method used the canonical ensemble makes the model solvable and transparent to physical assumptions and allows to get results without involving the Monte Carlo technique. The model exhibits the first order phase transition. Quantum statistics effects are clearly seen on the microscopic level of occupation numbers but are almost washed out for global thermodynamic variables and the averaged observables studied. In the latter case, the recurrence relations for multiplicity distributions of both intermediate-mass and all fragments are derived and the specific changes in the shape of multiplicity distributions in the narrow region of the transition temperature is stressed. The temperature domain favorable to search for the HBT effect is noted. (authors)

  15. Quantum statistical model of nuclear multifragmentation in the canonical ensemble method

    Energy Technology Data Exchange (ETDEWEB)

    Toneev, V.D.; Ploszajczak, M. [Grand Accelerateur National d' Ions Lourds (GANIL), 14 - Caen (France); Parvant, A.S. [Institute of Applied Physics, Moldova Academy of Sciences, MD Moldova (Ukraine); Parvant, A.S. [Joint Institute for Nuclear Research, Bogoliubov Lab. of Theoretical Physics, Dubna (Russian Federation)

    1999-07-01

    A quantum statistical model of nuclear multifragmentation is proposed. The recurrence equation method used the canonical ensemble makes the model solvable and transparent to physical assumptions and allows to get results without involving the Monte Carlo technique. The model exhibits the first order phase transition. Quantum statistics effects are clearly seen on the microscopic level of occupation numbers but are almost washed out for global thermodynamic variables and the averaged observables studied. In the latter case, the recurrence relations for multiplicity distributions of both intermediate-mass and all fragments are derived and the specific changes in the shape of multiplicity distributions in the narrow region of the transition temperature is stressed. The temperature domain favorable to search for the HBT effect is noted. (authors)

  16. Quantum Statistics and Entanglement Problems

    OpenAIRE

    Trainor, L. E. H.; Lumsden, Charles J.

    2002-01-01

    Interpretations of quantum measurement theory have been plagued by two questions, one concerning the role of observer consciousness and the other the entanglement phenomenon arising from the superposition of quantum states. We emphasize here the remarkable role of quantum statistics in describing the entanglement problem correctly and discuss the relationship to issues arising from current discussions of intelligent observers in entangled, decohering quantum worlds.

  17. Introduction to quantum statistical mechanics

    CERN Document Server

    Bogolyubov, N N

    2010-01-01

    Introduction to Quantum Statistical Mechanics (Second Edition) may be used as an advanced textbook by graduate students, even ambitious undergraduates in physics. It is also suitable for non experts in physics who wish to have an overview of some of the classic and fundamental quantum models in the subject. The explanation in the book is detailed enough to capture the interest of the reader, and complete enough to provide the necessary background material needed to dwell further into the subject and explore the research literature.

  18. Quantum Statistical Mechanics on a Quantum Computer

    NARCIS (Netherlands)

    Raedt, H. De; Hams, A.H.; Michielsen, K.; Miyashita, S.; Saito, K.; Saito, E.

    2000-01-01

    We describe a simulation method for a quantum spin model of a generic, general purpose quantum computer. The use of this quantum computer simulator is illustrated through several implementations of Grover’s database search algorithm. Some preliminary results on the stability of quantum algorithms

  19. Lecture notes on quantum statistics

    NARCIS (Netherlands)

    Gill, R.D.

    2000-01-01

    These notes are meant to form the material for an introductory course on quantum statistics at the graduate level aimed at mathematical statisticians and probabilists No background in physics quantum or otherwise is required They are still far from complete

  20. Eigenfunction statistics on quantum graphs

    International Nuclear Information System (INIS)

    Gnutzmann, S.; Keating, J.P.; Piotet, F.

    2010-01-01

    We investigate the spatial statistics of the energy eigenfunctions on large quantum graphs. It has previously been conjectured that these should be described by a Gaussian Random Wave Model, by analogy with quantum chaotic systems, for which such a model was proposed by Berry in 1977. The autocorrelation functions we calculate for an individual quantum graph exhibit a universal component, which completely determines a Gaussian Random Wave Model, and a system-dependent deviation. This deviation depends on the graph only through its underlying classical dynamics. Classical criteria for quantum universality to be met asymptotically in the large graph limit (i.e. for the non-universal deviation to vanish) are then extracted. We use an exact field theoretic expression in terms of a variant of a supersymmetric σ model. A saddle-point analysis of this expression leads to the estimates. In particular, intensity correlations are used to discuss the possible equidistribution of the energy eigenfunctions in the large graph limit. When equidistribution is asymptotically realized, our theory predicts a rate of convergence that is a significant refinement of previous estimates. The universal and system-dependent components of intensity correlation functions are recovered by means of an exact trace formula which we analyse in the diagonal approximation, drawing in this way a parallel between the field theory and semiclassics. Our results provide the first instance where an asymptotic Gaussian Random Wave Model has been established microscopically for eigenfunctions in a system with no disorder.

  1. Quantum Statistical Mechanics on a Quantum Computer

    OpenAIRE

    De Raedt, H.; Hams, A. H.; Michielsen, K.; Miyashita, S.; Saito, K.

    1999-01-01

    We describe a quantum algorithm to compute the density of states and thermal equilibrium properties of quantum many-body systems. We present results obtained by running this algorithm on a software implementation of a 21-qubit quantum computer for the case of an antiferromagnetic Heisenberg model on triangular lattices of different size.

  2. Quantum theory as an emergent phenomenon the statistical mechanics of matrix models as the precursor of quantum field theory

    CERN Document Server

    Adler, Stephen L

    2004-01-01

    Quantum mechanics is our most successful physical theory. However, it raises conceptual issues that have perplexed physicists and philosophers of science for decades. This 2004 book develops an approach, based on the proposal that quantum theory is not a complete, final theory, but is in fact an emergent phenomenon arising from a deeper level of dynamics. The dynamics at this deeper level are taken to be an extension of classical dynamics to non-commuting matrix variables, with cyclic permutation inside a trace used as the basic calculational tool. With plausible assumptions, quantum theory is shown to emerge as the statistical thermodynamics of this underlying theory, with the canonical commutation/anticommutation relations derived from a generalized equipartition theorem. Brownian motion corrections to this thermodynamics are argued to lead to state vector reduction and to the probabilistic interpretation of quantum theory, making contact with phenomenological proposals for stochastic modifications to Schr�...

  3. Quantum mechanics from classical statistics

    International Nuclear Information System (INIS)

    Wetterich, C.

    2010-01-01

    Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by only a few probabilistic observables. Their expectation values define a density matrix if they obey a 'purity constraint'. Then all the usual laws of quantum mechanics follow, including Heisenberg's uncertainty relation, entanglement and a violation of Bell's inequalities. No concepts beyond classical statistics are needed for quantum physics - the differences are only apparent and result from the particularities of those classical statistical systems which admit a quantum mechanical description. Born's rule for quantum mechanical probabilities follows from the probability concept for a classical statistical ensemble. In particular, we show how the non-commuting properties of quantum operators are associated to the use of conditional probabilities within the classical system, and how a unitary time evolution reflects the isolation of the subsystem. As an illustration, we discuss a classical statistical implementation of a quantum computer.

  4. Effects of quantum coherence on work statistics

    Science.gov (United States)

    Xu, Bao-Ming; Zou, Jian; Guo, Li-Sha; Kong, Xiang-Mu

    2018-05-01

    In the conventional two-point measurement scheme of quantum thermodynamics, quantum coherence is destroyed by the first measurement. But as we know the coherence really plays an important role in the quantum thermodynamics process, and how to describe the work statistics for a quantum coherent process is still an open question. In this paper, we use the full counting statistics method to investigate the effects of quantum coherence on work statistics. First, we give a general discussion and show that for a quantum coherent process, work statistics is very different from that of the two-point measurement scheme, specifically the average work is increased or decreased and the work fluctuation can be decreased by quantum coherence, which strongly depends on the relative phase, the energy level structure, and the external protocol. Then, we concretely consider a quenched one-dimensional transverse Ising model and show that quantum coherence has a more significant influence on work statistics in the ferromagnetism regime compared with that in the paramagnetism regime, so that due to the presence of quantum coherence the work statistics can exhibit the critical phenomenon even at high temperature.

  5. A quantum information approach to statistical mechanics

    International Nuclear Information System (INIS)

    Cuevas, G.

    2011-01-01

    The field of quantum information and computation harnesses and exploits the properties of quantum mechanics to perform tasks more efficiently than their classical counterparts, or that may uniquely be possible in the quantum world. Its findings and techniques have been applied to a number of fields, such as the study of entanglement in strongly correlated systems, new simulation techniques for many-body physics or, generally, to quantum optics. This thesis aims at broadening the scope of quantum information theory by applying it to problems in statistical mechanics. We focus on classical spin models, which are toy models used in a variety of systems, ranging from magnetism, neural networks, to quantum gravity. We tackle these models using quantum information tools from three different angles. First, we show how the partition function of a class of widely different classical spin models (models in different dimensions, different types of many-body interactions, different symmetries, etc) can be mapped to the partition function of a single model. We prove this by first establishing a relation between partition functions and quantum states, and then transforming the corresponding quantum states to each other. Second, we give efficient quantum algorithms to estimate the partition function of various classical spin models, such as the Ising or the Potts model. The proof is based on a relation between partition functions and quantum circuits, which allows us to determine the quantum computational complexity of the partition function by studying the corresponding quantum circuit. Finally, we outline the possibility of applying quantum information concepts and tools to certain models of dis- crete quantum gravity. The latter provide a natural route to generalize our results, insofar as the central quantity has the form of a partition function, and as classical spin models are used as toy models of matter. (author)

  6. Unifying quantum heat transfer in a nonequilibrium spin-boson model with full counting statistics

    Science.gov (United States)

    Wang, Chen; Ren, Jie; Cao, Jianshu

    2017-02-01

    To study the full counting statistics of quantum heat transfer in a driven nonequilibrium spin-boson model, we develop a generalized nonequilibrium polaron-transformed Redfield equation with an auxiliary counting field. This enables us to study the impact of qubit-bath coupling ranging from weak to strong regimes. Without external modulations, we observe maximal values of both steady-state heat flux and noise power in moderate coupling regimes, below which we find that these two transport quantities are enhanced by the finite-qubit-energy bias. With external modulations, the geometric-phase-induced heat flux shows a monotonic decrease upon increasing the qubit-bath coupling at zero qubit energy bias (without bias). While under the finite-qubit-energy bias (with bias), the geometric-phase-induced heat flux exhibits an interesting reversal behavior in the strong coupling regime. Our results unify the seemingly contradictory results in weak and strong qubit-bath coupling regimes and provide detailed dissections for the quantum fluctuation of nonequilibrium heat transfer.

  7. On Quantum Statistical Inference, II

    OpenAIRE

    Barndorff-Nielsen, O. E.; Gill, R. D.; Jupp, P. E.

    2003-01-01

    Interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially, in step with dramatic new developments in experimental techniques for studying small quantum systems. Furthermore, theoretical developments in the theory of quantum measurements have brought the basic mathematical framework for the probability calculations much closer to that of classical probability theory. The present paper reviews this field and proposes and inte...

  8. Quantum information theory and quantum statistics

    International Nuclear Information System (INIS)

    Petz, D.

    2008-01-01

    Based on lectures given by the author, this book focuses on providing reliable introductory explanations of key concepts of quantum information theory and quantum statistics - rather than on results. The mathematically rigorous presentation is supported by numerous examples and exercises and by an appendix summarizing the relevant aspects of linear analysis. Assuming that the reader is familiar with the content of standard undergraduate courses in quantum mechanics, probability theory, linear algebra and functional analysis, the book addresses graduate students of mathematics and physics as well as theoretical and mathematical physicists. Conceived as a primer to bridge the gap between statistical physics and quantum information, a field to which the author has contributed significantly himself, it emphasizes concepts and thorough discussions of the fundamental notions to prepare the reader for deeper studies, not least through the selection of well chosen exercises. (orig.)

  9. Introduction to quantum statistical mechanics

    International Nuclear Information System (INIS)

    Bogolyubov, N.N.; Bogolyubov, N.N.

    1980-01-01

    In a set of lectures, which has been delivered at the Physical Department of Moscow State University as a special course for students represented are some basic ideas of quantum statistical mechanics. Considered are in particular, the Liouville equations in classical and quantum mechanics, canonical distribution and thermodynamical functions, two-time correlation functions and Green's functions in the theory of thermal equilibrium

  10. QUANTUM MECHANICS WITHOUT STATISTICAL POSTULATES

    International Nuclear Information System (INIS)

    Geiger, G.

    2000-01-01

    The Bohmian formulation of quantum mechanics describes the measurement process in an intuitive way without a reduction postulate. Due to the chaotic motion of the hidden classical particle all statistical features of quantum mechanics during a sequence of repeated measurements can be derived in the framework of a deterministic single system theory

  11. Intermediate statistics in quantum maps

    Energy Technology Data Exchange (ETDEWEB)

    Giraud, Olivier [H H Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL (United Kingdom); Marklof, Jens [School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW (United Kingdom); O' Keefe, Stephen [School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW (United Kingdom)

    2004-07-16

    We present a one-parameter family of quantum maps whose spectral statistics are of the same intermediate type as observed in polygonal quantum billiards. Our central result is the evaluation of the spectral two-point correlation form factor at small argument, which in turn yields the asymptotic level compressibility for macroscopic correlation lengths. (letter to the editor)

  12. Quantum Statistical Testing of a Quantum Random Number Generator

    Energy Technology Data Exchange (ETDEWEB)

    Humble, Travis S [ORNL

    2014-01-01

    The unobservable elements in a quantum technology, e.g., the quantum state, complicate system verification against promised behavior. Using model-based system engineering, we present methods for verifying the opera- tion of a prototypical quantum random number generator. We begin with the algorithmic design of the QRNG followed by the synthesis of its physical design requirements. We next discuss how quantum statistical testing can be used to verify device behavior as well as detect device bias. We conclude by highlighting how system design and verification methods must influence effort to certify future quantum technologies.

  13. Quantum formalism for classical statistics

    Science.gov (United States)

    Wetterich, C.

    2018-06-01

    In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg picture for this problem, we develop here the associated Schrödinger picture that keeps track of the local probabilistic information. The transport of the probabilistic information between neighboring hypersurfaces obeys a linear evolution equation, and therefore the superposition principle for the possible solutions. Operators are associated to local observables, with rules for the computation of expectation values similar to quantum mechanics. We discuss how non-commutativity naturally arises in this setting. Also other features characteristic of quantum mechanics, such as complex structure, change of basis or symmetry transformations, can be found in classical statistics once formulated in terms of wave functions or density matrices. We construct for every quantum system an equivalent classical statistical system, such that time in quantum mechanics corresponds to the location of hypersurfaces in the classical probabilistic ensemble. For suitable choices of local observables in the classical statistical system one can, in principle, compute all expectation values and correlations of observables in the quantum system from the local probabilistic information of the associated classical statistical system. Realizing a static memory material as a quantum simulator for a given quantum system is not a matter of principle, but rather of practical simplicity.

  14. Statistical ensembles in quantum mechanics

    International Nuclear Information System (INIS)

    Blokhintsev, D.

    1976-01-01

    The interpretation of quantum mechanics presented in this paper is based on the concept of quantum ensembles. This concept differs essentially from the canonical one by that the interference of the observer into the state of a microscopic system is of no greater importance than in any other field of physics. Owing to this fact, the laws established by quantum mechanics are not of less objective character than the laws governing classical statistical mechanics. The paradoxical nature of some statements of quantum mechanics which result from the interpretation of the wave functions as the observer's notebook greatly stimulated the development of the idea presented. (Auth.)

  15. Quantum-statistical kinetic equations

    International Nuclear Information System (INIS)

    Loss, D.; Schoeller, H.

    1989-01-01

    Considering a homogeneous normal quantum fluid consisting of identical interacting fermions or bosons, the authors derive an exact quantum-statistical generalized kinetic equation with a collision operator given as explicit cluster series where exchange effects are included through renormalized Liouville operators. This new result is obtained by applying a recently developed superoperator formalism (Liouville operators, cluster expansions, symmetrized projectors, P q -rule, etc.) to nonequilibrium systems described by a density operator ρ(t) which obeys the von Neumann equation. By means of this formalism a factorization theorem is proven (being essential for obtaining closed equations), and partial resummations (leading to renormalized quantities) are performed. As an illustrative application, the quantum-statistical versions (including exchange effects due to Fermi-Dirac or Bose-Einstein statistics) of the homogeneous Boltzmann (binary collisions) and Choh-Uhlenbeck (triple collisions) equations are derived

  16. Quantum local asymptotic normality and other questions of quantum statistics

    NARCIS (Netherlands)

    Kahn, Jonas

    2008-01-01

    This thesis is entitled Quantum Local Asymptotic Normality and other questions of Quantum Statistics ,. Quantum statistics are statistics on quantum objects. In classical statistics, we usually start from the data. Indeed, if we want to predict the weather, and can measure the wind or the

  17. Zeno dynamics in quantum statistical mechanics

    International Nuclear Information System (INIS)

    Schmidt, Andreas U

    2003-01-01

    We study the quantum Zeno effect in quantum statistical mechanics within the operator algebraic framework. We formulate a condition for the appearance of the effect in W*-dynamical systems, in terms of the short-time behaviour of the dynamics. Examples of quantum spin systems show that this condition can be effectively applied to quantum statistical mechanical models. Furthermore, we derive an explicit form of the Zeno generator, and use it to construct Gibbs equilibrium states for the Zeno dynamics. As a concrete example, we consider the X-Y model, for which we show that a frequent measurement at a microscopic level, e.g. a single lattice site, can produce a macroscopic effect in changing the global equilibrium

  18. Hidden Statistics Approach to Quantum Simulations

    Science.gov (United States)

    Zak, Michail

    2010-01-01

    Recent advances in quantum information theory have inspired an explosion of interest in new quantum algorithms for solving hard computational (quantum and non-quantum) problems. The basic principle of quantum computation is that the quantum properties can be used to represent structure data, and that quantum mechanisms can be devised and built to perform operations with this data. Three basic non-classical properties of quantum mechanics superposition, entanglement, and direct-product decomposability were main reasons for optimism about capabilities of quantum computers that promised simultaneous processing of large massifs of highly correlated data. Unfortunately, these advantages of quantum mechanics came with a high price. One major problem is keeping the components of the computer in a coherent state, as the slightest interaction with the external world would cause the system to decohere. That is why the hardware implementation of a quantum computer is still unsolved. The basic idea of this work is to create a new kind of dynamical system that would preserve the main three properties of quantum physics superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods. In other words, such a system would reinforce the advantages and minimize limitations of both quantum and classical aspects. Based upon a concept of hidden statistics, a new kind of dynamical system for simulation of Schroedinger equation is proposed. The system represents a modified Madelung version of Schroedinger equation. It preserves superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods. Such an optimal combination of characteristics is a perfect match for simulating quantum systems. The model includes a transitional component of quantum potential (that has been overlooked in previous treatment of the Madelung equation). The role of the

  19. Quantum-like microeconomics: Statistical model of distribution of investments and production

    Science.gov (United States)

    Khrennikov, Andrei

    2008-10-01

    In this paper we demonstrate that the probabilistic quantum-like (QL) behavior-the Born’s rule, interference of probabilities, violation of Bell’s inequality, representation of variables by in general noncommutative self-adjoint operators, Schrödinger’s dynamics-can be exhibited not only by processes in the micro world, but also in economics. In our approach the QL-behavior is induced not by properties of systems. Here systems (commodities) are macroscopic. They could not be superpositions of two different states. In our approach the QL-behavior of economical statistics is a consequence of the organization of the process of production as well as investments. In particular, Hamiltonian (“financial energy”) is determined by rate of return.

  20. Spin-Wave Wave Function for Quantum Spin Models : Condensed Matter and Statistical Physics

    OpenAIRE

    Franjo, FRANJIC; Sandro, SORELLA; Istituto Nazionale di Fisica della Materia International School for Advance Studies; Istituto Nazionale di Fisica della Materia International School for Advance Studies

    1997-01-01

    We present a new approach to determine an accurate variational wave function for general quantum spin models, completely defined by a consistency requirement with the simple and well-known linear spin-wave expansion. With this wave function, it is also possible to obtain the correct behavior of the long distance correlation functions for the 1D S=1/2 antiferromagnet. In 2D the proposed spin-wave wave function represents an excellent approximation to the exact ground state of the S=1.2 XY mode...

  1. Quantum - statistical equation of state

    International Nuclear Information System (INIS)

    Kalitkin, N.N.; Kuz'mina, L.V.

    1976-01-01

    An atom model is considered which allows uniform description of the equation of an equilibrium plasma state in the range of densities from gas to superhigh ones and in the temperature range from 1-5 eV to a ten of keV. Quantum and exchange corrections to the Thomas-Fermi thermodynamic functions at non zero temperatures have been calculated. The calculated values have been compared with experimental data and with calculations performed by more accurate models. The differences result from the fact that a quantum approach does not allow for shell effects. The evaluation of these differences makes it possible to indicate the limits of applicability of the Thomas-Fermi model with quantum and exchange corrections. It turns out that if at zero temperature the model may be applied only for high compressions, at the temperature more than 1 eV it well describes the behaviour of plasma in a very wide range of densities and agrees satisfactorily with experiment even for non-ideal plasma

  2. Analysis of proton-induced fragment production cross sections by the Quantum Molecular Dynamics plus Statistical Decay Model

    Energy Technology Data Exchange (ETDEWEB)

    Chiba, Satoshi; Iwamoto, Osamu; Fukahori, Tokio; Niita, Koji; Maruyama, Toshiki; Maruyama, Tomoyuki; Iwamoto, Akira [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment

    1997-03-01

    The production cross sections of various fragments from proton-induced reactions on {sup 56}Fe and {sup 27}Al have been analyzed by the Quantum Molecular Dynamics (QMD) plus Statistical Decay Model (SDM). It was found that the mass and charge distributions calculated with and without the statistical decay have very different shapes. These results also depend strongly on the impact parameter, showing an importance of the dynamical treatment as realized by the QMD approach. The calculated results were compared with experimental data in the energy region from 50 MeV to 5 GeV. The QMD+SDM calculation could reproduce the production cross sections of the light clusters and intermediate-mass to heavy fragments in a good accuracy. The production cross section of {sup 7}Be was, however, underpredicted by approximately 2 orders of magnitude, showing the necessity of another reaction mechanism not taken into account in the present model. (author)

  3. [Establishment of the mathematic model of total quantum statistical moment standard similarity for application to medical theoretical research].

    Science.gov (United States)

    He, Fu-yuan; Deng, Kai-wen; Huang, Sheng; Liu, Wen-long; Shi, Ji-lian

    2013-09-01

    The paper aims to elucidate and establish a new mathematic model: the total quantum statistical moment standard similarity (TQSMSS) on the base of the original total quantum statistical moment model and to illustrate the application of the model to medical theoretical research. The model was established combined with the statistical moment principle and the normal distribution probability density function properties, then validated and illustrated by the pharmacokinetics of three ingredients in Buyanghuanwu decoction and of three data analytical method for them, and by analysis of chromatographic fingerprint for various extracts with different solubility parameter solvents dissolving the Buyanghanwu-decoction extract. The established model consists of four mainly parameters: (1) total quantum statistical moment similarity as ST, an overlapped area by two normal distribution probability density curves in conversion of the two TQSM parameters; (2) total variability as DT, a confidence limit of standard normal accumulation probability which is equal to the absolute difference value between the two normal accumulation probabilities within integration of their curve nodical; (3) total variable probability as 1-Ss, standard normal distribution probability within interval of D(T); (4) total variable probability (1-beta)alpha and (5) stable confident probability beta(1-alpha): the correct probability to make positive and negative conclusions under confident coefficient alpha. With the model, we had analyzed the TQSMS similarities of pharmacokinetics of three ingredients in Buyanghuanwu decoction and of three data analytical methods for them were at range of 0.3852-0.9875 that illuminated different pharmacokinetic behaviors of each other; and the TQSMS similarities (ST) of chromatographic fingerprint for various extracts with different solubility parameter solvents dissolving Buyanghuanwu-decoction-extract were at range of 0.6842-0.999 2 that showed different constituents

  4. Annotations to quantum statistical mechanics

    CERN Document Server

    Kim, In-Gee

    2018-01-01

    This book is a rewritten and annotated version of Leo P. Kadanoff and Gordon Baym’s lectures that were presented in the book Quantum Statistical Mechanics: Green’s Function Methods in Equilibrium and Nonequilibrium Problems. The lectures were devoted to a discussion on the use of thermodynamic Green’s functions in describing the properties of many-particle systems. The functions provided a method for discussing finite-temperature problems with no more conceptual difficulty than ground-state problems, and the method was equally applicable to boson and fermion systems and equilibrium and nonequilibrium problems. The lectures also explained nonequilibrium statistical physics in a systematic way and contained essential concepts on statistical physics in terms of Green’s functions with sufficient and rigorous details. In-Gee Kim thoroughly studied the lectures during one of his research projects but found that the unspecialized method used to present them in the form of a book reduced their readability. He st...

  5. Probabilistic and Statistical Aspects of Quantum Theory

    CERN Document Server

    Holevo, Alexander S

    2011-01-01

    This book is devoted to aspects of the foundations of quantum mechanics in which probabilistic and statistical concepts play an essential role. The main part of the book concerns the quantitative statistical theory of quantum measurement, based on the notion of positive operator-valued measures. During the past years there has been substantial progress in this direction, stimulated to a great extent by new applications such as Quantum Optics, Quantum Communication and high-precision experiments. The questions of statistical interpretation, quantum symmetries, theory of canonical commutation re

  6. Quantum Statistical Operator and Classically Chaotic Hamiltonian ...

    African Journals Online (AJOL)

    Quantum Statistical Operator and Classically Chaotic Hamiltonian System. ... Journal of the Nigerian Association of Mathematical Physics ... In a Hamiltonian system von Neumann Statistical Operator is used to tease out the quantum consequence of (classical) chaos engendered by the nonlinear coupling of system to its ...

  7. Emergence of quantum mechanics from classical statistics

    International Nuclear Information System (INIS)

    Wetterich, C

    2009-01-01

    The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical interpretations to practical issues as quantum computing. In this note we demonstrate how quantum mechanics can emerge from classical statistical systems. We discuss conditions and circumstances for this to happen. Quantum systems describe isolated subsystems of classical statistical systems with infinitely many states. While infinitely many classical observables 'measure' properties of the subsystem and its environment, the state of the subsystem can be characterized by the expectation values of only a few probabilistic observables. They define a density matrix, and all the usual laws of quantum mechanics follow. No concepts beyond classical statistics are needed for quantum physics - the differences are only apparent and result from the particularities of those classical statistical systems which admit a quantum mechanical description. In particular, we show how the non-commuting properties of quantum operators are associated to the use of conditional probabilities within the classical system, and how a unitary time evolution reflects the isolation of the subsystem.

  8. Statistical mechanics for a class of quantum statistics

    International Nuclear Information System (INIS)

    Isakov, S.B.

    1994-01-01

    Generalized statistical distributions for identical particles are introduced for the case where filling a single-particle quantum state by particles depends on filling states of different momenta. The system of one-dimensional bosons with a two-body potential that can be solved by means of the thermodynamic Bethe ansatz is shown to be equivalent thermodynamically to a system of free particles obeying statistical distributions of the above class. The quantum statistics arising in this way are completely determined by the two-particle scattering phases of the corresponding interacting systems. An equation determining the statistical distributions for these statistics is derived

  9. Statistical analysis of time-resolved emission from ensembles of semiconductor quantum dots: interpretations of exponantial decay models

    NARCIS (Netherlands)

    van Driel, A.F.; Nikolaev, I.; Vergeer, P.; Lodahl, P.; Vanmaekelbergh, D.; Vos, Willem L.

    2007-01-01

    We present a statistical analysis of time-resolved spontaneous emission decay curves from ensembles of emitters, such as semiconductor quantum dots, with the aim of interpreting ubiquitous non-single-exponential decay. Contrary to what is widely assumed, the density of excited emitters and the

  10. Statistical representation of quantum states

    Energy Technology Data Exchange (ETDEWEB)

    Montina, A [Dipartimento di Fisica, Universita di Firenze, Via Sansone 1, 50019 Sesto Fiorentino (Italy)

    2007-05-15

    In the standard interpretation of quantum mechanics, the state is described by an abstract wave function in the representation space. Conversely, in a realistic interpretation, the quantum state is replaced by a probability distribution of physical quantities. Bohm mechanics is a consistent example of realistic theory, where the wave function and the particle positions are classically defined quantities. Recently, we proved that the probability distribution in a realistic theory cannot be a quadratic function of the quantum state, in contrast to the apparently obvious suggestion given by the Born rule for transition probabilities. Here, we provide a simplified version of this proof.

  11. Quantum field theory and statistical mechanics

    International Nuclear Information System (INIS)

    Jegerlehner, F.

    1975-01-01

    At first a heuristic understanding is given how the relation between quantum field theory and statistical mechanics near phase transitions comes about. A long range scale invariant theory is constructed, critical indices are calculated and the relations among them are proved, field theoretical Kadanoff-scale transformations are formulated and scaling corrections calculated. A precise meaning to many of Kadanoffs considerations and a model matching Wegners phenomenological scheme is given. It is shown, that soft parametrization is most transparent for the discussion of scaling behaviour. (BJ) [de

  12. Quantum entanglement and teleportation using statistical correlations

    Indian Academy of Sciences (India)

    Administrator

    Abstract. A study of quantum teleportation using two and three-particle correlated density matrix is presented. A criterion based on standard quantum statistical correlations employed in the many-body virial expansion is used to determine the extent of entanglement for a 2N-particle system. A relation between the probability ...

  13. Quantum fermions and quantum field theory from classical statistics

    International Nuclear Information System (INIS)

    Wetterich, Christof

    2012-01-01

    An Ising-type classical statistical ensemble can describe the quantum physics of fermions if one chooses a particular law for the time evolution of the probability distribution. It accounts for the time evolution of a quantum field theory for Dirac particles in an external electromagnetic field. This yields in the non-relativistic one-particle limit the Schrödinger equation for a quantum particle in a potential. Interference or tunneling arise from classical probabilities.

  14. Quantum level statistics of pseudointegrable billiards

    International Nuclear Information System (INIS)

    Cheon, T.; Cohen, T.D.

    1989-01-01

    We study the spectral statistics of systems of two-dimensional pseudointegrable billiards. These systems are classically nonergodic, but nonseparable. It is found that such systems possess quantum spectra which are closely simulated by the Gaussian orthogonal ensemble. We discuss the implications of these results on the conjectured relation between classical chaos and quantum level statistics. We emphasize the importance of the semiclassical nature of any such relation

  15. Statistical algebraic approach to quantum mechanics

    International Nuclear Information System (INIS)

    Slavnov, D.A.

    2001-01-01

    The scheme for plotting the quantum theory with application of the statistical algebraic approach is proposed. The noncommutative algebra elements (observed ones) and nonlinear functionals on this algebra (physical state) are used as the primary constituents. The latter ones are associated with the single-unit measurement results. Certain physical state groups are proposed to consider as quantum states of the standard quantum mechanics. It is shown that the mathematical apparatus of the standard quantum mechanics may be reproduced in such a scheme in full volume [ru

  16. Multiscale representation of generating and correlation functions for some models of statistical mechanics and quantum field theory

    International Nuclear Information System (INIS)

    O'Carroll, M.

    1993-01-01

    The author considers models of statistical mechanics and quantum field theory (in the Euclidean formulation) which are treated using renormalization group methods and where the action is a small perturbation of a quadratic action. The author obtains multiscale formulas for the generating and correlation functions after n renormalization group transformations which bring out the relation with the nth effective action. The author derives and compares the formulas for different RGs. The formulas for correlation functions involve (1) two propagators which are determined by a sequence of approximate wave function renormalization constants and renormalization group operators associated with the decomposition into scales of the quadratic form and (2) field derivatives of the nth effective action. For the case of the block field open-quotes δ-functionclose quotes RG the formulas are especially simple and for asymptotic free theories only the derivatives at zero field are needed; the formulas have been previously used directly to obtain bounds on correlation functions using information obtained from the analysis of effective actions. The simplicity can be traced to an open-quotes orthogonality-of-scalesclose quotes property which follows from an implicit wavelet structure. Other commonly used RGs do not have the open-quotes orthogonality of scalesclose quotes property. 19 refs

  17. Semi-Poisson statistics in quantum chaos.

    Science.gov (United States)

    García-García, Antonio M; Wang, Jiao

    2006-03-01

    We investigate the quantum properties of a nonrandom Hamiltonian with a steplike singularity. It is shown that the eigenfunctions are multifractals and, in a certain range of parameters, the level statistics is described exactly by semi-Poisson statistics (SP) typical of pseudointegrable systems. It is also shown that our results are universal, namely, they depend exclusively on the presence of the steplike singularity and are not modified by smooth perturbations of the potential or the addition of a magnetic flux. Although the quantum properties of our system are similar to those of a disordered conductor at the Anderson transition, we report important quantitative differences in both the level statistics and the multifractal dimensions controlling the transition. Finally, the study of quantum transport properties suggests that the classical singularity induces quantum anomalous diffusion. We discuss how these findings may be experimentally corroborated by using ultracold atoms techniques.

  18. Quantum Statistical Approach to Superconductivity

    Science.gov (United States)

    Nam, Eunsoo

    The Frohlich Hamiltonian representing an interaction between electron and phonon is derived. By exchanging a virtual phonon, a system of two electrons can lower the system's total energy if the difference of their kinetic energies is less than the energy of the phonon exchanged. This is shown by using quantum mechanical perturbation theory, which is fully developed. A general theory of superconductivity is developed, starting with a BCS Hamiltonian in which the interaction strengths (V_{11}, V_{22 }, V_{12}) among and between "electron" (1) and "hole" (2) Cooper pairs are differentiated. The supercondensate is shown to be composed of equal numbers of "electron" and "hole" ground (zero-momentum) Cooper pairs with charges mp 2e.. Based on the Hamiltonian, the normal-to-super phase transition is investigated, approaching the critical temperature T_{c} from the high temperature side. Non zero momentum Cooper pairs, that is, pairs of electrons (holes) with antiparallel spins and nearly opposite momenta above T_{c } in the bulk limit, are shown to move like independent bosons with the energy momentum relation varepsilon = (1/2)upsilon_ {F}p, where upsilon_ {F} represents the Fermi velocity. We have investigated the Bose-Einstein condensation of pairons. The system of free Cooper pairs in a 3D superconductors undergoes a phase transition of the second order with the critical temperature T_{c} given byk_{B}T_{c } = (1/2)(pi^2hbar^3v_sp {F}{3}n/1.20257)^{1over3 }where n is the number density of Cooper pairs. We calculate various properties associated with superconductivity at finite temperature. We derive general expressions for the energy gaps for both quasi electrons and pairons. Based on the independent pairon model, we explain the flux quantization, London's equation and the Josephson effects, stressing the importance of the macroscopic wave -function which represents the supercondensate in motion. We derived the basic equations governing the behavior of the

  19. Quantum physics and statistical physics. 5. ed.

    International Nuclear Information System (INIS)

    Alonso, Marcelo; Finn, Edward J.

    2012-01-01

    By logical and uniform presentation this recognized introduction in modern physics treats both the experimental and theoretical aspects. The first part of the book deals with quantum mechanics and their application to atoms, molecules, nuclei, solids, and elementary particles. The statistical physics with classical statistics, thermodynamics, and quantum statistics is theme of the second part. Alsonso and Finn avoid complicated mathematical developments; by numerous sketches and diagrams as well as many problems and examples they make the reader early and above all easily understandably familiar with the formations of concepts of modern physics.

  20. Quantum mechanics as applied mathematical statistics

    International Nuclear Information System (INIS)

    Skala, L.; Cizek, J.; Kapsa, V.

    2011-01-01

    Basic mathematical apparatus of quantum mechanics like the wave function, probability density, probability density current, coordinate and momentum operators, corresponding commutation relation, Schroedinger equation, kinetic energy, uncertainty relations and continuity equation is discussed from the point of view of mathematical statistics. It is shown that the basic structure of quantum mechanics can be understood as generalization of classical mechanics in which the statistical character of results of measurement of the coordinate and momentum is taken into account and the most important general properties of statistical theories are correctly respected.

  1. Quantum chaos: Statistical relaxation in discrete spectrum

    International Nuclear Information System (INIS)

    Chirikov, B.V.

    1991-01-01

    The controversial phenomenon of quantum chaos is discussed using the quantized standard map, or the kicked rotator, as a simple model. The relation to the classical dynamical chaos is tracked down on the basis of the correspondence principle. Various mechanisms of the quantum suppression of classical chaos are considered with an application to the excitation and ionization of Rydberg atoms in a microwave field. Several definitions of the quantum chaos are discussed. (author). 27 refs

  2. Statistical analysis of time-resolved emission from ensembles of semiconductor quantum dots: Interpretation of exponential decay models

    DEFF Research Database (Denmark)

    Van Driel, A.F.; Nikolaev, I.S.; Vergeer, P.

    2007-01-01

    We present a statistical analysis of time-resolved spontaneous emission decay curves from ensembles of emitters, such as semiconductor quantum dots, with the aim of interpreting ubiquitous non-single-exponential decay. Contrary to what is widely assumed, the density of excited emitters...... and the intensity in an emission decay curve are not proportional, but the density is a time integral of the intensity. The integral relation is crucial to correctly interpret non-single-exponential decay. We derive the proper normalization for both a discrete and a continuous distribution of rates, where every...... decay component is multiplied by its radiative decay rate. A central result of our paper is the derivation of the emission decay curve when both radiative and nonradiative decays are independently distributed. In this case, the well-known emission quantum efficiency can no longer be expressed...

  3. Quantum statistics of many-particle systems

    International Nuclear Information System (INIS)

    Kraeft, W.D.; Ebeling, W.; Kremp, D.; Ropke, G.

    1986-01-01

    This paper presents the elements of quantum statistics and discusses the quantum mechanics of many-particle systems. The method of second quantization is discussed and the Bogolyubov hierarchy is examined. The general properties of the correlation function and one-particle Green's function are examined. The paper presents dynamical and thermodynamical information contained in the spectral function. An equation of motion is given for the one-particle Green's function. T-matrix and thermodynamic properties in binary collision approximation are discussed

  4. Statistical distribution of quantum particles

    Indian Academy of Sciences (India)

    S B Khasare

    2018-02-08

    Feb 8, 2018 ... In this work, the statistical distribution functions for boson, fermions and their mixtures have been ... index is greater than unity, then it is easy in the present approach to ... ability W. Section 3 gives the derivation and graphical.

  5. Quantum chaos: statistical relaxation in discrete spectrum

    International Nuclear Information System (INIS)

    Chirikov, B.V.

    1990-01-01

    The controversial phenomenon of quantum chaos is discussed using the quantized standard map, or the kicked rotator, as a simple model. The relation to the classical dynamical chaos is tracked down on the basis of the correspondence principle. Several definitions of the quantum chaos are discussed. 27 refs

  6. QInfer: Statistical inference software for quantum applications

    Directory of Open Access Journals (Sweden)

    Christopher Granade

    2017-04-01

    Full Text Available Characterizing quantum systems through experimental data is critical to applications as diverse as metrology and quantum computing. Analyzing this experimental data in a robust and reproducible manner is made challenging, however, by the lack of readily-available software for performing principled statistical analysis. We improve the robustness and reproducibility of characterization by introducing an open-source library, QInfer, to address this need. Our library makes it easy to analyze data from tomography, randomized benchmarking, and Hamiltonian learning experiments either in post-processing, or online as data is acquired. QInfer also provides functionality for predicting the performance of proposed experimental protocols from simulated runs. By delivering easy-to-use characterization tools based on principled statistical analysis, QInfer helps address many outstanding challenges facing quantum technology.

  7. Multiparticle quantum mechanics obeying fractional statistics

    International Nuclear Information System (INIS)

    Wu, Y.

    1984-01-01

    We obtain the rule governing many-body wave functions for particles obeying fractional statistics in two (space) dimensions. It generalizes and continuously interpolates the usual symmetrization and antisymmetrization. Quantum mechanics of more than two particles is discussed and some new features are found

  8. Quantum mechanics and field theory with fractional spin and statistics

    International Nuclear Information System (INIS)

    Forte, S.

    1992-01-01

    Planar systems admit quantum states that are neither bosons nor fermions, i.e., whose angular momentum is neither integer nor half-integer. After a discussion of some examples of familiar models in which fractional spin may arise, the relevant (nonrelativistic) quantum mechanics is developed from first principles. The appropriate generalization of statistics is also discussed. Some physical effects of fractional spin and statistics are worked out explicitly. The group theory underlying relativistic models with fractional spin and statistics is then introduced and applied to relativistic particle mechanics and field theory. Field-theoretical models in 2+1 dimensions are presented which admit solitons that carry fractional statistics, and are discussed in a semiclassical approach, in the functional integral approach, and in the canonical approach. Finally, fundamental field theories whose Fock states carry fractional spin and statistics are discussed

  9. Statistical physics of black holes as quantum-mechanical systems

    OpenAIRE

    Giddings, Steven B.

    2013-01-01

    Some basic features of black-hole statistical mechanics are investigated, assuming that black holes respect the principles of quantum mechanics. Care is needed in defining an entropy S_bh corresponding to the number of microstates of a black hole, given that the black hole interacts with its surroundings. An open question is then the relationship between this entropy and the Bekenstein-Hawking entropy S_BH. For a wide class of models with interactions needed to ensure unitary quantum evolutio...

  10. Constructions of quantum fields with anyonic statistics

    International Nuclear Information System (INIS)

    Plaschke, M.

    2015-01-01

    From the principles of algebraic quantum field theory it follows that in low dimensions particles are not necessarily bosons or fermions, but their statistics can in general be governed by the braid group. Such particles are called anyons and their possible statistics is intimately related to their localization properties and their covariance with respect to rotations. This work is concerned with the explicit construction of quantum fields with anyonic statistics which are localized in various different regions on two- and three-dimensional Minkowski space, and we will analyze the connection between localization, statistics and spin. The reason why this is considerably more difficult than for bosons or fermions is the no-go theorem regarding free cone-localized anyons in d=2+1. This problem is approached in this work from different directions leaving out some of the underlying assumptions one makes in the abstract algebraic quantum field theory. Despite a similar no-go theorem for free local anyons, it is in two dimensions possible to construct compactly localized quantum field nets with anyonic commutation relations for every mass m ≥ 0 and every statistics parameter by using the theory of loop groups and implementable Bogoliubov transformations. This does not work in higher dimensions so in d=2+1 we will first construct polarization free generators, which are only wedge-local, using a recent work about multiplicative deformations of free quantum fields on the Fock space. By generalizing this procedure to the charged case it is possible to extend the set of admissible deformations and end up with fields satisfying anyonic commutation relations, which are covariant w.r.t a Poincaré group representation with arbitrary real-valued spin. Another approach, which further demonstrates the connection between localization, statistics and spin of quantum field nets, is to focus first only on the rotational degrees of freedom and construct field operators on the circle

  11. Quantum models of classical systems

    International Nuclear Information System (INIS)

    Hájíček, P

    2015-01-01

    Quantum statistical methods that are commonly used for the derivation of classical thermodynamic properties are extended to classical mechanical properties. The usual assumption that every real motion of a classical mechanical system is represented by a sharp trajectory is not testable and is replaced by a class of fuzzy models, the so-called maximum entropy (ME) packets. The fuzzier are the compared classical and quantum ME packets, the better seems to be the match between their dynamical trajectories. Classical and quantum models of a stiff rod will be constructed to illustrate the resulting unified quantum theory of thermodynamic and mechanical properties. (paper)

  12. Classical and Quantum Models in Non-Equilibrium Statistical Mechanics: Moment Methods and Long-Time Approximations

    Directory of Open Access Journals (Sweden)

    Ramon F. Alvarez-Estrada

    2012-02-01

    Full Text Available We consider non-equilibrium open statistical systems, subject to potentials and to external “heat baths” (hb at thermal equilibrium at temperature T (either with ab initio dissipation or without it. Boltzmann’s classical equilibrium distributions generate, as Gaussian weight functions in momenta, orthogonal polynomials in momenta (the position-independent Hermite polynomialsHn’s. The moments of non-equilibrium classical distributions, implied by the Hn’s, fulfill a hierarchy: for long times, the lowest moment dominates the evolution towards thermal equilibrium, either with dissipation or without it (but under certain approximation. We revisit that hierarchy, whose solution depends on operator continued fractions. We review our generalization of that moment method to classical closed many-particle interacting systems with neither a hb nor ab initio dissipation: with initial states describing thermal equilibrium at T at large distances but non-equilibrium at finite distances, the moment method yields, approximately, irreversible thermalization of the whole system at T, for long times. Generalizations to non-equilibrium quantum interacting systems meet additional difficulties. Three of them are: (i equilibrium distributions (represented through Wigner functions are neither Gaussian in momenta nor known in closed form; (ii they may depend on dissipation; and (iii the orthogonal polynomials in momenta generated by them depend also on positions. We generalize the moment method, dealing with (i, (ii and (iii, to some non-equilibrium one-particle quantum interacting systems. Open problems are discussed briefly.

  13. The quantum theory of statistical multistep nucleus reactions

    CERN Document Server

    Zhivopistsev, F A

    2002-01-01

    The phenomenological models and quantum approaches to the description of the statistical multistep nuclear reactions are discussed. The basic advantages and deficiencies of various modifications of the quantum theory of the statistical multistep direct reactions: Feshbach-Kerman-Koonin formalism, the generalized model of the statistical multistep reactions (GMSMR) are considered in detail. The possibility of obtaining the consistent description of the experimental spectra for the reactions with nucleons is shown by the particular examples. Further improvement and development of the quantum formalism for the more complete and consecutive description of various mechanisms of the component particle formalism in the output channel, the correct of the unbound state densities of the intermediate and finite nuclei are needed for the analysis of the inclusive reactions with participation of the component particles, (and with an account of the contributions to the cross sections of the nucleus cluster and shell areas)...

  14. Mathematical methods in quantum and statistical mechanics

    International Nuclear Information System (INIS)

    Fishman, L.

    1977-01-01

    The mathematical structure and closed-form solutions pertaining to several physical problems in quantum and statistical mechanics are examined in some detail. The J-matrix method, introduced previously for s-wave scattering and based upon well-established Hilbert Space theory and related generalized integral transformation techniques, is extended to treat the lth partial wave kinetic energy and Coulomb Hamiltonians within the context of square integrable (L 2 ), Laguerre (Slater), and oscillator (Gaussian) basis sets. The theory of relaxation in statistical mechanics within the context of the theory of linear integro-differential equations of the Master Equation type and their corresponding Markov processes is examined. Several topics of a mathematical nature concerning various computational aspects of the L 2 approach to quantum scattering theory are discussed

  15. Applications of quantum entropy to statistics

    International Nuclear Information System (INIS)

    Silver, R.N.; Martz, H.F.

    1994-01-01

    This paper develops two generalizations of the maximum entropy (ME) principle. First, Shannon classical entropy is replaced by von Neumann quantum entropy to yield a broader class of information divergences (or penalty functions) for statistics applications. Negative relative quantum entropy enforces convexity, positivity, non-local extensivity and prior correlations such as smoothness. This enables the extension of ME methods from their traditional domain of ill-posed in-verse problems to new applications such as non-parametric density estimation. Second, given a choice of information divergence, a combination of ME and Bayes rule is used to assign both prior and posterior probabilities. Hyperparameters are interpreted as Lagrange multipliers enforcing constraints. Conservation principles are proposed to act statistical regularization and other hyperparameters, such as conservation of information and smoothness. ME provides an alternative to heirarchical Bayes methods

  16. Quantum Entropy and Its Applications to Quantum Communication and Statistical Physics

    Directory of Open Access Journals (Sweden)

    Masanori Ohya

    2010-05-01

    Full Text Available Quantum entropy is a fundamental concept for quantum information recently developed in various directions. We will review the mathematical aspects of quantum entropy (entropies and discuss some applications to quantum communication, statistical physics. All topics taken here are somehow related to the quantum entropy that the present authors have been studied. Many other fields recently developed in quantum information theory, such as quantum algorithm, quantum teleportation, quantum cryptography, etc., are totally discussed in the book (reference number 60.

  17. Electron Energy Level Statistics in Graphene Quantum Dots

    NARCIS (Netherlands)

    De Raedt, H.; Katsnellson, M. I.; Katsnelson, M.I.

    2008-01-01

    Motivated by recent experimental observations of size quantization of electron energy levels in graphene quantum dots [7] we investigate the level statistics in the simplest tight-binding model for different dot shapes by computer simulation. The results are in a reasonable agreement with the

  18. Lie-superalgebraical aspects of quantum statistics

    International Nuclear Information System (INIS)

    Palev, T.D.

    1978-01-01

    The Lie-superalgebraical properties of the ordinary quantum statistics are discussed with the aim of possible generalization in quantum theory and in theoretical physics. It is indicated that the algebra generated by n pairs of Fermi or paraFermi operators is isomorphic to the classical simple Lie algebra Bsub(n) of the SO(2n+1) orthogonal group, whereas n pairs of Bose or paraBose operators generate the simple orthosympletic superalgebra B(O,n). The transition to infinite number of creation and annihilation operators (n → infinity) does not change a superalgebraic structure. Hence, ordinary Bose and Fermi quantization can be considered as quantization over definite irreducible representations of two simple Lie superalgebras. The idea is given of how one can introduce creation and annihilation operators that satisfy the second quantization postulates and generate other simple Lie superalgebras

  19. Quantum fields on manifolds: an interplay between quantum theory, statistical thermodynamics and general relativity

    International Nuclear Information System (INIS)

    Sewell, G.L.

    1986-01-01

    The author shows how the basic axioms of quantum field theory, general relativity and statistical thermodynamics lead, in a model-independent way, to a generalized Hawking-Unruh effect, whereby the gravitational fields carried by a class of space-time manifolds with event horizons thermalize ambient quantum fields. The author is concerned with a quantum field on a space-time x containing a submanifold X' bounded by event horizons. The objective is to show that, for a wide class of space-times, the global vacuum state of the field reduces, in X', to a thermal state, whose temperature depends on the geometry. The statistical thermodynaical, geometrical, and quantum field theoretical essential ingredients for the reduction of the vacuum state are discussed

  20. Quantum theoretical physics is statistical and relativistic

    International Nuclear Information System (INIS)

    Harding, C.

    1980-01-01

    A new theoretical framework for the quantum mechanism is presented. It is based on a strict deterministic behavior of single systems. The conventional QM equation, however, is found to describe statistical results of many classical systems. It will be seen, moreover, that a rigorous synthesis of our theory requires relativistic kinematics. So, QM is not only a classical statistical theory, it is, of necessity, a relativistic theory. The equation of the theory does not just duplicate QM, it indicates an inherent nonlinearity in QM which is subject to experimental verification. It is shown, therefore, that conventional QM is a corollary of classical deterministic principles. It is suggested that this concept of nature conflicts with that prevalent in modern physics. (author)

  1. Classical model of intermediate statistics

    International Nuclear Information System (INIS)

    Kaniadakis, G.

    1994-01-01

    In this work we present a classical kinetic model of intermediate statistics. In the case of Brownian particles we show that the Fermi-Dirac (FD) and Bose-Einstein (BE) distributions can be obtained, just as the Maxwell-Boltzmann (MD) distribution, as steady states of a classical kinetic equation that intrinsically takes into account an exclusion-inclusion principle. In our model the intermediate statistics are obtained as steady states of a system of coupled nonlinear kinetic equations, where the coupling constants are the transmutational potentials η κκ' . We show that, besides the FD-BE intermediate statistics extensively studied from the quantum point of view, we can also study the MB-FD and MB-BE ones. Moreover, our model allows us to treat the three-state mixing FD-MB-BE intermediate statistics. For boson and fermion mixing in a D-dimensional space, we obtain a family of FD-BE intermediate statistics by varying the transmutational potential η BF . This family contains, as a particular case when η BF =0, the quantum statistics recently proposed by L. Wu, Z. Wu, and J. Sun [Phys. Lett. A 170, 280 (1992)]. When we consider the two-dimensional FD-BE statistics, we derive an analytic expression of the fraction of fermions. When the temperature T→∞, the system is composed by an equal number of bosons and fermions, regardless of the value of η BF . On the contrary, when T=0, η BF becomes important and, according to its value, the system can be completely bosonic or fermionic, or composed both by bosons and fermions

  2. Sampling, Probability Models and Statistical Reasoning Statistical

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 5. Sampling, Probability Models and Statistical Reasoning Statistical Inference. Mohan Delampady V R Padmawar. General Article Volume 1 Issue 5 May 1996 pp 49-58 ...

  3. Is quantum theory a form of statistical mechanics?

    Science.gov (United States)

    Adler, S. L.

    2007-05-01

    We give a review of the basic themes of my recent book: Adler S L 2004 Quantum Theory as an Emergent Phenomenon (Cambridge: Cambridge University Press). We first give motivations for considering the possibility that quantum mechanics is not exact, but is instead an accurate asymptotic approximation to a deeper level theory. For this deeper level, we propose a non-commutative generalization of classical mechanics, that we call "trace dynamics", and we give a brief survey of how it works, considering for simplicity only the bosonic case. We then discuss the statistical mechanics of trace dynamics and give our argument that with suitable approximations, the Ward identities for trace dynamics imply that ensemble averages in the canonical ensemble correspond to Wightman functions in quantum field theory. Thus, quantum theory emerges as the statistical thermodynamics of trace dynamics. Finally, we argue that Brownian motion corrections to this thermodynamics lead to stochastic corrections to the Schrödinger equation, of the type that have been much studied in the "continuous spontaneous localization" model of objective state vector reduction. In appendices to the talk, we give details of the existence of a conserved operator in trace dynamics that encodes the structure of the canonical algebra, of the derivation of the Ward identities, and of the proof that the stochastically-modified Schrödinger equation leads to state vector reduction with Born rule probabilities.

  4. Statistical properties of quantum entanglement and information entropy

    International Nuclear Information System (INIS)

    Abdel-Aty, M.M.A.

    2007-03-01

    Key words: entropy, entanglement, atom-field interaction, trapped ions, cold atoms, information entropy. Objects of research: Pure state entanglement, entropy squeezing mazer. The aim of the work: Study of the new entanglement features and new measures for both pure-state and mixed state of particle-field interaction. Also, the impact of the information entropy on the quantum information theory. Method of investigation: Methods of theoretical physics and applied mathematics (statistical physics, quantum optics) are used. Results obtained and their novelty are: All the results of the dissertation are new and many new features have been discovered. Particularly: the most general case of the pure state entanglement has been introduced. Although various special aspects of the quantum entropy have been investigated previously, the general features of the dynamics, when a multi-level system and a common environment are considered, have not been treated before and our work therefore, field a gap in the literature. Specifically: 1) A new entanglement measure due to quantum mutual entropy (mixed-state entanglement) we called it DEM, has been introduced, 2) A new treatment of the atomic information entropy in higher level systems has been presented. The problem has been completely solved in the case of three-level system, 3) A new solution of the interaction between the ultra cold atoms and cavity field has been discovered, 4) Some new models of the atom-field interaction have been adopted. Practical value: The subject carries out theoretic character. Application region: Results can be used in quantum computer developments. Also, the presented results can be used for further developments of the quantum information and quantum communications. (author)

  5. Infinite Random Graphs as Statistical Mechanical Models

    DEFF Research Database (Denmark)

    Durhuus, Bergfinnur Jøgvan; Napolitano, George Maria

    2011-01-01

    We discuss two examples of infinite random graphs obtained as limits of finite statistical mechanical systems: a model of two-dimensional dis-cretized quantum gravity defined in terms of causal triangulated surfaces, and the Ising model on generic random trees. For the former model we describe a ...

  6. Statistical separability and the impossibility of the superluminal quantum communication

    International Nuclear Information System (INIS)

    Zhang Qiren

    2004-01-01

    The authors analyse the relation and the difference between the quantum correlation of two points in space and the communication between them. The statistical separability of two points in the space is defined and proven. From this statistical separability, authors prove that the superluminal quantum communication between different points is impossible. To emphasis the compatibility between the quantum theory and the relativity, authors write the von Neumann equation of density operator evolution in the multi-time form. (author)

  7. Diffeomorphic Statistical Deformation Models

    DEFF Research Database (Denmark)

    Hansen, Michael Sass; Hansen, Mads/Fogtman; Larsen, Rasmus

    2007-01-01

    In this paper we present a new method for constructing diffeomorphic statistical deformation models in arbitrary dimensional images with a nonlinear generative model and a linear parameter space. Our deformation model is a modified version of the diffeomorphic model introduced by Cootes et al....... The modifications ensure that no boundary restriction has to be enforced on the parameter space to prevent folds or tears in the deformation field. For straightforward statistical analysis, principal component analysis and sparse methods, we assume that the parameters for a class of deformations lie on a linear...... with ground truth in form of manual expert annotations, and compared to Cootes's model. We anticipate applications in unconstrained diffeomorphic synthesis of images, e.g. for tracking, segmentation, registration or classification purposes....

  8. Statistical approach to quantum field theory. An introduction

    International Nuclear Information System (INIS)

    Wipf, Andreas

    2013-01-01

    Based on course-tested notes and pedagogical in style. Authored by a leading researcher in the field. Contains end-of-chapter problems and listings of short, useful computer programs. Authored by a leading researcher in the field. Contains end-of-chapter problems and listings of short, useful computer programs. Contains end-of-chapter problems and listings of short, useful computer programs. Over the past few decades the powerful methods of statistical physics and Euclidean quantum field theory have moved closer together, with common tools based on the use of path integrals. The interpretation of Euclidean field theories as particular systems of statistical physics has opened up new avenues for understanding strongly coupled quantum systems or quantum field theories at zero or finite temperatures. Accordingly, the first chapters of this book contain a self-contained introduction to path integrals in Euclidean quantum mechanics and statistical mechanics. The resulting high-dimensional integrals can be estimated with the help of Monte Carlo simulations based on Markov processes. The most commonly used algorithms are presented in detail so as to prepare the reader for the use of high-performance computers as an ''experimental'' tool for this burgeoning field of theoretical physics. Several chapters are then devoted to an introduction to simple lattice field theories and a variety of spin systems with discrete and continuous spins, where the ubiquitous Ising model serves as an ideal guide for introducing the fascinating area of phase transitions. As an alternative to the lattice formulation of quantum field theories, variants of the flexible renormalization group methods are discussed in detail. Since, according to our present-day knowledge, all fundamental interactions in nature are described by gauge theories, the remaining chapters of the book deal with gauge theories without and with matter. This text is based on course-tested notes for graduate students and, as

  9. The quantum Rabi model: solution and dynamics

    International Nuclear Information System (INIS)

    Xie, Qiongtao; Zhong, Honghua; Lee, Chaohong; Batchelor, Murray T

    2017-01-01

    This article presents a review of recent developments on various aspects of the quantum Rabi model. Particular emphasis is given on the exact analytic solution obtained in terms of confluent Heun functions. The analytic solutions for various generalisations of the quantum Rabi model are also discussed. Results are also reviewed on the level statistics and the dynamics of the quantum Rabi model. The article concludes with an introductory overview of several experimental realisations of the quantum Rabi model. An outlook towards future developments is also given. (topical review)

  10. Quantum secure communication models comparison

    Directory of Open Access Journals (Sweden)

    Georgi Petrov Bebrov

    2017-12-01

    Full Text Available The paper concerns the quantum cryptography, more specifically, the quantum secure communication type of schemes. The main focus here is on making a comparison between the distinct secure quantum communication modelsquantum secure direct communication and deterministic secure quantum communication, in terms of three parameters: resource efficiency, eavesdropping check efficiency, and security (degree of preserving the confidentiality.

  11. Quantum statistical metastability for a finite spin

    Science.gov (United States)

    Garanin, D. A.; Chudnovsky, E. M.

    2001-01-01

    We study quantum-classical escape-rate transitions for uniaxial and biaxial models with finite spins S=10 (such as Mn12Ac and Fe8) and S=100 by a direct numerical approach. At second-order transitions the level making a dominant contribution into thermally assisted tunneling changes gradually with temperature whereas at first-order transitions a group of levels is skipped. For finite spins, the quasiclassical boundaries between first- and second-order transitions are shifted, favoring a second-order transition: For Fe8 in zero field the transition should be first order according to a theory with S-->∞, but we show that there are no skipped levels at the transition. Applying a field along the hard axis in Fe8 makes transition the strongest first order. For the same model with S=100 we confirmed the existence of a region where a second-order transition is followed by a first-order transition [X. Martínes Hidalgo and E. M. Chudnovsky, J. Phys.: Condensed Matter 12, 4243 (2000)].

  12. Quantum statistics and liquid helium 3 - helum 4 mixtures

    International Nuclear Information System (INIS)

    Cohen, E.G.D.

    1979-01-01

    The behaviour of liquid helium 3-helium 4 mixtures is considered from the point of view of manifestation of quantum statistics effects in macrophysics. The Boze=Einstein statistics is shown to be of great importance for understanding superfluid helium-4 properties whereas the Fermi-Dirac statistics is of importance for understanding helium-3 properties. Without taking into consideration the interaction between the helium atoms it is impossible to understand the basic properties of liquid helium 33 - helium 4 mixtures at constant pressure. Proposed is a simple model of the liquid helium 3-helium 4 mixture, namely the binary mixture consisting of solid spheres of two types subjecting to the Fermi-Dirac and Bose-Einstein statistics relatively. This model predicts correctly the most surprising peculiarities of phase diagrams of concentration dependence on temperature for helium solutions. In particular, the helium 4 Bose-Einstein statistics is responsible for the phase lamination of helium solutions at low temperatures. It starts in the peculiar critical point. The helium 4 Fermi-Dirac statistics results in incomplete phase lamination close to the absolute zero temperatures, that permits operation of a powerful cooling facility, namely refrigerating machine on helium solution

  13. Integrable lattice models and quantum groups

    International Nuclear Information System (INIS)

    Saleur, H.; Zuber, J.B.

    1990-01-01

    These lectures aim at introducing some basic algebraic concepts on lattice integrable models, in particular quantum groups, and to discuss some connections with knot theory and conformal field theories. The list of contents is: Vertex models and Yang-Baxter equation; Quantum sl(2) algebra and the Yang-Baxter equation; U q sl(2) as a symmetry of statistical mechanical models; Face models; Face models attached to graphs; Yang-Baxter equation, braid group and link polynomials

  14. Are Quantum Models for Order Effects Quantum?

    Science.gov (United States)

    Moreira, Catarina; Wichert, Andreas

    2017-12-01

    The application of principles of Quantum Mechanics in areas outside of physics has been getting increasing attention in the scientific community in an emergent disciplined called Quantum Cognition. These principles have been applied to explain paradoxical situations that cannot be easily explained through classical theory. In quantum probability, events are characterised by a superposition state, which is represented by a state vector in a N-dimensional vector space. The probability of an event is given by the squared magnitude of the projection of this superposition state into the desired subspace. This geometric approach is very useful to explain paradoxical findings that involve order effects, but do we really need quantum principles for models that only involve projections? This work has two main goals. First, it is still not clear in the literature if a quantum projection model has any advantage towards a classical projection. We compared both models and concluded that the Quantum Projection model achieves the same results as its classical counterpart, because the quantum interference effects play no role in the computation of the probabilities. Second, it intends to propose an alternative relativistic interpretation for rotation parameters that are involved in both classical and quantum models. In the end, instead of interpreting these parameters as a similarity measure between questions, we propose that they emerge due to the lack of knowledge concerned with a personal basis state and also due to uncertainties towards the state of world and towards the context of the questions.

  15. Quantum Statistical Entropy of Five-Dimensional Black Hole

    Institute of Scientific and Technical Information of China (English)

    ZHAO Ren; WU Yue-Qin; ZHANG Sheng-Li

    2006-01-01

    The generalized uncertainty relation is introduced to calculate quantum statistic entropy of a black hole.By using the new equation of state density motivated by the generalized uncertainty relation, we discuss entropies of Bose field and Fermi field on the background of the five-dimensional spacetime. In our calculation, we need not introduce cutoff. There is not the divergent logarithmic term as in the original brick-wall method. And it is obtained that the quantum statistic entropy corresponding to black hole horizon is proportional to the area of the horizon. Further it is shown that the entropy of black hole is the entropy of quantum state on the surface of horizon. The black hole's entropy is the intrinsic property of the black hole. The entropy is a quantum effect. It makes people further understand the quantum statistic entropy.

  16. Quantum Statistical Entropy of Five-Dimensional Black Hole

    International Nuclear Information System (INIS)

    Zhao Ren; Zhang Shengli; Wu Yueqin

    2006-01-01

    The generalized uncertainty relation is introduced to calculate quantum statistic entropy of a black hole. By using the new equation of state density motivated by the generalized uncertainty relation, we discuss entropies of Bose field and Fermi field on the background of the five-dimensional spacetime. In our calculation, we need not introduce cutoff. There is not the divergent logarithmic term as in the original brick-wall method. And it is obtained that the quantum statistic entropy corresponding to black hole horizon is proportional to the area of the horizon. Further it is shown that the entropy of black hole is the entropy of quantum state on the surface of horizon. The black hole's entropy is the intrinsic property of the black hole. The entropy is a quantum effect. It makes people further understand the quantum statistic entropy.

  17. Quantum versus classical statistical dynamics of an ultracold Bose gas

    International Nuclear Information System (INIS)

    Berges, Juergen; Gasenzer, Thomas

    2007-01-01

    We investigate the conditions under which quantum fluctuations are relevant for the quantitative interpretation of experiments with ultracold Bose gases. This requires to go beyond the description in terms of the Gross-Pitaevskii and Hartree-Fock-Bogoliubov mean-field theories, which can be obtained as classical (statistical) field-theory approximations of the quantum many-body problem. We employ functional-integral techniques based on the two-particle irreducible (2PI) effective action. The role of quantum fluctuations is studied within the nonperturbative 2PI 1/N expansion to next-to-leading order. At this accuracy level memory integrals enter the dynamic equations, which differ for quantum and classical statistical descriptions. This can be used to obtain a classicality condition for the many-body dynamics. We exemplify this condition by studying the nonequilibrium evolution of a one-dimensional Bose gas of sodium atoms, and discuss some distinctive properties of quantum versus classical statistical dynamics

  18. Analogies between classical statistical mechanics and quantum mechanics

    International Nuclear Information System (INIS)

    Uehara, M.

    1986-01-01

    Some analogies between nonequilibrium classical statistical mechanics and quantum mechanics, at the level of the Liouville equation and at the kinetic level, are commented on. A theorem, related to the Vlasov equation applied to a plasma, is proved. The theorem presents an analogy with Ehrenfest's theorem of quantum mechanics. An analogy between the plasma kinetic theory and Bohm's quantum theory with 'hidden variables' is also shown. (Author) [pt

  19. Integrable quantum impurity models

    International Nuclear Information System (INIS)

    Eckle, H.P.

    1998-01-01

    By modifying some of the local L operators of the algebraic form of the Bethe Ansatz inhomogeneous one dimensional quantum lattice models can be constructed. This fact has recently attracted new attention, the inhomogeneities being interpreted as local impurities. The Hamiltonians of the so constructed one-dimensional quantum models have a nearest neighbour structure except in the vicinity of the local impurities which involve three-site interactions. The pertinent feature of these models is the absence of backscattering at the impurities: the impurities are transparent. (Copyright (1998) World Scientific Publishing Co. Pte. Ltd)

  20. Satyendranath Bose: Co-Founder of Quantum Statistics

    Science.gov (United States)

    Blanpied, William A.

    1972-01-01

    Satyendranath Bose was first to prove Planck's Law by using ideal quantum gas. Einstein credited Bose for this first step in the development of quantum statistical mechanics. Bose did not realize the importance of his work, perhaps because of peculiar academic settings in India under British rule. (PS)

  1. Agents with left and right dominant hemispheres and quantum statistics

    Science.gov (United States)

    Ezhov, Alexandr A.; Khrennikov, Andrei Yu.

    2005-01-01

    We present a multiagent model illustrating the emergence of two different quantum statistics, Bose-Einstein and Fermi-Dirac, in a friendly population of individuals with the right-brain dominance and in a competitive population of individuals with the left-brain hemisphere dominance, correspondingly. Doing so, we adduce the arguments that Lefebvre’s “algebra of conscience” can be used in a natural way to describe decision-making strategies of agents simulating people with different brain dominance. One can suggest that the emergence of the two principal statistical distributions is able to illustrate different types of society organization and also to be used in order to simulate market phenomena and psychic disorders, when a switching of hemisphere dominance is involved.

  2. Quantum kinetic Ising models

    International Nuclear Information System (INIS)

    Augusiak, R; Cucchietti, F M; Lewenstein, M; Haake, F

    2010-01-01

    In this paper, we introduce a quantum generalization of classical kinetic Ising models (KIM), described by a certain class of quantum many-body master equations. Similarly to KIMs with detailed balance that are equivalent to certain Hamiltonian systems, our models reduce to a set of Hamiltonian systems determining the dynamics of the elements of the many-body density matrix. The ground states of these Hamiltonians are well described by the matrix product, or pair entangled projected states. We discuss critical properties of such Hamiltonians, as well as entanglement properties of their low-energy states.

  3. Critical examination of logical formulations in quantum theory. Statistical inference and Hilbertian distance between quantum states

    International Nuclear Information System (INIS)

    Hadjisawas, Nicolas.

    1982-01-01

    After a critical study of the logical quantum mechanics formulations of Jauch and Piron, classical and quantum versions of statistical inference are studied. In order to do this, the significance of the Jaynes and Kulback principles (maximum likelihood, least squares principles) is revealed from the theorems established. In the quantum mechanics inference problem, a ''distance'' between states is defined. This concept is used to solve the quantum equivalent of the classical problem studied by Kulback. The ''projection postulate'' proposition is subsequently deduced [fr

  4. Fast Quantum Algorithm for Predicting Descriptive Statistics of Stochastic Processes

    Science.gov (United States)

    Williams Colin P.

    1999-01-01

    Stochastic processes are used as a modeling tool in several sub-fields of physics, biology, and finance. Analytic understanding of the long term behavior of such processes is only tractable for very simple types of stochastic processes such as Markovian processes. However, in real world applications more complex stochastic processes often arise. In physics, the complicating factor might be nonlinearities; in biology it might be memory effects; and in finance is might be the non-random intentional behavior of participants in a market. In the absence of analytic insight, one is forced to understand these more complex stochastic processes via numerical simulation techniques. In this paper we present a quantum algorithm for performing such simulations. In particular, we show how a quantum algorithm can predict arbitrary descriptive statistics (moments) of N-step stochastic processes in just O(square root of N) time. That is, the quantum complexity is the square root of the classical complexity for performing such simulations. This is a significant speedup in comparison to the current state of the art.

  5. Energy-level statistics and time relaxation in quantum systems

    International Nuclear Information System (INIS)

    Gruver, J.L.; Cerdeira, H.A.; Aliaga, J.; Mello, P.A.; Proto, A.N.

    1997-05-01

    We study a quantum-mechanical system, prepared, at t = 0, in a model state, that subsequently decays into a sea of other states whose energy levels form a discrete spectrum with given statistical properties. An important quantity is the survival probability P(t), defined as the probability, at time t, to find the system in the original model state. Our main purpose is to analyze the influence of the discreteness and statistical properties of the spectrum on the behavior of P(t). Since P(t) itself is a statistical quantity, we restrict our attention to its ensemble average , which is calculated analytically using random-matrix techniques, within certain approximations discussed in the text. We find, for , an exponential decay, followed by a revival, governed by the two-point structure of the statistical spectrum, thus giving a nonzero asymptotic value for large t's. The analytic result compares well with a number of computer simulations, over a time range discussed in the text. (author). 17 refs, 1 fig

  6. Statistical benchmarking for orthogonal electrostatic quantum dot qubit devices

    Science.gov (United States)

    Gamble, John; Frees, Adam; Friesen, Mark; Coppersmith, S. N.

    2014-03-01

    Quantum dots in semiconductor systems have emerged as attractive candidates for the implementation of quantum information processors because of the promise of scalability, manipulability, and integration with existing classical electronics. A limitation in current devices is that the electrostatic gates used for qubit manipulation exhibit strong cross-capacitance, presenting a barrier for practical scale-up. Here, we introduce a statistical framework for making precise the notion of orthogonality. We apply our method to analyze recently implemented designs at the University of Wisconsin-Madison that exhibit much increased orthogonal control than was previously possible. We then use our statistical modeling to future device designs, providing practical guidelines for devices to have robust control properties. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy Nuclear Security Administration under contract DE-AC04-94AL85000. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressly or implied, of the US Government. This work was supported in part by the Laboratory Directed Research and Development program at Sandia National Laboratories, by ARO (W911NF-12-0607), and by the United States Department of Defense.

  7. A model of quantum communication device for quantum hashing

    International Nuclear Information System (INIS)

    Vasiliev, A

    2016-01-01

    In this paper we consider a model of quantum communications between classical computers aided with quantum processors, connected by a classical and a quantum channel. This type of communications implying both classical and quantum messages with moderate use of quantum processing is implicitly used in many quantum protocols, such as quantum key distribution or quantum digital signature. We show that using the model of a quantum processor on multiatomic ensembles in the common QED cavity we can speed up quantum hashing, which can be the basis of quantum digital signature and other communication protocols. (paper)

  8. A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals.

    Science.gov (United States)

    Sinitskiy, Anton V; Voth, Gregory A

    2015-09-07

    Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantum systems at equilibrium has been based on Feynman's imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionist perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantum mechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments.

  9. A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals

    International Nuclear Information System (INIS)

    Sinitskiy, Anton V.; Voth, Gregory A.

    2015-01-01

    Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantum systems at equilibrium has been based on Feynman’s imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionist perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantum mechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments

  10. 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.

  11. Incorporation of quantum statistical features in molecular dynamics

    International Nuclear Information System (INIS)

    Ohnishi, Akira; Randrup, J.

    1995-01-01

    We formulate a method for incorporating quantum fluctuations into molecular-dynamics simulations of many-body systems, such as those employed for energetic nuclear collision processes. Based on Fermi's Golden Rule, we allow spontaneous transitions to occur between the wave packets which are not energy eigenstates. The ensuing diffusive evolution in the space of the wave packet parameters exhibits appealing physical properties, including relaxation towards quantum-statistical equilibrium. (author)

  12. Quantum statistical Monte Carlo methods and applications to spin systems

    International Nuclear Information System (INIS)

    Suzuki, M.

    1986-01-01

    A short review is given concerning the quantum statistical Monte Carlo method based on the equivalence theorem that d-dimensional quantum systems are mapped onto (d+1)-dimensional classical systems. The convergence property of this approximate tansformation is discussed in detail. Some applications of this general appoach to quantum spin systems are reviewed. A new Monte Carlo method, ''thermo field Monte Carlo method,'' is presented, which is an extension of the projection Monte Carlo method at zero temperature to that at finite temperatures

  13. Quantum Link Models and Quantum Simulation of Gauge Theories

    International Nuclear Information System (INIS)

    Wiese, U.J.

    2015-01-01

    This lecture is about Quantum Link Models and Quantum Simulation of Gauge Theories. The lecture consists out of 4 parts. The first part gives a brief history of Computing and Pioneers of Quantum Computing and Quantum Simulations of Quantum Spin Systems are introduced. The 2nd lecture is about High-Temperature Superconductors versus QCD, Wilson’s Lattice QCD and Abelian Quantum Link Models. The 3rd lecture deals with Quantum Simulators for Abelian Lattice Gauge Theories and Non-Abelian Quantum Link Models. The last part of the lecture discusses Quantum Simulators mimicking ‘Nuclear’ physics and the continuum limit of D-Theorie models. (nowak)

  14. Modeling Quantum Well Lasers

    Directory of Open Access Journals (Sweden)

    Dan Alexandru Anghel

    2012-01-01

    Full Text Available In semiconductor laser modeling, a good mathematical model gives near-reality results. Three methods of modeling solutions from the rate equations are presented and analyzed. A method based on the rate equations modeled in Simulink to describe quantum well lasers was presented. For different signal types like step function, saw tooth and sinus used as input, a good response of the used equations is obtained. Circuit model resulting from one of the rate equations models is presented and simulated in SPICE. Results show a good modeling behavior. Numerical simulation in MathCad gives satisfactory results for the study of the transitory and dynamic operation at small level of the injection current. The obtained numerical results show the specific limits of each model, according to theoretical analysis. Based on these results, software can be built that integrates circuit simulation and other modeling methods for quantum well lasers to have a tool that model and analysis these devices from all points of view.

  15. The scientifiv way of thinking in statistics, statistical physics and quantum mechanics

    OpenAIRE

    Săvoiu, Gheorghe

    2008-01-01

    This paper focuses on the way of thinking in both classical and modern Physics and Statistics, Statistical Mechanics or Statistical Physics and Quantum Mechanics. These different statistical ways of thinking and their specific methods have generated new fields for new activities and new scientific disciplines, like Econophysics (between Economics and Physics), Sociophysics (between Sociology and Physics), Mediaphysics (between all media and comunication sciences), etc. After describing some r...

  16. The scientific way of thinking in statistics, statistical physics and quantum mechanics

    OpenAIRE

    Săvoiu, Gheorghe

    2008-01-01

    This paper focuses on the way of thinking in both classical and modern Physics and Statistics, Statistical Mechanics or Statistical Physics and Quantum Mechanics. These different statistical ways of thinking and their specific methods have generated new fields for new activities and new scientific disciplines, like Econophysics (between Economics and Physics), Sociophysics (between Sociology and Physics), Mediaphysics (between all media and comunication sciences), etc. After describing some r...

  17. Stability and equilibrium in quantum statistical mechanics

    International Nuclear Information System (INIS)

    Kastler, Daniel.

    1975-01-01

    A derivation of the Gibbs Ansatz, base of the equilibrium statistical mechanics is provided from a stability requirements, in technical connection with the harmonic analysis of non-commutative dynamical systems. By the same token a relation is established between stability and the positivity of Hamiltonian in the zero temperature case [fr

  18. Composite quantum collision models

    Science.gov (United States)

    Lorenzo, Salvatore; Ciccarello, Francesco; Palma, G. Massimo

    2017-09-01

    A collision model (CM) is a framework to describe open quantum dynamics. In its memoryless version, it models the reservoir R as consisting of a large collection of elementary ancillas: the dynamics of the open system S results from successive collisions of S with the ancillas of R . Here, we present a general formulation of memoryless composite CMs, where S is partitioned into the very open system under study S coupled to one or more auxiliary systems {Si} . Their composite dynamics occurs through internal S -{Si} collisions interspersed with external ones involving {Si} and the reservoir R . We show that important known instances of quantum non-Markovian dynamics of S —such as the emission of an atom into a reservoir featuring a Lorentzian, or multi-Lorentzian, spectral density or a qubit subject to random telegraph noise—can be mapped on to such memoryless composite CMs.

  19. Quantum cosmological models

    International Nuclear Information System (INIS)

    Coule, D H

    2005-01-01

    We contrast the initial condition requirements of various contemporary cosmological models including inflationary and bouncing cosmologies. Canonical quantization of general relativity is used, as a first approximation to full quantum gravity, to determine whether suitable initial conditions are present. Various proposals such as Hartle-Hawking's 'no boundary' or tunnelling boundary conditions are assessed on grounds of naturalness and fine tuning. Alternatively, a quiescent initial state or an initial closed timelike curve 'time machine' is considered. Possible extensions to brane models are also addressed. Further ideas about universe creation from a meta-universe are outlined. Semiclassical and time asymmetry requirements of cosmology are briefly discussed and contrasted with the black-hole final-state proposal. We compare the recent loop quantum cosmology of Bojowald and co-workers with these earlier schemes. A number of possible difficulties and limitations are outlined. (topical review)

  20. Communication: satisfying fermionic statistics in the modeling of open time-dependent quantum systems with one-electron reduced density matrices.

    Science.gov (United States)

    Head-Marsden, Kade; Mazziotti, David A

    2015-02-07

    For an open, time-dependent quantum system, Lindblad derived the most general modification of the quantum Liouville equation in the Markovian approximation that models environmental effects while preserving the non-negativity of the system's density matrix. While Lindblad's modification is correct for N-electron density matrices, solution of the Liouville equation with a Lindblad operator causes the one-electron reduced density matrix (1-RDM) to violate the Pauli exclusion principle. Consequently, after a short time, the 1-RDM is not representable by an ensemble N-electron density matrix (not ensemble N-representable). In this communication, we derive the necessary and sufficient constraints on the Lindbladian matrix within the Lindblad operator to ensure that the 1-RDM remains N-representable for all time. The theory is illustrated by considering the relaxation of an excitation in several molecules F2, N2, CO, and BeH2 subject to environmental noise.

  1. Quantum statistical theory of solid plasma (Com.1)

    International Nuclear Information System (INIS)

    Kim Yon Il

    1986-01-01

    In order to obtain the Hamiltonian of the electron system in solid plasma, the self-consistent electromagnetic field formed by the electron system is quantalized. In this process the longitudinal vector potential is introduced through the relation. The obtained Hamiltonian is expressed by the collective coordinate, consistent with D. Pines' result. Various quantum statistical expressions, the dispersion relation and sum rules of the transverse dielectric function are derived using the fact that the collectived cooredinates are connected with the electromagnetic field in the method in this paper. In additon, various quantum statistical expressions for the longitudinal dielectric function convenient for practical calculations are obtained besides the Nozieres-Pines' expression. (author)

  2. Curvature, zero modes and quantum statistics

    Energy Technology Data Exchange (ETDEWEB)

    Calixto, M [Departamento de Matematica Aplicada y EstadIstica, Universidad Politecnica de Cartagena, Paseo Alfonso XIII 56, 30203 Cartagena (Spain); Aldaya, V [Instituto de AstrofIsica de AndalucIa, Apartado Postal 3004, 18080 Granada (Spain)

    2006-08-18

    We explore an intriguing connection between the Fermi-Dirac and Bose-Einstein statistics and the thermal baths obtained from a vacuum radiation of coherent states of zero modes in a second quantized (many-particle) theory on the compact O(3) and noncompact O(2, 1) isometry subgroups of the de Sitter and anti-de Sitter spaces, respectively. The high frequency limit is retrieved as a (zero-curvature) group contraction to the Newton-Hooke (harmonic oscillator) group. We also make some comments on the vacuum energy density and the cosmological constant problem. (letter to the editor)

  3. Exclusion statistics and integrable models

    International Nuclear Information System (INIS)

    Mashkevich, S.

    1998-01-01

    The definition of exclusion statistics, as given by Haldane, allows for a statistical interaction between distinguishable particles (multi-species statistics). The thermodynamic quantities for such statistics ca be evaluated exactly. The explicit expressions for the cluster coefficients are presented. Furthermore, single-species exclusion statistics is realized in one-dimensional integrable models. The interesting questions of generalizing this correspondence onto the higher-dimensional and the multi-species cases remain essentially open

  4. Dynamics and statistics of unstable quantum states

    International Nuclear Information System (INIS)

    Sokolov, V.V.; Zelevinsky, V.G.

    1989-01-01

    The statistical theory of spectra formulated in terms of random matrices is extended to unstable states. The energies and widths of these states are treated as real and imaginary parts of complex eigenvalues for an effective non-hermitian hamiltonian. Eigenvalue statistics are investigated under simple assumptions. If the coupling through common decay channels is weak we obtain a Wigner distribution for the level spacings and a Porter-Thomas one for the widths, with the only exception for spacings less than widths where level repulsion fades out. Meanwhile in the complex energy plane the repulsion of eigenvalues is quadratic in accordance with the T-noninvariant character of decaying systems. In the opposite case of strong coupling with the continuum, k short-lived states are formed (k is the number of open decay channels). These states accumulate almost the whole total width, the rest of the states becoming long-lived. Such a perestroika corresponds to separation of direct processes (a nuclear analogue of Dicke coherent superradiance). At small channel number, Ericson fluctuations of the cross sections are found to be suppressed. The one-channel case is considered in detail. The joint distribution of energies and widths is obtained. The average cross sections and density of unstable states are calculated. (orig.)

  5. Counting statistics of many-particle quantum walks

    Science.gov (United States)

    Mayer, Klaus; Tichy, Malte C.; Mintert, Florian; Konrad, Thomas; Buchleitner, Andreas

    2011-06-01

    We study quantum walks of many noninteracting particles on a beam splitter array as a paradigmatic testing ground for the competition of single- and many-particle interference in a multimode system. We derive a general expression for multimode particle-number correlation functions, valid for bosons and fermions, and infer pronounced signatures of many-particle interferences in the counting statistics.

  6. Counting statistics of many-particle quantum walks

    International Nuclear Information System (INIS)

    Mayer, Klaus; Tichy, Malte C.; Buchleitner, Andreas; Mintert, Florian; Konrad, Thomas

    2011-01-01

    We study quantum walks of many noninteracting particles on a beam splitter array as a paradigmatic testing ground for the competition of single- and many-particle interference in a multimode system. We derive a general expression for multimode particle-number correlation functions, valid for bosons and fermions, and infer pronounced signatures of many-particle interferences in the counting statistics.

  7. Quantum random oracle model for quantum digital signature

    Science.gov (United States)

    Shang, Tao; Lei, Qi; Liu, Jianwei

    2016-10-01

    The goal of this work is to provide a general security analysis tool, namely, the quantum random oracle (QRO), for facilitating the security analysis of quantum cryptographic protocols, especially protocols based on quantum one-way function. QRO is used to model quantum one-way function and different queries to QRO are used to model quantum attacks. A typical application of quantum one-way function is the quantum digital signature, whose progress has been hampered by the slow pace of the experimental realization. Alternatively, we use the QRO model to analyze the provable security of a quantum digital signature scheme and elaborate the analysis procedure. The QRO model differs from the prior quantum-accessible random oracle in that it can output quantum states as public keys and give responses to different queries. This tool can be a test bed for the cryptanalysis of more quantum cryptographic protocols based on the quantum one-way function.

  8. Local box-counting dimensions of discrete quantum eigenvalue spectra: Analytical connection to quantum spectral statistics

    Science.gov (United States)

    Sakhr, Jamal; Nieminen, John M.

    2018-03-01

    Two decades ago, Wang and Ong, [Phys. Rev. A 55, 1522 (1997)], 10.1103/PhysRevA.55.1522 hypothesized that the local box-counting dimension of a discrete quantum spectrum should depend exclusively on the nearest-neighbor spacing distribution (NNSD) of the spectrum. In this Rapid Communication, we validate their hypothesis by deriving an explicit formula for the local box-counting dimension of a countably-infinite discrete quantum spectrum. This formula expresses the local box-counting dimension of a spectrum in terms of single and double integrals of the NNSD of the spectrum. As applications, we derive an analytical formula for Poisson spectra and closed-form approximations to the local box-counting dimension for spectra having Gaussian orthogonal ensemble (GOE), Gaussian unitary ensemble (GUE), and Gaussian symplectic ensemble (GSE) spacing statistics. In the Poisson and GOE cases, we compare our theoretical formulas with the published numerical data of Wang and Ong and observe excellent agreement between their data and our theory. We also study numerically the local box-counting dimensions of the Riemann zeta function zeros and the alternate levels of GOE spectra, which are often used as numerical models of spectra possessing GUE and GSE spacing statistics, respectively. In each case, the corresponding theoretical formula is found to accurately describe the numerically computed local box-counting dimension.

  9. Exclusion statistics and integrable models

    International Nuclear Information System (INIS)

    Mashkevich, S.

    1998-01-01

    The definition of exclusion statistics that was given by Haldane admits a 'statistical interaction' between distinguishable particles (multispecies statistics). For such statistics, thermodynamic quantities can be evaluated exactly; explicit expressions are presented here for cluster coefficients. Furthermore, single-species exclusion statistics is realized in one-dimensional integrable models of the Calogero-Sutherland type. The interesting questions of generalizing this correspondence to the higher-dimensional and the multispecies cases remain essentially open; however, our results provide some hints as to searches for the models in question

  10. Single-server blind quantum computation with quantum circuit model

    Science.gov (United States)

    Zhang, Xiaoqian; Weng, Jian; Li, Xiaochun; Luo, Weiqi; Tan, Xiaoqing; Song, Tingting

    2018-06-01

    Blind quantum computation (BQC) enables the client, who has few quantum technologies, to delegate her quantum computation to a server, who has strong quantum computabilities and learns nothing about the client's quantum inputs, outputs and algorithms. In this article, we propose a single-server BQC protocol with quantum circuit model by replacing any quantum gate with the combination of rotation operators. The trap quantum circuits are introduced, together with the combination of rotation operators, such that the server is unknown about quantum algorithms. The client only needs to perform operations X and Z, while the server honestly performs rotation operators.

  11. Semiclassical quantum gravity: statistics of combinatorial Riemannian geometries

    International Nuclear Information System (INIS)

    Bombelli, L.; Corichi, A.; Winkler, O.

    2005-01-01

    This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at ''quantum scales'' and continuum, classical geometries at large scales. Such a correspondence can be meaningfully established when one has a ''semiclassical'' state in the underlying quantum gravity theory, and the uncertainties in the correspondence arise both from quantum fluctuations in this state and from the kinematical procedure of matching a smooth geometry to a discrete one. We focus on the latter type of uncertainty, and suggest the use of statistical geometry as a way to quantify it. With a cell complex as an example of discrete structure, we discuss how to construct quantities that define a smooth geometry, and how to estimate the associated uncertainties. We also comment briefly on how to combine our results with uncertainties in the underlying quantum state, and on their use when considering phenomenological aspects of quantum gravity. (Abstract Copyright [2005], Wiley Periodicals, Inc.)

  12. Collision models in quantum optics

    Science.gov (United States)

    Ciccarello, Francesco

    2017-12-01

    Quantum collision models (CMs) provide advantageous case studies for investigating major issues in open quantum systems theory, and especially quantum non-Markovianity. After reviewing their general definition and distinctive features, we illustrate the emergence of a CM in a familiar quantum optics scenario. This task is carried out by highlighting the close connection between the well-known input-output formalism and CMs. Within this quantum optics framework, usual assumptions in the CMs' literature - such as considering a bath of noninteracting yet initially correlated ancillas - have a clear physical origin.

  13. Machine learning Z2 quantum spin liquids with quasiparticle statistics

    Science.gov (United States)

    Zhang, Yi; Melko, Roger G.; Kim, Eun-Ah

    2017-12-01

    After decades of progress and effort, obtaining a phase diagram for a strongly correlated topological system still remains a challenge. Although in principle one could turn to Wilson loops and long-range entanglement, evaluating these nonlocal observables at many points in phase space can be prohibitively costly. With growing excitement over topological quantum computation comes the need for an efficient approach for obtaining topological phase diagrams. Here we turn to machine learning using quantum loop topography (QLT), a notion we have recently introduced. Specifically, we propose a construction of QLT that is sensitive to quasiparticle statistics. We then use mutual statistics between the spinons and visons to detect a Z2 quantum spin liquid in a multiparameter phase space. We successfully obtain the quantum phase boundary between the topological and trivial phases using a simple feed-forward neural network. Furthermore, we demonstrate advantages of our approach for the evaluation of phase diagrams relating to speed and storage. Such statistics-based machine learning of topological phases opens new efficient routes to studying topological phase diagrams in strongly correlated systems.

  14. Quantum probability, choice in large worlds, and the statistical structure of reality.

    Science.gov (United States)

    Ross, Don; Ladyman, James

    2013-06-01

    Classical probability models of incentive response are inadequate in "large worlds," where the dimensions of relative risk and the dimensions of similarity in outcome comparisons typically differ. Quantum probability models for choice in large worlds may be motivated pragmatically - there is no third theory - or metaphysically: statistical processing in the brain adapts to the true scale-relative structure of the universe.

  15. Algebraic methods in statistical mechanics and quantum field theory

    CERN Document Server

    Emch, Dr Gérard G

    2009-01-01

    This systematic algebraic approach concerns problems involving a large number of degrees of freedom. It extends the traditional formalism of quantum mechanics, and it eliminates conceptual and mathematical difficulties common to the development of statistical mechanics and quantum field theory. Further, the approach is linked to research in applied and pure mathematics, offering a reflection of the interplay between formulation of physical motivations and self-contained descriptions of the mathematical methods.The four-part treatment begins with a survey of algebraic approaches to certain phys

  16. Statistical Model of Extreme Shear

    DEFF Research Database (Denmark)

    Larsen, Gunner Chr.; Hansen, Kurt Schaldemose

    2004-01-01

    In order to continue cost-optimisation of modern large wind turbines, it is important to continously increase the knowledge on wind field parameters relevant to design loads. This paper presents a general statistical model that offers site-specific prediction of the probability density function...... by a model that, on a statistically consistent basis, describe the most likely spatial shape of an extreme wind shear event. Predictions from the model have been compared with results from an extreme value data analysis, based on a large number of high-sampled full-scale time series measurements...... are consistent, given the inevitabel uncertainties associated with model as well as with the extreme value data analysis. Keywords: Statistical model, extreme wind conditions, statistical analysis, turbulence, wind loading, statistical analysis, turbulence, wind loading, wind shear, wind turbines....

  17. Solvable model of quantum microcanonical states

    International Nuclear Information System (INIS)

    Bender, Carl M; Brody, Dorje C; Hook, Daniel W

    2005-01-01

    This letter examines the consequences of a recently proposed modification of the postulate of equal a priori probability in quantum statistical mechanics. This modification, called the quantum microcanonical postulate (QMP), asserts that for a system in microcanonical equilibrium all pure quantum states having the same energy expectation value are realized with equal probability. A simple model of a quantum system that obeys the QMP and that has a nondegenerate spectrum with equally spaced energy eigenvalues is studied. This model admits a closed-form expression for the density of states in terms of the energy eigenvalues. It is shown that in the limit as the number of energy levels approaches infinity, the expression for the density of states converges to a δ function centred at the intermediate value (E max + E min )/2 of the energy. Determining this limit requires an elaborate asymptotic study of an infinite sum whose terms alternate in sign. (letter to the editor)

  18. Statistical modeling for degradation data

    CERN Document Server

    Lio, Yuhlong; Ng, Hon; Tsai, Tzong-Ru

    2017-01-01

    This book focuses on the statistical aspects of the analysis of degradation data. In recent years, degradation data analysis has come to play an increasingly important role in different disciplines such as reliability, public health sciences, and finance. For example, information on products’ reliability can be obtained by analyzing degradation data. In addition, statistical modeling and inference techniques have been developed on the basis of different degradation measures. The book brings together experts engaged in statistical modeling and inference, presenting and discussing important recent advances in degradation data analysis and related applications. The topics covered are timely and have considerable potential to impact both statistics and reliability engineering.

  19. Interaction of a quantum well with squeezed light: Quantum-statistical properties

    International Nuclear Information System (INIS)

    Sete, Eyob A.; Eleuch, H.

    2010-01-01

    We investigate the quantum statistical properties of the light emitted by a quantum well interacting with squeezed light from a degenerate subthreshold optical parametric oscillator. We obtain analytical solutions for the pertinent quantum Langevin equations in the strong-coupling and low-excitation regimes. Using these solutions we calculate the intensity spectrum, autocorrelation function, and quadrature squeezing for the fluorescent light. We show that the fluorescent light exhibits bunching and quadrature squeezing. We also show that the squeezed light leads to narrowing of the width of the spectrum of the fluorescent light.

  20. Statistical modelling with quantile functions

    CERN Document Server

    Gilchrist, Warren

    2000-01-01

    Galton used quantiles more than a hundred years ago in describing data. Tukey and Parzen used them in the 60s and 70s in describing populations. Since then, the authors of many papers, both theoretical and practical, have used various aspects of quantiles in their work. Until now, however, no one put all the ideas together to form what turns out to be a general approach to statistics.Statistical Modelling with Quantile Functions does just that. It systematically examines the entire process of statistical modelling, starting with using the quantile function to define continuous distributions. The author shows that by using this approach, it becomes possible to develop complex distributional models from simple components. A modelling kit can be developed that applies to the whole model - deterministic and stochastic components - and this kit operates by adding, multiplying, and transforming distributions rather than data.Statistical Modelling with Quantile Functions adds a new dimension to the practice of stati...

  1. Negative values of quasidistributions and quantum wave and number statistics

    Science.gov (United States)

    Peřina, J.; Křepelka, J.

    2018-04-01

    We consider nonclassical wave and number quantum statistics, and perform a decomposition of quasidistributions for nonlinear optical down-conversion processes using Bessel functions. We show that negative values of the quasidistribution do not directly represent probabilities; however, they directly influence measurable number statistics. Negative terms in the decomposition related to the nonclassical behavior with negative amplitudes of probability can be interpreted as positive amplitudes of probability in the negative orthogonal Bessel basis, whereas positive amplitudes of probability in the positive basis describe classical cases. However, probabilities are positive in all cases, including negative values of quasidistributions. Negative and positive contributions of decompositions to quasidistributions are estimated. The approach can be adapted to quantum coherence functions.

  2. Probing the statistical properties of Anderson localization with quantum emitters

    International Nuclear Information System (INIS)

    Smolka, Stephan; Thyrrestrup, Henri; Sapienza, Luca; Lehmann, Tau B; Rix, Kristian R; GarcIa, Pedro D; Lodahl, Peter; Froufe-Perez, Luis S

    2011-01-01

    Wave propagation in disordered media can be strongly modified by multiple scattering and wave interference. Ultimately, the so-called Anderson-localized regime is reached when the waves become strongly confined in space. So far, Anderson localization of light has been probed in transmission experiments by measuring the intensity of an external light source after propagation through a disordered medium. However, discriminating between Anderson localization and losses in these experiments remains a major challenge. In this paper, we present an alternative approach where we use quantum emitters embedded in disordered photonic crystal waveguides as light sources. Anderson-localized modes are efficiently excited and the analysis of the photoluminescence spectra allows us to explore their statistical properties, for example the localization length and average loss length. With increasing the amount of disorder induced in the photonic crystal, we observe a pronounced increase in the localization length that is attributed to changes in the local density of states, a behavior that is in stark contrast to entirely random systems. The analysis may pave the way for accurate models and the control of Anderson localization in disordered photonic crystals.

  3. Quantum mean-field approximation for lattice quantum models: Truncating quantum correlations and retaining classical ones

    Science.gov (United States)

    Malpetti, Daniele; Roscilde, Tommaso

    2017-02-01

    The mean-field approximation is at the heart of our understanding of complex systems, despite its fundamental limitation of completely neglecting correlations between the elementary constituents. In a recent work [Phys. Rev. Lett. 117, 130401 (2016), 10.1103/PhysRevLett.117.130401], we have shown that in quantum many-body systems at finite temperature, two-point correlations can be formally separated into a thermal part and a quantum part and that quantum correlations are generically found to decay exponentially at finite temperature, with a characteristic, temperature-dependent quantum coherence length. The existence of these two different forms of correlation in quantum many-body systems suggests the possibility of formulating an approximation, which affects quantum correlations only, without preventing the correct description of classical fluctuations at all length scales. Focusing on lattice boson and quantum Ising models, we make use of the path-integral formulation of quantum statistical mechanics to introduce such an approximation, which we dub quantum mean-field (QMF) approach, and which can be readily generalized to a cluster form (cluster QMF or cQMF). The cQMF approximation reduces to cluster mean-field theory at T =0 , while at any finite temperature it produces a family of systematically improved, semi-classical approximations to the quantum statistical mechanics of the lattice theory at hand. Contrary to standard MF approximations, the correct nature of thermal critical phenomena is captured by any cluster size. In the two exemplary cases of the two-dimensional quantum Ising model and of two-dimensional quantum rotors, we study systematically the convergence of the cQMF approximation towards the exact result, and show that the convergence is typically linear or sublinear in the boundary-to-bulk ratio of the clusters as T →0 , while it becomes faster than linear as T grows. These results pave the way towards the development of semiclassical numerical

  4. Quantum mechanics as a natural generalization of classical statistical mechanics

    International Nuclear Information System (INIS)

    Xu Laizi; Qian Shangwu

    1994-01-01

    By comparison between equations of motion of geometrical optics (GO) and that of classical statistical mechanics (CSM), it is found that there should be an analogy between GO and CSM instead of GO and classical mechanics (CM). Furthermore, by comparison between the classical limit (CL) of quantum mechanics (QM) and CSM, the authors find that CL of QM is CSM not CM, hence they demonstrated that QM is a natural generalization of CSM instead of CM

  5. Lifetime statistics of quantum chaos studied by a multiscale analysis

    KAUST Repository

    Di Falco, A.

    2012-04-30

    In a series of pump and probe experiments, we study the lifetime statistics of a quantum chaotic resonator when the number of open channels is greater than one. Our design embeds a stadium billiard into a two dimensional photonic crystal realized on a silicon-on-insulator substrate. We calculate resonances through a multiscale procedure that combines energy landscape analysis and wavelet transforms. Experimental data is found to follow the universal predictions arising from random matrix theory with an excellent level of agreement.

  6. A Statistical Programme Assignment Model

    DEFF Research Database (Denmark)

    Rosholm, Michael; Staghøj, Jonas; Svarer, Michael

    When treatment effects of active labour market programmes are heterogeneous in an observable way  across the population, the allocation of the unemployed into different programmes becomes a particularly  important issue. In this paper, we present a statistical model designed to improve the present...... duration of unemployment spells may result if a statistical programme assignment model is introduced. We discuss several issues regarding the  plementation of such a system, especially the interplay between the statistical model and  case workers....

  7. Introduction to nonequilibrium statistical mechanics with quantum field theory

    International Nuclear Information System (INIS)

    Kita, Takafumi

    2010-01-01

    In this article, we present a concise and self-contained introduction to nonequilibrium statistical mechanics with quantum field theory by considering an ensemble of interacting identical bosons or fermions as an example. Readers are assumed to be familiar with the Matsubara formalism of equilibrium statistical mechanics such as Feynman diagrams, the proper self-energy, and Dyson's equation. The aims are threefold: (1) to explain the fundamentals of nonequilibrium quantum field theory as simple as possible on the basis of the knowledge of the equilibrium counterpart; (2) to elucidate the hierarchy in describing nonequilibrium systems from Dyson's equation on the Keldysh contour to the Navier-Stokes equation in fluid mechanics via quantum transport equations and the Boltzmann equation; (3) to derive an expression of nonequilibrium entropy that evolves with time. In stage (1), we introduce nonequilibrium Green's function and the self-energy uniquely on the round-trip Keldysh contour, thereby avoiding possible confusions that may arise from defining multiple Green's functions at the very beginning. We try to present the Feynman rules for the perturbation expansion as simple as possible. In particular, we focus on the self-consistent perturbation expansion with the Luttinger-Ward thermodynamic functional, i.e., Baym's Φ-derivable approximation, which has a crucial property for nonequilibrium systems of obeying various conservation laws automatically. We also show how the two-particle correlations can be calculated within the Φ-derivable approximation, i.e., an issue of how to handle the 'Bogoliubov-Born-Green-Kirkwood-Yvons (BBGKY) hierarchy'. Aim (2) is performed through successive reductions of relevant variables with the Wigner transformation, the gradient expansion based on the Groenewold-Moyal product, and Enskog's expansion from local equilibrium. This part may be helpful for convincing readers that nonequilibrium systems can be handled microscopically with

  8. Spectral deformation techniques applied to the study of quantum statistical irreversible processes

    International Nuclear Information System (INIS)

    Courbage, M.

    1978-01-01

    A procedure of analytic continuation of the resolvent of Liouville operators for quantum statistical systems is discussed. When applied to the theory of irreversible processes of the Brussels School, this method supports the idea that the restriction to a class of initial conditions is necessary to obtain an irreversible behaviour. The general results are tested on the Friedrichs model. (Auth.)

  9. Models of optical quantum computing

    Directory of Open Access Journals (Sweden)

    Krovi Hari

    2017-03-01

    Full Text Available I review some work on models of quantum computing, optical implementations of these models, as well as the associated computational power. In particular, we discuss the circuit model and cluster state implementations using quantum optics with various encodings such as dual rail encoding, Gottesman-Kitaev-Preskill encoding, and coherent state encoding. Then we discuss intermediate models of optical computing such as boson sampling and its variants. Finally, we review some recent work in optical implementations of adiabatic quantum computing and analog optical computing. We also provide a brief description of the relevant aspects from complexity theory needed to understand the results surveyed.

  10. Digital Quantum Simulation of Spin Models with Circuit Quantum Electrodynamics

    OpenAIRE

    Salathé, Y.; Mondal, M.; Oppliger, M.; Heinsoo, J.; Kurpiers, P.; Potočnik, A.; Mezzacapo, Antonio; Las Heras García, Urtzi; Lamata Manuel, Lucas; Solano Villanueva, Enrique Leónidas; Filipp, S.; Wallraff, A.

    2015-01-01

    Systems of interacting quantum spins show a rich spectrum of quantum phases and display interesting many-body dynamics. Computing characteristics of even small systems on conventional computers poses significant challenges. A quantum simulator has the potential to outperform standard computers in calculating the evolution of complex quantum systems. Here, we perform a digital quantum simulation of the paradigmatic Heisenberg and Ising interacting spin models using a two transmon-qubit circuit...

  11. Quantum theory and statistical thermodynamics principles and worked examples

    CERN Document Server

    Hertel, Peter

    2017-01-01

    This textbook presents a concise yet detailed introduction to quantum physics. Concise, because it condenses the essentials to a few principles. Detailed, because these few principles –  necessarily rather abstract – are illustrated by several telling examples. A fairly complete overview of the conventional quantum mechanics curriculum is the primary focus, but the huge field of statistical thermodynamics is covered as well. The text explains why a few key discoveries shattered the prevailing broadly accepted classical view of physics. First, matter appears to consist of particles which, when propagating, resemble waves. Consequently, some observable properties cannot be measured simultaneously with arbitrary precision. Second, events with single particles are not determined, but are more or less probable. The essence of this is that the observable properties of a physical system are to be represented by non-commuting mathematical objects instead of real numbers.  Chapters on exceptionally simple, but h...

  12. Vortices in superconducting films: Statistics and fractional quantum Hall effect

    International Nuclear Information System (INIS)

    Dziarmaga, J.

    1996-01-01

    We present a derivation of the Berry phase picked up during exchange of parallel vortices. This derivation is based on the Bogolubov endash de Gennes formalism. The origin of the Magnus force is also critically reanalyzed. The Magnus force can be interpreted as an interaction with the effective magnetic field. The effective magnetic field may be even of the order 10 6 T/A. We discuss a possibility of the fractional quantum Hall effect (FQHE) in vortex systems. As the real magnetic field is varied to drive changes in vortex density, the vortex density will prefer to stay at some quantized values. The mere existence of the FQHE does not depend on vortex quantum statistics, although the pattern of the plateaux does. We also discuss how the density of anyonic vortices can lower the effective strengh of the Magnus force, what might be observable in measurements of Hall resistivity. copyright 1996 The American Physical Society

  13. Tropical geometry of statistical models.

    Science.gov (United States)

    Pachter, Lior; Sturmfels, Bernd

    2004-11-16

    This article presents a unified mathematical framework for inference in graphical models, building on the observation that graphical models are algebraic varieties. From this geometric viewpoint, observations generated from a model are coordinates of a point in the variety, and the sum-product algorithm is an efficient tool for evaluating specific coordinates. Here, we address the question of how the solutions to various inference problems depend on the model parameters. The proposed answer is expressed in terms of tropical algebraic geometry. The Newton polytope of a statistical model plays a key role. Our results are applied to the hidden Markov model and the general Markov model on a binary tree.

  14. Statistical Model of Extreme Shear

    DEFF Research Database (Denmark)

    Hansen, Kurt Schaldemose; Larsen, Gunner Chr.

    2005-01-01

    In order to continue cost-optimisation of modern large wind turbines, it is important to continuously increase the knowledge of wind field parameters relevant to design loads. This paper presents a general statistical model that offers site-specific prediction of the probability density function...... by a model that, on a statistically consistent basis, describes the most likely spatial shape of an extreme wind shear event. Predictions from the model have been compared with results from an extreme value data analysis, based on a large number of full-scale measurements recorded with a high sampling rate...

  15. Statistical Models for Social Networks

    NARCIS (Netherlands)

    Snijders, Tom A. B.; Cook, KS; Massey, DS

    2011-01-01

    Statistical models for social networks as dependent variables must represent the typical network dependencies between tie variables such as reciprocity, homophily, transitivity, etc. This review first treats models for single (cross-sectionally observed) networks and then for network dynamics. For

  16. Quantum Oscillator in the Thermostat as a Model in the Thermodynamics of Open Quantum Systems

    OpenAIRE

    Sukhanov, Aleksander

    2005-01-01

    The quantum oscillator in the thermostat is considered as the model of an open quantum system. Our analysis will be heavily founded on the use of the Schroedinger generalized uncertainties relations (SUR). Our first aim is to demonstrate that for the quantum oscillator the state of thermal equilibrium belongs to the correlated coherent states (CCS), which imply the saturation of SUR at any temperature. The obtained results open the perspective for the search of some statistical theory, which ...

  17. Quantum-like Modeling of Cognition

    Science.gov (United States)

    Khrennikov, Andrei

    2015-09-01

    This paper begins with a historical review of the mutual influence of physics and psychology, from Freud's invention of psychic energy inspired by von Boltzmann' thermodynamics to the enrichment quantum physics gained from the side of psychology by the notion of complementarity (the invention of Niels Bohr who was inspired by William James), besides we consider the resonance of the correspondence between Wolfgang Pauli and Carl Jung in both physics and psychology. Then we turn to the problem of development of mathematical models for laws of thought starting with Boolean logic and progressing towards foundations of classical probability theory. Interestingly, the laws of classical logic and probability are routinely violated not only by quantum statistical phenomena but by cognitive phenomena as well. This is yet another common feature between quantum physics and psychology. In particular, cognitive data can exhibit a kind of the probabilistic interference effect. This similarity with quantum physics convinced a multi-disciplinary group of scientists (physicists, psychologists, economists, sociologists) to apply the mathematical apparatus of quantum mechanics to modeling of cognition. We illustrate this activity by considering a few concrete phenomena: the order and disjunction effects, recognition of ambiguous figures, categorization-decision making. In Appendix 1 we briefly present essentials of theory of contextual probability and a method of representations of contextual probabilities by complex probability amplitudes (solution of the ``inverse Born's problem'') based on a quantum-like representation algorithm (QLRA).

  18. Quantum-like Modeling of Cognition

    Directory of Open Access Journals (Sweden)

    Andrei eKhrennikov

    2015-09-01

    Full Text Available This paper begins with a historical review of the mutual influence of physics and psychology, from Freud's invention of psychic energy inspired by von Boltzmann' thermodynamics to the enrichment quantum physics gained from the side of psychology by the notion of complementarity (the invention of Niels Bohr who was inspired by William James, besides we consider the resonance of the correspondence between Wolfgang Pauli and Carl Jung in both physics and psychology. Then we turn to the problem of development of mathematical models for laws of thought starting with Boolean logic and progressing towards foundations of classical probability theory. Interestingly, the laws of classical logic and probability are routinely violated not only by quantum statistical phenomena but by cognitive phenomena as well. This is yet another common feature between quantum physics and psychology.In particular, cognitive data can exhibit a kind of the probabilistic interference effect. This similarity with quantum physics convinced a multi-disciplinary group of scientists (physicists, psychologists, economists, sociologists to apply the mathematical apparatus of quantum mechanics to modeling of cognition. We illustrate this activity by considering a few concrete phenomena: the order and disjunction effects, recognition of ambiguous figures, categorization-decision making.In Appendix 1 we briefly present essentials of theory of contextual probability and a method of representations of contextual probabilities by complex probability amplitudes(solution of the ``inverse Born's problem'' based on a quantum-like representation algorithm (QLRA.

  19. The spin-statistics connection in quantum gravity

    International Nuclear Information System (INIS)

    Balachandran, A.P.; Batista, E.; Costa e Silva, I.P.; Teotonio-Sobrinho, P.

    2000-01-01

    It is well known that in spite of sharing some properties with conventional particles, topological geons in general violate the spin-statistics theorem. On the other hand, it is generally believed that in quantum gravity theories allowing for topology change, using pair creation and annihilation of geons, one should be able to recover this theorem. In this paper, we take an alternative route, and use an algebraic formalism developed in previous work. We give a description of topological geons where an algebra of 'observables' is identified and quantized. Different irreducible representations of this algebra correspond to different kinds of geons, and are labeled by a non-abelian 'charge' and 'magnetic flux'. We then find that the usual spin-statistics theorem is indeed violated, but a new spin-statistics relation arises, when we assume that the fluxes are superselected. This assumption can be proved if all observables are local, as is generally the case in physical theories. Finally, we also discuss how our approach fits into conventional formulations of quantum gravity

  20. Reversibility in Quantum Models of Stochastic Processes

    Science.gov (United States)

    Gier, David; Crutchfield, James; Mahoney, John; James, Ryan

    Natural phenomena such as time series of neural firing, orientation of layers in crystal stacking and successive measurements in spin-systems are inherently probabilistic. The provably minimal classical models of such stochastic processes are ɛ-machines, which consist of internal states, transition probabilities between states and output values. The topological properties of the ɛ-machine for a given process characterize the structure, memory and patterns of that process. However ɛ-machines are often not ideal because their statistical complexity (Cμ) is demonstrably greater than the excess entropy (E) of the processes they represent. Quantum models (q-machines) of the same processes can do better in that their statistical complexity (Cq) obeys the relation Cμ >= Cq >= E. q-machines can be constructed to consider longer lengths of strings, resulting in greater compression. With code-words of sufficiently long length, the statistical complexity becomes time-symmetric - a feature apparently novel to this quantum representation. This result has ramifications for compression of classical information in quantum computing and quantum communication technology.

  1. Sensometrics: Thurstonian and Statistical Models

    DEFF Research Database (Denmark)

    Christensen, Rune Haubo Bojesen

    . sensR is a package for sensory discrimination testing with Thurstonian models and ordinal supports analysis of ordinal data with cumulative link (mixed) models. While sensR is closely connected to the sensometrics field, the ordinal package has developed into a generic statistical package applicable......This thesis is concerned with the development and bridging of Thurstonian and statistical models for sensory discrimination testing as applied in the scientific discipline of sensometrics. In sensory discrimination testing sensory differences between products are detected and quantified by the use...... and sensory discrimination testing in particular in a series of papers by advancing Thurstonian models for a range of sensory discrimination protocols in addition to facilitating their application by providing software for fitting these models. The main focus is on identifying Thurstonian models...

  2. Fisher information and quantum potential well model for finance

    Energy Technology Data Exchange (ETDEWEB)

    Nastasiuk, V.A., E-mail: nasa@i.ua

    2015-09-25

    The probability distribution function (PDF) for prices on financial markets is derived by extremization of Fisher information. It is shown how on that basis the quantum-like description for financial markets arises and different financial market models are mapped by quantum mechanical ones. - Highlights: • The financial Schrödinger equation is derived using the principle of minimum Fisher information. • Statistical models for price variation are mapped by the quantum models of coupled particle. • The model of quantum particle in parabolic potential well corresponds to Efficient market.

  3. Fisher information and quantum potential well model for finance

    International Nuclear Information System (INIS)

    Nastasiuk, V.A.

    2015-01-01

    The probability distribution function (PDF) for prices on financial markets is derived by extremization of Fisher information. It is shown how on that basis the quantum-like description for financial markets arises and different financial market models are mapped by quantum mechanical ones. - Highlights: • The financial Schrödinger equation is derived using the principle of minimum Fisher information. • Statistical models for price variation are mapped by the quantum models of coupled particle. • The model of quantum particle in parabolic potential well corresponds to Efficient market

  4. Statistical quasi-particle theory for open quantum systems

    Science.gov (United States)

    Zhang, Hou-Dao; Xu, Rui-Xue; Zheng, Xiao; Yan, YiJing

    2018-04-01

    This paper presents a comprehensive account on the recently developed dissipaton-equation-of-motion (DEOM) theory. This is a statistical quasi-particle theory for quantum dissipative dynamics. It accurately describes the influence of bulk environments, with a few number of quasi-particles, the dissipatons. The novel dissipaton algebra is then followed, which readily bridges the Schrödinger equation to the DEOM theory. As a fundamental theory of quantum mechanics in open systems, DEOM characterizes both the stationary and dynamic properties of system-and-bath interferences. It treats not only the quantum dissipative systems of primary interest, but also the hybrid environment dynamics that could be experimentally measurable. Examples are the linear or nonlinear Fano interferences and the Herzberg-Teller vibronic couplings in optical spectroscopies. This review covers the DEOM construction, the underlying dissipaton algebra and theorems, the physical meanings of dynamical variables, the possible identifications of dissipatons, and some recent advancements in efficient DEOM evaluations on various problems. The relations of the present theory to other nonperturbative methods are also critically presented.

  5. The spectrum and the quantum Hall effect on the square lattice with next-nearest-neighbor hopping: Statistics of holons and spinons in the t-J model

    International Nuclear Information System (INIS)

    Hatsugai, Y.; Kohmoto, M.

    1992-01-01

    We investigate the energy spectrum and the Hall effect of electrons on the square lattice with next-nearest-neighbor (NNN) hopping as well as nearest-neighbor hopping. General rational values of magnetic flux per unit cell φ=p/q are considered. In the absence of NNN hopping, the two bands at the center touch for q even, thus the Hall conductance is not well defined at half filling. An energy gap opens there by introducing NNN hoping. When φ=1/2, the NNN model coincides with the mean field Hamiltonian for the chiral spin state proposed by Wen, Wilczek and Zee (WWZ). The Hall conductance is calculated from the Diophantine equation and the E-φ diagram. We find that gaps close for other fillings at certain values of NNN hopping strength. The quantized value of the Hall conductance changes once this phenomenon occurs. In a mean field treatment of the t-J model, the effective Hamiltonian is the same as our NNN model. From this point of view, the statistics of the quasi-particles is not always semion and depends on the filling and the strength of the mean field. (orig.)

  6. Index of subfactors and statistics of quantum fields. Pt. 2

    International Nuclear Information System (INIS)

    Longo, R.

    1990-01-01

    The endomorphism semigroup End(M) of an infinite factor M is endowed with a natural conjugation (modulo inner automorphisms) anti ρ=ρ -1. γ, where γ is the canonical endomorphism of ρ(M) into M. In Quantum Field Theory conjugate endomorphisms are shown to correspond to conjugate superselection sectors in the description of Doplicher, Haag and Roberts. On the other hand one easily sees that conjugate endormorphisms correspond to conjugate correspondences in the setting of A. Connes. In particular we identify the canonical tower associated with the inclusion ρ(A(O)is contained inA(O) relative to a sector ρ. As a corollary, making use of our previously established index-statistics correspondence, we conpletely describe, in low dimensional theories, the statistics of a selfconjugate superselection sector ρ with 3 or less channels, in particular with statistical dimension d(ρ)<2, by obtaining the braid group representations of V. Jones and Birman, Wenzyl and Murakami. The statistics is thus described in these cases by the polynomial invariants for knots and links of Jones and Kauffman. Selfconjugate sectors are subdivided in real and pseudoreal ones and the effect of this distinction on the statistics is analyzed. The FYHLMO polynomial describes arbitrary 2-channels sectors. (orig.)

  7. Quantum lattice model solver HΦ

    Science.gov (United States)

    Kawamura, Mitsuaki; Yoshimi, Kazuyoshi; Misawa, Takahiro; Yamaji, Youhei; Todo, Synge; Kawashima, Naoki

    2017-08-01

    HΦ [aitch-phi ] is a program package based on the Lanczos-type eigenvalue solution applicable to a broad range of quantum lattice models, i.e., arbitrary quantum lattice models with two-body interactions, including the Heisenberg model, the Kitaev model, the Hubbard model and the Kondo-lattice model. While it works well on PCs and PC-clusters, HΦ also runs efficiently on massively parallel computers, which considerably extends the tractable range of the system size. In addition, unlike most existing packages, HΦ supports finite-temperature calculations through the method of thermal pure quantum (TPQ) states. In this paper, we explain theoretical background and user-interface of HΦ. We also show the benchmark results of HΦ on supercomputers such as the K computer at RIKEN Advanced Institute for Computational Science (AICS) and SGI ICE XA (Sekirei) at the Institute for the Solid State Physics (ISSP).

  8. Quantum statistics of dense gases and nonideal plasmas

    CERN Document Server

    Ebeling, Werner; Filinov, Vladimir

    2017-01-01

    The aim of this book is the pedagogical exploration of the basic principles of quantum-statistical thermodynamics as applied to various states of matter – ranging from rare gases to astrophysical matter with high-energy density. The reader will learn in this work that thermodynamics and quantum statistics are still the concepts on which even the most advanced research is operating - despite of a flood of modern concepts, classical entities like temperature, pressure, energy and entropy are shown to remain fundamental. The physics of gases, plasmas and high-energy density matter is still a growing field and even though solids and liquids dominate our daily life, more than 99 percent of the visible Universe is in the state of gases and plasmas and the overwhelming part of matter exists at extreme conditions connected with very large energy densities, such as in the interior of stars. This text, combining material from lectures and advanced seminars given by the authors over many decades, is a must-have intr...

  9. Textual information access statistical models

    CERN Document Server

    Gaussier, Eric

    2013-01-01

    This book presents statistical models that have recently been developed within several research communities to access information contained in text collections. The problems considered are linked to applications aiming at facilitating information access:- information extraction and retrieval;- text classification and clustering;- opinion mining;- comprehension aids (automatic summarization, machine translation, visualization).In order to give the reader as complete a description as possible, the focus is placed on the probability models used in the applications

  10. Statistical and stochastic aspects of the delocalization problem in quantum mechanics

    International Nuclear Information System (INIS)

    Claverie, P.; Diner, S.

    1976-01-01

    The space-time behaviour of electrons in atoms and molecules is reviewed. The wave conception of the electron is criticized and the poverty of the non-reductionist attitude is underlined. Further, the two main interpretations of quantum mechanics are recalled: the Copenhagen and the Statistical Interpretations. The meaning and the successes of the Statistical Interpretation are explained and it is shown that it does not solve all problems because quantum mechanics is irreducible to a classical statistical theory. The fluctuation of the particle number and its relationship to loge theory, delocalization and correlation is studied. Finally, different stochastic models for microphysics are reviewed. The markovian Fenyes-Nelson process allows an interpretation of the original heuristic considerations of Schroedinger. Non-markov processes with Schroedinger time evolution are shown to be equivalent to the base state analysis of Feynmann but they are unsatisfactory from a probabilistic point of view. Stochastic electrodynamics is presented as the most satisfactory conception nowadays

  11. Conjugate pair of non-extensive statistics in quantum scattering

    International Nuclear Information System (INIS)

    Ion, D.B.; Ion, M.L.D.

    1999-01-01

    In this paper, by defining the Fourier transform of the scattering amplitudes as a bounded linear mapping from the space L 2p to the space L 2q when 1/(2p)+1/(2q)=1, we introduced a new concept in quantum physics in terms of Tsallis-like entropies S J (p) and S θ (q), namely, that of conjugate pair of non-extensive statistics. This new concept is experimentally illustrated by using 88 + 49 sets of pion-nucleon and pion-nucleus phase shifts. From the experimental determination of the (p,q) - non-extensivity indices by choosing the pairs for which the [χ L 2 (p) + χ θ 2 (q min )] - optimal - test function is minimum we get the conjugate pair of [(p min ,J),(q min , θ)]- non-extensive statistics with 0.50 ≤ p min ≤ 0.60. This new non-extensive statistical effect is experimentally evidenced with high degree of accuracy (CL≥ 99%). Moreover, it is worth to mention that the modification of the statistics has been more efficient than the modification of the PMD-SQS-optimum principle in obtaining the best overall fitting to the experimental data. (authors)

  12. Improved model for statistical alignment

    Energy Technology Data Exchange (ETDEWEB)

    Miklos, I.; Toroczkai, Z. (Zoltan)

    2001-01-01

    The statistical approach to molecular sequence evolution involves the stochastic modeling of the substitution, insertion and deletion processes. Substitution has been modeled in a reliable way for more than three decades by using finite Markov-processes. Insertion and deletion, however, seem to be more difficult to model, and thc recent approaches cannot acceptably deal with multiple insertions and deletions. A new method based on a generating function approach is introduced to describe the multiple insertion process. The presented algorithm computes the approximate joint probability of two sequences in 0(13) running time where 1 is the geometric mean of the sequence lengths.

  13. Modeling of quantum nanomechanics

    DEFF Research Database (Denmark)

    Jauho, Antti-Pekka; Novotny, Tomas; Donarini, Andrea

    2004-01-01

    Microelectromechanical systems (MEMS) are approaching the nanoscale, which ultimately implies that the mechanical motion needs to be treated quantum mechanically. In recent years our group has developed theoretical methods to analyze the shuttle transition in the quantum regime (Novotny, 2004......), focusing not only in the IV-curve, but also considering noise, which is an important diagnostic tool in unraveling the microscopic transport mechanisms. Our theoretical analysis is based on a numerical solution of a generalized master equation (GME) for the density matrix. This equation is obtained...... by tracing the Liouville equation over the bath degrees of freedom (i.e., the free fermions of the electronic contacts, and the damping of the mechanical degree of freedom due to a bosonic environment)....

  14. Active Learning with Statistical Models.

    Science.gov (United States)

    1995-01-01

    Active Learning with Statistical Models ASC-9217041, NSF CDA-9309300 6. AUTHOR(S) David A. Cohn, Zoubin Ghahramani, and Michael I. Jordan 7. PERFORMING...TERMS 15. NUMBER OF PAGES Al, MIT, Artificial Intelligence, active learning , queries, locally weighted 6 regression, LOESS, mixtures of gaussians...COMPUTATIONAL LEARNING DEPARTMENT OF BRAIN AND COGNITIVE SCIENCES A.I. Memo No. 1522 January 9. 1995 C.B.C.L. Paper No. 110 Active Learning with

  15. Quantum-Like Bayesian Networks for Modeling Decision Making

    Directory of Open Access Journals (Sweden)

    Catarina eMoreira

    2016-01-01

    Full Text Available In this work, we explore an alternative quantum structure to perform quantum probabilistic inferences to accommodate the paradoxical findings of the Sure Thing Principle. We propose a Quantum-Like Bayesian Network, which consists in replacing classical probabilities by quantum probability amplitudes. However, since this approach suffers from the problem of exponential growth of quantum parameters, we also propose a similarity heuristic that automatically fits quantum parameters through vector similarities. This makes the proposed model general and predictive in contrast to the current state of the art models, which cannot be generalized for more complex decision scenarios and that only provide an explanatory nature for the observed paradoxes. In the end, the model that we propose consists in a nonparametric method for estimating inference effects from a statistical point of view. It is a statistical model that is simpler than the previous quantum dynamic and quantum-like models proposed in the literature. We tested the proposed network with several empirical data from the literature, mainly from the Prisoner's Dilemma game and the Two Stage Gambling game. The results obtained show that the proposed quantum Bayesian Network is a general method that can accommodate violations of the laws of classical probability theory and make accurate predictions regarding human decision-making in these scenarios.

  16. Eigenvalue and Entropy Statistics for Products of Conjugate Random Quantum Channels

    Directory of Open Access Journals (Sweden)

    Benoît Collins

    2010-06-01

    Full Text Available Using the graphical calculus and integration techniques introduced by the authors, we study the statistical properties of outputs of products of random quantum channels for entangled inputs. In particular, we revisit and generalize models of relevance for the recent counterexamples to the minimum output entropy additivity problems. Our main result is a classification of regimes for which the von Neumann entropy is lower on average than the elementary bounds that can be obtained with linear algebra techniques.

  17. Derivation of quantum statistics from Gauss's principle and the second law

    International Nuclear Information System (INIS)

    Lavenda, B.H.

    1988-01-01

    Quantum statistical laws are derived from bona fide stationary probability distributions of physical stochastic processes. These distributions are shown to be the laws of error for which the average occupation numbers are the most probable values. They determine uniquely the statistical entropy functions and the second law gives the quantum statistical distributions

  18. Role of quantum statistics in multi-particle decay dynamics

    Science.gov (United States)

    Marchewka, Avi; Granot, Er'el

    2015-04-01

    The role of quantum statistics in the decay dynamics of a multi-particle state, which is suddenly released from a confining potential, is investigated. For an initially confined double particle state, the exact dynamics is presented for both bosons and fermions. The time-evolution of the probability to measure two-particle is evaluated and some counterintuitive features are discussed. For instance, it is shown that although there is a higher chance of finding the two bosons (as oppose to fermions, and even distinguishable particles) at the initial trap region, there is a higher chance (higher than fermions) of finding them on two opposite sides of the trap as if the repulsion between bosons is higher than the repulsion between fermions. The results are demonstrated by numerical simulations and are calculated analytically in the short-time approximation. Furthermore, experimental validation is suggested.

  19. Role of quantum statistics in multi-particle decay dynamics

    International Nuclear Information System (INIS)

    Marchewka, Avi; Granot, Er’el

    2015-01-01

    The role of quantum statistics in the decay dynamics of a multi-particle state, which is suddenly released from a confining potential, is investigated. For an initially confined double particle state, the exact dynamics is presented for both bosons and fermions. The time-evolution of the probability to measure two-particle is evaluated and some counterintuitive features are discussed. For instance, it is shown that although there is a higher chance of finding the two bosons (as oppose to fermions, and even distinguishable particles) at the initial trap region, there is a higher chance (higher than fermions) of finding them on two opposite sides of the trap as if the repulsion between bosons is higher than the repulsion between fermions. The results are demonstrated by numerical simulations and are calculated analytically in the short-time approximation. Furthermore, experimental validation is suggested

  20. Role of quantum statistics in multi-particle decay dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Marchewka, Avi, E-mail: avi.marchewka@gmail.com [Galei Tchelet St 8 Herzliya (Israel); Granot, Er’el [Department of Electrical and Electronics Engineering, Ariel University, Ariel (Israel)

    2015-04-15

    The role of quantum statistics in the decay dynamics of a multi-particle state, which is suddenly released from a confining potential, is investigated. For an initially confined double particle state, the exact dynamics is presented for both bosons and fermions. The time-evolution of the probability to measure two-particle is evaluated and some counterintuitive features are discussed. For instance, it is shown that although there is a higher chance of finding the two bosons (as oppose to fermions, and even distinguishable particles) at the initial trap region, there is a higher chance (higher than fermions) of finding them on two opposite sides of the trap as if the repulsion between bosons is higher than the repulsion between fermions. The results are demonstrated by numerical simulations and are calculated analytically in the short-time approximation. Furthermore, experimental validation is suggested.

  1. Full Counting Statistics for Interacting Fermions with Determinantal Quantum Monte Carlo Simulations.

    Science.gov (United States)

    Humeniuk, Stephan; Büchler, Hans Peter

    2017-12-08

    We present a method for computing the full probability distribution function of quadratic observables such as particle number or magnetization for the Fermi-Hubbard model within the framework of determinantal quantum Monte Carlo calculations. Especially in cold atom experiments with single-site resolution, such a full counting statistics can be obtained from repeated projective measurements. We demonstrate that the full counting statistics can provide important information on the size of preformed pairs. Furthermore, we compute the full counting statistics of the staggered magnetization in the repulsive Hubbard model at half filling and find excellent agreement with recent experimental results. We show that current experiments are capable of probing the difference between the Hubbard model and the limiting Heisenberg model.

  2. Geometric Approach to Quantum Statistical Mechanics and Application to Casimir Energy and Friction Properties

    International Nuclear Information System (INIS)

    Ichinose, Shoichi

    2010-01-01

    A geometric approach to general quantum statistical systems (including the harmonic oscillator) is presented. It is applied to Casimir energy and the dissipative system with friction. We regard the (N+1)-dimensional Euclidean coordinate system (X i ,τ) as the quantum statistical system of N quantum (statistical) variables (X τ ) and one Euclidean time variable (t). Introducing paths (lines or hypersurfaces) in this space (X τ ,t), we adopt the path-integral method to quantize the mechanical system. This is a new view of (statistical) quantization of the mechanical system. The system Hamiltonian appears as the area. We show quantization is realized by the minimal area principle in the present geometric approach. When we take a line as the path, the path-integral expressions of the free energy are shown to be the ordinary ones (such as N harmonic oscillators) or their simple variation. When we take a hyper-surface as the path, the system Hamiltonian is given by the area of the hyper-surface which is defined as a closed-string configuration in the bulk space. In this case, the system becomes a O(N) non-linear model. We show the recently-proposed 5 dimensional Casimir energy (ArXiv:0801.3064,0812.1263) is valid. We apply this approach to the visco-elastic system, and present a new method using the path-integral for the calculation of the dissipative properties.

  3. Toy Models of a Nonassociative Quantum Mechanics

    International Nuclear Information System (INIS)

    Dzhunushaliev, V.

    2007-01-01

    Toy models of a nonassociative quantum mechanics are presented. The Heisenberg equation of motion is modified using a nonassociative commutator. Possible physical applications of a nonassociative quantum mechanics are considered. The idea is discussed that a nonassociative algebra could be the operator language for the nonperturbative quantum theory. In such approach the nonperturbative quantum theory has observables and un observables quantities.

  4. Two-dimensional models in statistical mechanics and field theory

    International Nuclear Information System (INIS)

    Koberle, R.

    1980-01-01

    Several features of two-dimensional models in statistical mechanics and Field theory, such as, lattice quantum chromodynamics, Z(N), Gross-Neveu and CP N-1 are discussed. The problems of confinement and dynamical mass generation are also analyzed. (L.C.) [pt

  5. Path integral molecular dynamics for exact quantum statistics of multi-electronic-state systems.

    Science.gov (United States)

    Liu, Xinzijian; Liu, Jian

    2018-03-14

    An exact approach to compute physical properties for general multi-electronic-state (MES) systems in thermal equilibrium is presented. The approach is extended from our recent progress on path integral molecular dynamics (PIMD), Liu et al. [J. Chem. Phys. 145, 024103 (2016)] and Zhang et al. [J. Chem. Phys. 147, 034109 (2017)], for quantum statistical mechanics when a single potential energy surface is involved. We first define an effective potential function that is numerically favorable for MES-PIMD and then derive corresponding estimators in MES-PIMD for evaluating various physical properties. Its application to several representative one-dimensional and multi-dimensional models demonstrates that MES-PIMD in principle offers a practical tool in either of the diabatic and adiabatic representations for studying exact quantum statistics of complex/large MES systems when the Born-Oppenheimer approximation, Condon approximation, and harmonic bath approximation are broken.

  6. A quantum relativistic integrable model as the continuous limit of the six-vertex model

    International Nuclear Information System (INIS)

    Zhou, Y.K.

    1992-01-01

    The six-vertex model in two-dimensional statistical mechanics is used to construct the L-matrix of a one-dimensional quantum relativistic integrable model through a continuous limit. This is the first step to extend the method used earlier by the author to construct quantum completely integrable systems from other well-known two-dimensional vertex models. (orig.)

  7. Quantum statistical effects in the mass transport of interstitial solutes in a crystalline solid

    Science.gov (United States)

    Woo, C. H.; Wen, Haohua

    2017-09-01

    The impact of quantum statistics on the many-body dynamics of a crystalline solid at finite temperatures containing an interstitial solute atom (ISA) is investigated. The Mori-Zwanzig theory allows the many-body dynamics of the crystal to be formulated and solved analytically within a pseudo-one-particle approach using the Langevin equation with a quantum fluctuation-dissipation relation (FDR) based on the Debye model. At the same time, the many-body dynamics is also directly solved numerically via the molecular dynamics approach with a Langevin heat bath based on the quantum FDR. Both the analytical and numerical results consistently show that below the Debye temperature of the host lattice, quantum statistics significantly impacts the ISA transport properties, resulting in major departures from both the Arrhenius law of diffusion and the Einstein-Smoluchowski relation between the mobility and diffusivity. Indeed, we found that below one-third of the Debye temperature, effects of vibrations on the quantum mobility and diffusivity are both orders-of-magnitude larger and practically temperature independent. We have shown that both effects have their physical origin in the athermal lattice vibrations derived from the phonon ground state. The foregoing theory is tested in quantum molecular dynamics calculation of mobility and diffusivity of interstitial helium in bcc W. In this case, the Arrhenius law is only valid in a narrow range between ˜300 and ˜700 K. The diffusivity becomes temperature independent on the low-temperature side while increasing linearly with temperature on the high-temperature side.

  8. Statistical Characterization of Dispersed Single-Wall Carbon Nanotube Quantum Dots

    International Nuclear Information System (INIS)

    Shimizu, M; Moriyama, S; Suzuki, M; Fuse, T; Homma, Y; Ishibashi, K

    2006-01-01

    Quantum dots have been fabricated in single-wall carbon nanotubes (SWCNTs) simply by depositing metallic contacts on top of them. The fabricated quantum dots show different characteristics from sample to sample, which are even different in samples fabricated in the same chip. In this report, we study the statistical variations of the quantum dots fabricated with our method, and suggest their possible origin

  9. Introduction to modern theoretical physics. Volume II. Quantum theory and statistical physics

    International Nuclear Information System (INIS)

    Harris, E.G.

    1975-01-01

    The topics discussed include the history and principles, some solvable problems, and symmetry in quantum mechanics, interference phenomena, approximation methods, some applications of nonrelativistic quantum mechanics, relativistic wave equations, quantum theory of radiation, second quantization, elementary particles and their interactions, thermodynamics, equilibrium statistical mechanics and its applications, the kinetic theory of gases, and collective phenomena

  10. On the Effect of Dipole-Dipole Interactions on the Quantum Statistics of Surface Plasmons in Multiparticle Spaser Systems

    Science.gov (United States)

    Shesterikov, A. V.; Gubin, M. Yu.; Karpov, S. N.; Prokhorov, A. V.

    2018-04-01

    The problem of controlling the quantum dynamics of localized plasmons has been considered in the model of a four-particle spaser composed of metallic nanoparticles and semiconductor quantum dots. Conditions for the observation of stable steady-state regimes of the formation of surface plasmons in this model have been determined in the mean-field approximation. It has been shown that the presence of strong dipole-dipole interactions between metallic nanoparticles of the spaser system leads to a considerable change in the quantum statistics of plasmons generated on the nanoparticles.

  11. Studies on quantum field theory and statistical mechanics

    International Nuclear Information System (INIS)

    Zhang, S.

    1987-01-01

    This dissertation is a summary of research in various areas of theoretical physics and is divided into three parts. In the first part, quantum fluctuations of the recently proposed superconducting cosmic strings are studied. It is found that vortices on the string world sheet represent an important class of fluctuation modes which tend to disorder the system. Both heuristic arguments and detailed renormalization group analysis reveal that these vortices do not appear in bound pairs but rather from a gas of free vortices. Based on this observation we argue that this fluctuation mode violates the topological conservation law on which superconductivity is based. Anomalies and topological aspects of supersymmetric quantum field theories are studied in the second part of this dissertation. Using the superspace formulation of the N = 1 spinning string, we obtain a path integral measure which is free from the world-sheet general coordinate as well as the supersymmetry anomalies and therefore determine the conformal anomaly and critical dimension of the spinning string. We also apply Fujikawa's formalism to computer the chiral anomaly in conformal as well as ordinary supergravity. Finally, we given a Noether-method construction of the supersymmetrized Chern-Simons term in five dimensional supergravity. In the last part of this dissertation, the soliton excitations in the quarter-filled Peierls-Hubbard model are investigated in both the large and the small U limit. For a strictly one dimensional system at zero temperature, we find that solitons in both limits are in one-to-one correspondence, while in the presence of weak three dimensional couplings or at finite temperature, the large U systems differ qualitatively from the small U systems in that the spin associated with the solitons ceases to be a sharp quantum observable

  12. On some boundary value problems in quantum statistical mechanics

    International Nuclear Information System (INIS)

    Angelescu, N.

    1978-01-01

    The following two topics of equilibrium quantum statistical mechanics are discussed in this thesis: (i) the independence of the thermodynamic limit of grand-canonical pressure on the boundary conditions; (ii) the magnetic properties of free quantum gases. Problem (i) is handled with a functional integration technique. Wiener-type conditional measures are constructed for a given domain and a general class of mixed conditions on its boundary, these measures are used to write down Feynman-Kac formulae for the kernels of exp(-βH), where H is the Hamiltonian of N interacting particles in the given domain. These measures share the property that they assign the same mass as the usual Wiener measure to any set of trajectories not intersecting the boundary. Local estimates on the kernels of exp(-βH) are derived, which imply independence of the pressure on the boundary conditions in the thermodynamic limit. Problem (ii) has a historical development: since Landau's work (1930), much discussion has been devoted to the influence of the finite size on the susceptibility. In finite volume, Dirichlet boundary conditions are imposed, on the ground that they ensure gauge invariance. The thermodynamic limit of the pressure is proved, using again functional integration. The functional measure is now complex but absolutely continuous with respect to Wiener measure, so the usual local estimates hold true. The controversy in the literature was concentrated on the commutativity of the operations of H-derivation and thermodynamic limit, so the existence of this limit for the zero-field susceptibility and its surface term are proved separately, demonstrating this commutativity. The proof relies on the following result of independent interest: the perturbation theory of self-adjoint trace-class semigroups is trace-class convergent and analytic. (author)

  13. Theoretical physics vol. 2. Quantum mechanics, relativistic quantum mechanics, quantum field theory, elementar-particle theory, thermodynamics and statistics

    International Nuclear Information System (INIS)

    Rebhan, E.

    2005-01-01

    The present second volume treats quantum mechanics, relativistic quantum mechanics, the foundations of quantum-field and elementary-particle theory as well as thermodynamics and statistics. Both volumes comprehend all fields, which are usually offered in a course about theoretical physics. In all treated fields a very careful introduction to the basic natural laws forms the starting point, whereby it is thoroughly analysed, which of them is based on empirics, which is logically deducible, and which role play basic definitions. Extendingly the matter extend of the corresponding courses starting from the relativistic quantum theory an introduction to the elementary particles is developed. All problems are very thoroughly and such extensively studied, that each step is singularly reproducible. On motivation and good understandability is cared much about. The mixing of mathematical difficulties with problems of physical nature often obstructive in the learning is so circumvented, that important mathematical methods are presented in own chapters (for instance Hilbert spaces, Lie groups). By means of many examples and problems (for a large part with solutions) the matter worked out is deepened and exercised. Developments, which are indeed important, but seem for the first approach abandonable, are pursued in excurses. This book starts from courses, which the author has held at the Heinrich-Heine university in Duesseldorf, and was in many repetitions fitted to the requirements of the students. It is conceived in such a way, that it is also after the study suited as dictionary or for the regeneration

  14. Digital Quantum Simulation of Spin Models with Circuit Quantum Electrodynamics

    Directory of Open Access Journals (Sweden)

    Y. Salathé

    2015-06-01

    Full Text Available Systems of interacting quantum spins show a rich spectrum of quantum phases and display interesting many-body dynamics. Computing characteristics of even small systems on conventional computers poses significant challenges. A quantum simulator has the potential to outperform standard computers in calculating the evolution of complex quantum systems. Here, we perform a digital quantum simulation of the paradigmatic Heisenberg and Ising interacting spin models using a two transmon-qubit circuit quantum electrodynamics setup. We make use of the exchange interaction naturally present in the simulator to construct a digital decomposition of the model-specific evolution and extract its full dynamics. This approach is universal and efficient, employing only resources that are polynomial in the number of spins, and indicates a path towards the controlled simulation of general spin dynamics in superconducting qubit platforms.

  15. A quantum probability model of causal reasoning

    Directory of Open Access Journals (Sweden)

    Jennifer S Trueblood

    2012-05-01

    Full Text Available People can often outperform statistical methods and machine learning algorithms in situations that involve making inferences about the relationship between causes and effects. While people are remarkably good at causal reasoning in many situations, there are several instances where they deviate from expected responses. This paper examines three situations where judgments related to causal inference problems produce unexpected results and describes a quantum inference model based on the axiomatic principles of quantum probability theory that can explain these effects. Two of the three phenomena arise from the comparison of predictive judgments (i.e., the conditional probability of an effect given a cause with diagnostic judgments (i.e., the conditional probability of a cause given an effect. The third phenomenon is a new finding examining order effects in predictive causal judgments. The quantum inference model uses the notion of incompatibility among different causes to account for all three phenomena. Psychologically, the model assumes that individuals adopt different points of view when thinking about different causes. The model provides good fits to the data and offers a coherent account for all three causal reasoning effects thus proving to be a viable new candidate for modeling human judgment.

  16. GIGMF - A statistical model program

    International Nuclear Information System (INIS)

    Vladuca, G.; Deberth, C.

    1978-01-01

    The program GIGMF computes the differential and integrated statistical model cross sections for the reactions proceeding through a compound nuclear stage. The computational method is based on the Hauser-Feshbach-Wolfenstein theory, modified to include the modern version of Tepel et al. Although the program was written for a PDP-15 computer, with 16K high speed memory, many reaction channels can be taken into account with the following restrictions: the pro ectile spin must be less than 2, the maximum spin momenta of the compound nucleus can not be greater than 10. These restrictions are due solely to the storage allotments and may be easily relaxed. The energy of the impinging particle, the target and projectile masses, the spin and paritjes of the projectile, target, emergent and residual nuclei the maximum orbital momentum and transmission coefficients for each reaction channel are the input parameters of the program. (author)

  17. Theoretical modelling of quantum circuit systems

    International Nuclear Information System (INIS)

    Stiffell, Peter Barry

    2002-01-01

    The work in this thesis concentrates on the interactions between circuit systems operating in the quantum regime. The main thrust of this work involves the use of a new model for investigating the way in which different components in such systems behave when coupled together. This is achieved by utilising the matrix representation of quantum mechanics, in conjunction with a number of other theoretical techniques (such as Wigner functions and entanglement entropies). With these tools in place it then becomes possible to investigate and review different quantum circuit systems. These investigations cover systems ranging from simple electromagnetic (cm) field oscillators in isolation to coupled SQUID rings in more sophisticated multi-component arrangements. Primarily, we look at the way SQUID rings couple to em fields, and how the ring-field interaction can be mediated by the choice of external flux, Φ x , applied to the SQUID ring. A lot of interest is focused on the transfer of energy between the system modes. However, we also investigate the statistical properties of the system, including squeezing, entropy and entanglement. Among the phenomena uncovered in this research we note the ability to control coupling in SQUID rings via the external flux, the capacity for entanglement between quantum circuit modes, frequency conversions of photons, flux squeezing and the existence of Schroedinger Cat states. (author)

  18. Probing the statistical properties of Anderson localization with quantum emitters

    DEFF Research Database (Denmark)

    Smolka, Stephan; Nielsen, Henri Thyrrestrup; Sapienza, Luca

    2011-01-01

    experiments by measuring the intensity of an external light source after propagation through a disordered medium. However, discriminating between Anderson localization and losses in these experiments remains a major challenge. In this paper, we present an alternative approach where we use quantum emitters...... of disorder induced in the photonic crystal, we observe a pronounced increase in the localization length that is attributed to changes in the local density of states, a behavior that is in stark contrast to entirely random systems. The analysis may pave the way for accurate models and the control of Anderson......Wave propagation in disordered media can be strongly modified by multiple scattering and wave interference. Ultimately, the so-called Anderson-localized regime is reached when the waves become strongly confined in space. So far, Anderson localization of light has been probed in transmission...

  19. Quantum origin of the primordial fluctuation spectrum and its statistics

    Science.gov (United States)

    Landau, Susana; León, Gabriel; Sudarsky, Daniel

    2013-07-01

    The usual account for the origin of cosmic structure during inflation is not fully satisfactory, as it lacks a physical mechanism capable of generating the inhomogeneity and anisotropy of our Universe, from an exactly homogeneous and isotropic initial state associated with the early inflationary regime. The proposal in [A. Perez, H. Sahlmann, and D. Sudarsky, Classical Quantum Gravity 23, 2317 (2006)] considers the spontaneous dynamical collapse of the wave function as a possible answer to that problem. In this work, we review briefly the difficulties facing the standard approach, as well as the answers provided by the above proposal and explore their relevance to the investigations concerning the characterization of the primordial spectrum and other statistical aspects of the cosmic microwave background and large-scale matter distribution. We will see that the new approach leads to novel ways of considering some of the relevant questions, and, in particular, to distinct characterizations of the non-Gaussianities that might have left imprints on the available data.

  20. Statistical mechanics view of quantum chromodynamics: Lattice gauge theory

    International Nuclear Information System (INIS)

    Kogut, J.B.

    1984-01-01

    Recent developments in lattice gauge theory are discussed from a statistial mechanics viewpoint. The basic physics problems of quantum chromodynamics (QCD) are reviewed for an audience of critical phenomena theorists. The idea of local gauge symmetry and color, the connection between statistical mechanics and field theory, asymptotic freedom and the continuum limit of lattice gauge theories, and the order parameters (confinement and chiral symmetry) of QCD are reviewed. Then recent developments in the field are discussed. These include the proof of confinement in the lattice theory, numerical evidence for confinement in the continuum limit of lattice gauge theory, and perturbative improvement programs for lattice actions. Next, we turn to the new challenges facing the subject. These include the need for a better understanding of the lattice Dirac equation and recent progress in the development of numerical methods for fermions (the pseudofermion stochastic algorithm and the microcanonical, molecular dynamics equation of motion approach). Finally, some of the applications of lattice gauge theory to QCD spectrum calculations and the thermodynamics of QCD will be discussed and a few remarks concerning future directions of the field will be made

  1. Quantum statistical mechanics selected works of N N Bogolubov

    CERN Document Server

    Bogolyubov, N N

    2015-01-01

    In this book we have solved the complicated problem of constructing upper bounds for many-time averages for the case of a fairly broad class of model systems with four-fermion interaction. The methods proposed in this book for solving this problem will undoubtedly find application not only for the model systems associated with the theory of superconductivity considered here. The theoretical methods developed in Chapters 1 and 2 are already applicable to a much broader class of model systems from statistical physics and the theory of elementary particles. Contents: On the Theory of Superfluidit

  2. Hybrid quantum-classical modeling of quantum dot devices

    Science.gov (United States)

    Kantner, Markus; Mittnenzweig, Markus; Koprucki, Thomas

    2017-11-01

    The design of electrically driven quantum dot devices for quantum optical applications asks for modeling approaches combining classical device physics with quantum mechanics. We connect the well-established fields of semiclassical semiconductor transport theory and the theory of open quantum systems to meet this requirement. By coupling the van Roosbroeck system with a quantum master equation in Lindblad form, we introduce a new hybrid quantum-classical modeling approach, which provides a comprehensive description of quantum dot devices on multiple scales: it enables the calculation of quantum optical figures of merit and the spatially resolved simulation of the current flow in realistic semiconductor device geometries in a unified way. We construct the interface between both theories in such a way, that the resulting hybrid system obeys the fundamental axioms of (non)equilibrium thermodynamics. We show that our approach guarantees the conservation of charge, consistency with the thermodynamic equilibrium and the second law of thermodynamics. The feasibility of the approach is demonstrated by numerical simulations of an electrically driven single-photon source based on a single quantum dot in the stationary and transient operation regime.

  3. Higher-Order Statistical Correlations and Mutual Information Among Particles in a Quantum Well

    International Nuclear Information System (INIS)

    Yépez, V. S.; Sagar, R. P.; Laguna, H. G.

    2017-01-01

    The influence of wave function symmetry on statistical correlation is studied for the case of three non-interacting spin-free quantum particles in a unidimensional box, in position and in momentum space. Higher-order statistical correlations occurring among the three particles in this quantum system is quantified via higher-order mutual information and compared to the correlation between pairs of variables in this model, and to the correlation in the two-particle system. The results for the higher-order mutual information show that there are states where the symmetric wave functions are more correlated than the antisymmetric ones with same quantum numbers. This holds in position as well as in momentum space. This behavior is opposite to that observed for the correlation between pairs of variables in this model, and the two-particle system, where the antisymmetric wave functions are in general more correlated. These results are also consistent with those observed in a system of three uncoupled oscillators. The use of higher-order mutual information as a correlation measure, is monitored and examined by considering a superposition of states or systems with two Slater determinants. (author)

  4. Higher-Order Statistical Correlations and Mutual Information Among Particles in a Quantum Well

    Science.gov (United States)

    Yépez, V. S.; Sagar, R. P.; Laguna, H. G.

    2017-12-01

    The influence of wave function symmetry on statistical correlation is studied for the case of three non-interacting spin-free quantum particles in a unidimensional box, in position and in momentum space. Higher-order statistical correlations occurring among the three particles in this quantum system is quantified via higher-order mutual information and compared to the correlation between pairs of variables in this model, and to the correlation in the two-particle system. The results for the higher-order mutual information show that there are states where the symmetric wave functions are more correlated than the antisymmetric ones with same quantum numbers. This holds in position as well as in momentum space. This behavior is opposite to that observed for the correlation between pairs of variables in this model, and the two-particle system, where the antisymmetric wave functions are in general more correlated. These results are also consistent with those observed in a system of three uncoupled oscillators. The use of higher-order mutual information as a correlation measure, is monitored and examined by considering a superposition of states or systems with two Slater determinants.

  5. A quantum mechanical model of "dark matter"

    OpenAIRE

    Belokurov, V. V.; Shavgulidze, E. T.

    2014-01-01

    The role of singular solutions in some simple quantum mechanical models is studied. The space of the states of two-dimensional quantum harmonic oscillator is shown to be separated into sets of states with different properties.

  6. Canonical transformations in problems of quantum statistical mechanics

    International Nuclear Information System (INIS)

    Sankovich, D.P.

    1985-01-01

    The problem of general canonical transformations in quantum systems possessing a classical analog is considered. The main role plays the Weyl representation of dynamic variables of the quantum system considered. One managed to build a general diagram of canonical transformations in a quantum case and to develop a method for reducing one or another operator to the simplest canonical form. In this case the procedure, being analogous to the Poincare-Birkhof normalization based on the Lie series theory, occurs

  7. Quantum statistical field theory an introduction to Schwinger's variational method with Green's function nanoapplications, graphene and superconductivity

    CERN Document Server

    Morgenstern Horing, Norman J

    2017-01-01

    This book provides an introduction to the methods of coupled quantum statistical field theory and Green's functions. The methods of coupled quantum field theory have played a major role in the extensive development of nonrelativistic quantum many-particle theory and condensed matter physics. This introduction to the subject is intended to facilitate delivery of the material in an easily digestible form to advanced undergraduate physics majors at a relatively early stage of their scientific development. The main mechanism to accomplish this is the early introduction of variational calculus and the Schwinger Action Principle, accompanied by Green's functions. Important achievements of the theory in condensed matter and quantum statistical physics are reviewed in detail to help develop research capability. These include the derivation of coupled field Green's function equations-of-motion for a model electron-hole-phonon system, extensive discussions of retarded, thermodynamic and nonequilibrium Green's functions...

  8. On quantum models of the human mind.

    Science.gov (United States)

    Wang, Hongbin; Sun, Yanlong

    2014-01-01

    Recent years have witnessed rapidly increasing interests in developing quantum theoretical models of human cognition. Quantum mechanisms have been taken seriously to describe how the mind reasons and decides. Papers in this special issue report the newest results in the field. Here we discuss why the two levels of commitment, treating the human brain as a quantum computer and merely adopting abstract quantum probability principles to model human cognition, should be integrated. We speculate that quantum cognition models gain greater modeling power due to a richer representation scheme. Copyright © 2013 Cognitive Science Society, Inc.

  9. A quantum hydrodynamic model for multicomponent quantum magnetoplasma with Jeans term

    International Nuclear Information System (INIS)

    Masood, W.; Salimullah, M.; Shah, H.A.

    2008-01-01

    The effect of Jeans term in a multicomponent self-gravitating quantum magnetoplasma is investigated employing the quantum hydrodynamic (QHD) model. The effects of quantum Bohm potential and statistical terms as well as the ambient magnetic field are also investigated on both dust and ion dynamics driven waves in this Letter. We state the conditions that can drive the system unstable in the presence of Jeans term. The limiting cases are also presented. The present work may have relevance in the dense astrophysical environments where the self-gravitating effects are expected to play a pivotal role

  10. Sub-Poissonian statistics of quantum jumps in single molecule or atomic ion

    International Nuclear Information System (INIS)

    Osad'ko, I.S.; Gus'kov, D.N.

    2007-01-01

    A theory for statistics of quantum jumps in single molecule or ion driven by continues wave laser field is developed. These quantum jumps can relate to nonradiative singlet-triplet transitions in a molecule or to on → off jumps in a single ion with shelving processes. Distribution function w N (T) of quantum jumps in time interval T is found. Computer simulation of quantum jumps is realized. Statistical treatment of simulated jumps reveals sub-Poissonian statistics of quantum jumps. The theoretical distribution function w N (T) fits well the distribution of jumps found from simulated data. Experimental data on quantum jumps found in experiments with single Hg + ion are described by the function w N (T) well

  11. Toward a Parastatistics in Quantum Nonextensive Statistical Mechanics

    Science.gov (United States)

    Zaripov, R. G.

    2018-05-01

    On the basis of Bose quantum states in parastatistics the equations for the equilibrium distribution of quantum additive and nonextensive systems are determined. The fluctuations and variances of physical quantities for the equilibrium system are found. The Abelian group of microscopic entropies is determined for the composition law with a quadratic nonlinearity.

  12. A stochastic model for quantum measurement

    International Nuclear Information System (INIS)

    Budiyono, Agung

    2013-01-01

    We develop a statistical model of microscopic stochastic deviation from classical mechanics based on a stochastic process with a transition probability that is assumed to be given by an exponential distribution of infinitesimal stationary action. We apply the statistical model to stochastically modify a classical mechanical model for the measurement of physical quantities reproducing the prediction of quantum mechanics. The system+apparatus always has a definite configuration at all times, as in classical mechanics, fluctuating randomly following a continuous trajectory. On the other hand, the wavefunction and quantum mechanical Hermitian operator corresponding to the physical quantity arise formally as artificial mathematical constructs. During a single measurement, the wavefunction of the whole system+apparatus evolves according to a Schrödinger equation and the configuration of the apparatus acts as the pointer of the measurement so that there is no wavefunction collapse. We will also show that while the outcome of each single measurement event does not reveal the actual value of the physical quantity prior to measurement, its average in an ensemble of identical measurements is equal to the average of the actual value of the physical quantity prior to measurement over the distribution of the configuration of the system. (paper)

  13. Statistical modeling of Earth's plasmasphere

    Science.gov (United States)

    Veibell, Victoir

    The behavior of plasma near Earth's geosynchronous orbit is of vital importance to both satellite operators and magnetosphere modelers because it also has a significant influence on energy transport, ion composition, and induced currents. The system is highly complex in both time and space, making the forecasting of extreme space weather events difficult. This dissertation examines the behavior and statistical properties of plasma mass density near geosynchronous orbit by using both linear and nonlinear models, as well as epoch analyses, in an attempt to better understand the physical processes that precipitates and drives its variations. It is shown that while equatorial mass density does vary significantly on an hourly timescale when a drop in the disturbance time scale index ( Dst) was observed, it does not vary significantly between the day of a Dst event onset and the day immediately following. It is also shown that increases in equatorial mass density were not, on average, preceded or followed by any significant change in the examined solar wind or geomagnetic variables, including Dst, despite prior results that considered a few selected events and found a notable influence. It is verified that equatorial mass density and and solar activity via the F10.7 index have a strong correlation, which is stronger over longer timescales such as 27 days than it is over an hourly timescale. It is then shown that this connection seems to affect the behavior of equatorial mass density most during periods of strong solar activity leading to large mass density reactions to Dst drops for high values of F10.7. It is also shown that equatorial mass density behaves differently before and after events based on the value of F10.7 at the onset of an equatorial mass density event or a Dst event, and that a southward interplanetary magnetic field at onset leads to slowed mass density growth after event onset. These behavioral differences provide insight into how solar and geomagnetic

  14. Quantum vertex model for reversible classical computing.

    Science.gov (United States)

    Chamon, C; Mucciolo, E R; Ruckenstein, A E; Yang, Z-C

    2017-05-12

    Mappings of classical computation onto statistical mechanics models have led to remarkable successes in addressing some complex computational problems. However, such mappings display thermodynamic phase transitions that may prevent reaching solution even for easy problems known to be solvable in polynomial time. Here we map universal reversible classical computations onto a planar vertex model that exhibits no bulk classical thermodynamic phase transition, independent of the computational circuit. Within our approach the solution of the computation is encoded in the ground state of the vertex model and its complexity is reflected in the dynamics of the relaxation of the system to its ground state. We use thermal annealing with and without 'learning' to explore typical computational problems. We also construct a mapping of the vertex model into the Chimera architecture of the D-Wave machine, initiating an approach to reversible classical computation based on state-of-the-art implementations of quantum annealing.

  15. Maximum entropy principle and hydrodynamic models in statistical mechanics

    International Nuclear Information System (INIS)

    Trovato, M.; Reggiani, L.

    2012-01-01

    This review presents the state of the art of the maximum entropy principle (MEP) in its classical and quantum (QMEP) formulation. Within the classical MEP we overview a general theory able to provide, in a dynamical context, the macroscopic relevant variables for carrier transport in the presence of electric fields of arbitrary strength. For the macroscopic variables the linearized maximum entropy approach is developed including full-band effects within a total energy scheme. Under spatially homogeneous conditions, we construct a closed set of hydrodynamic equations for the small-signal (dynamic) response of the macroscopic variables. The coupling between the driving field and the energy dissipation is analyzed quantitatively by using an arbitrary number of moments of the distribution function. Analogously, the theoretical approach is applied to many one-dimensional n + nn + submicron Si structures by using different band structure models, different doping profiles, different applied biases and is validated by comparing numerical calculations with ensemble Monte Carlo simulations and with available experimental data. Within the quantum MEP we introduce a quantum entropy functional of the reduced density matrix, the principle of quantum maximum entropy is then asserted as fundamental principle of quantum statistical mechanics. Accordingly, we have developed a comprehensive theoretical formalism to construct rigorously a closed quantum hydrodynamic transport within a Wigner function approach. The theory is formulated both in thermodynamic equilibrium and nonequilibrium conditions, and the quantum contributions are obtained by only assuming that the Lagrange multipliers can be expanded in powers of ħ 2 , being ħ the reduced Planck constant. In particular, by using an arbitrary number of moments, we prove that: i) on a macroscopic scale all nonlocal effects, compatible with the uncertainty principle, are imputable to high-order spatial derivatives both of the

  16. Trajectory phases of a quantum dot model

    International Nuclear Information System (INIS)

    Genway, Sam; Hickey, James M; Garrahan, Juan P; Armour, Andrew D

    2014-01-01

    We present a thermodynamic formalism to study the trajectories of charge transport through a quantum dot coupled to two leads in the resonant-level model. We show that a close analogue of equilibrium phase transitions exists for the statistics of transferred charge; by tuning an appropriate ‘counting field’, crossovers to different trajectory phases are possible. Our description reveals a mapping between the statistics of a given device and current measurements over a range of devices with different dot–lead coupling strengths. Furthermore insight into features of the trajectory phases are found by studying the occupation of the dot conditioned on the transported charge between the leads; this is calculated from first principles using a trajectory biased two-point projective measurement scheme. (paper)

  17. Statistical thermodynamics

    International Nuclear Information System (INIS)

    Lim, Gyeong Hui

    2008-03-01

    This book consists of 15 chapters, which are basic conception and meaning of statistical thermodynamics, Maxwell-Boltzmann's statistics, ensemble, thermodynamics function and fluctuation, statistical dynamics with independent particle system, ideal molecular system, chemical equilibrium and chemical reaction rate in ideal gas mixture, classical statistical thermodynamics, ideal lattice model, lattice statistics and nonideal lattice model, imperfect gas theory on liquid, theory on solution, statistical thermodynamics of interface, statistical thermodynamics of a high molecule system and quantum statistics

  18. Probing NWP model deficiencies by statistical postprocessing

    DEFF Research Database (Denmark)

    Rosgaard, Martin Haubjerg; Nielsen, Henrik Aalborg; Nielsen, Torben S.

    2016-01-01

    The objective in this article is twofold. On one hand, a Model Output Statistics (MOS) framework for improved wind speed forecast accuracy is described and evaluated. On the other hand, the approach explored identifies unintuitive explanatory value from a diagnostic variable in an operational....... Based on the statistical model candidates inferred from the data, the lifted index NWP model diagnostic is consistently found among the NWP model predictors of the best performing statistical models across sites....

  19. A quantum-implementable neural network model

    Science.gov (United States)

    Chen, Jialin; Wang, Lingli; Charbon, Edoardo

    2017-10-01

    A quantum-implementable neural network, namely quantum probability neural network (QPNN) model, is proposed in this paper. QPNN can use quantum parallelism to trace all possible network states to improve the result. Due to its unique quantum nature, this model is robust to several quantum noises under certain conditions, which can be efficiently implemented by the qubus quantum computer. Another advantage is that QPNN can be used as memory to retrieve the most relevant data and even to generate new data. The MATLAB experimental results of Iris data classification and MNIST handwriting recognition show that much less neuron resources are required in QPNN to obtain a good result than the classical feedforward neural network. The proposed QPNN model indicates that quantum effects are useful for real-life classification tasks.

  20. Bohm's mysterious 'quantum force' and 'active information': alternative interpretation and statistical properties

    International Nuclear Information System (INIS)

    Lan, B.L.

    2001-01-01

    An alternative interpretation to Bohm's 'quantum force' and 'active information' is proposed. Numerical evidence is presented, which suggests that the time series of Bohm's 'quantum force' evaluated at the Bohmian position for non-stationary quantum states are typically non-Gaussian stable distributed with a flat power spectrum in classically chaotic Hamiltonian systems. An important implication of these statistical properties is briefly mentioned. (orig.)

  1. Quantum Theory for the Binomial Model in Finance Thoery

    OpenAIRE

    Chen, Zeqian

    2001-01-01

    In this paper, a quantum model for the binomial market in finance is proposed. We show that its risk-neutral world exhibits an intriguing structure as a disk in the unit ball of ${\\bf R}^3,$ whose radius is a function of the risk-free interest rate with two thresholds which prevent arbitrage opportunities from this quantum market. Furthermore, from the quantum mechanical point of view we re-deduce the Cox-Ross-Rubinstein binomial option pricing formula by considering Maxwell-Boltzmann statist...

  2. Sanov and central limit theorems for output statistics of quantum Markov chains

    Energy Technology Data Exchange (ETDEWEB)

    Horssen, Merlijn van, E-mail: merlijn.vanhorssen@nottingham.ac.uk [School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD (United Kingdom); Guţă, Mădălin, E-mail: madalin.guta@nottingham.ac.uk [School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD (United Kingdom)

    2015-02-15

    In this paper, we consider the statistics of repeated measurements on the output of a quantum Markov chain. We establish a large deviations result analogous to Sanov’s theorem for the multi-site empirical measure associated to finite sequences of consecutive outcomes of a classical stochastic process. Our result relies on the construction of an extended quantum transition operator (which keeps track of previous outcomes) in terms of which we compute moment generating functions, and whose spectral radius is related to the large deviations rate function. As a corollary to this, we obtain a central limit theorem for the empirical measure. Such higher level statistics may be used to uncover critical behaviour such as dynamical phase transitions, which are not captured by lower level statistics such as the sample mean. As a step in this direction, we give an example of a finite system whose level-1 (empirical mean) rate function is independent of a model parameter while the level-2 (empirical measure) rate is not.

  3. Quantum-like model of unconscious–conscious dynamics

    Science.gov (United States)

    Khrennikov, Andrei

    2015-01-01

    We present a quantum-like model of sensation–perception dynamics (originated in Helmholtz theory of unconscious inference) based on the theory of quantum apparatuses and instruments. We illustrate our approach with the model of bistable perception of a particular ambiguous figure, the Schröder stair. This is a concrete model for unconscious and conscious processing of information and their interaction. The starting point of our quantum-like journey was the observation that perception dynamics is essentially contextual which implies impossibility of (straightforward) embedding of experimental statistical data in the classical (Kolmogorov, 1933) framework of probability theory. This motivates application of nonclassical probabilistic schemes. And the quantum formalism provides a variety of the well-approved and mathematically elegant probabilistic schemes to handle results of measurements. The theory of quantum apparatuses and instruments is the most general quantum scheme describing measurements and it is natural to explore it to model the sensation–perception dynamics. In particular, this theory provides the scheme of indirect quantum measurements which we apply to model unconscious inference leading to transition from sensations to perceptions. PMID:26283979

  4. On estimating perturbative coefficients in quantum field theory and statistical physics

    International Nuclear Information System (INIS)

    Samuel, M.A.; Stanford Univ., CA

    1994-05-01

    The authors present a method for estimating perturbative coefficients in quantum field theory and Statistical Physics. They are able to obtain reliable error-bars for each estimate. The results, in all cases, are excellent

  5. Transformation & uncertainty : some thoughts on quantum probability theory, quantum statistics, and natural bundles

    NARCIS (Netherlands)

    Janssens, B.

    2010-01-01

    This PHD thesis is concerned partly with uncertainty relations in quantum probability theory, partly with state estimation in quantum stochastics, and partly with natural bundles in differential geometry. The laws of quantum mechanics impose severe restrictions on the performance of measurement.

  6. Quantum statistical mechanics of dense partially ionized hydrogen.

    Science.gov (United States)

    Dewitt, H. E.; Rogers, F. J.

    1972-01-01

    The theory of dense hydrogenic plasmas beginning with the two component quantum grand partition function is reviewed. It is shown that ionization equilibrium and molecular dissociation equilibrium can be treated in the same manner with proper consideration of all two-body states. A quantum perturbation expansion is used to give an accurate calculation of the equation of state of the gas for any degree of dissociation and ionization. In this theory, the effective interaction between any two charges is the dynamic screened potential obtained from the plasma dielectric function. We make the static approximation; and we carry out detailed numerical calculations with the bound and scattering states of the Debye potential, using the Beth-Uhlenbeck form of the quantum second virial coefficient. We compare our results with calculations from the Saha equation.

  7. Integrable models in classical and quantum mechanics

    International Nuclear Information System (INIS)

    Jurco, B.

    1991-01-01

    Integrable systems are investigated, especially the rational and trigonometric Gaudin models. The Gaudin models are diagonalized for the case of classical Lie algebras. Their relation to the other integrable models and to the quantum inverse scattering method is investigated. Applications in quantum optics and plasma physics are discussed. (author). 94 refs

  8. Opinion dynamics model based on quantum formalism

    Energy Technology Data Exchange (ETDEWEB)

    Artawan, I. Nengah, E-mail: nengahartawan@gmail.com [Theoretical Physics Division, Department of Physics, Udayana University (Indonesia); Trisnawati, N. L. P., E-mail: nlptrisnawati@gmail.com [Biophysics, Department of Physics, Udayana University (Indonesia)

    2016-03-11

    Opinion dynamics model based on quantum formalism is proposed. The core of the quantum formalism is on the half spin dynamics system. In this research the implicit time evolution operators are derived. The analogy between the model with Deffuant dan Sznajd models is discussed.

  9. Statistics of decay dynamics of quantum emitters in disordered photonic-crystal waveguides

    DEFF Research Database (Denmark)

    Javadi, Alisa; Garcia-Fernandez, Pedro David; Sapienza, Luca

    2014-01-01

    We present a statistical analysis of the spontaneous emission of quantum dots coupled to Anderson-localized cavities in disordered photonic-crystal waveguides.We observe an average Purcell factor of ∼ 5 with a maximum value of 24.......We present a statistical analysis of the spontaneous emission of quantum dots coupled to Anderson-localized cavities in disordered photonic-crystal waveguides.We observe an average Purcell factor of ∼ 5 with a maximum value of 24....

  10. Thermodynamics of ideal quantum gas with fractional statistics in D dimensions.

    Science.gov (United States)

    Potter, Geoffrey G; Müller, Gerhard; Karbach, Michael

    2007-06-01

    We present exact and explicit results for the thermodynamic properties (isochores, isotherms, isobars, response functions, velocity of sound) of a quantum gas in dimensions D > or = 1 and with fractional exclusion statistics 0 < or = g < or =1 connecting bosons (g=0) and fermions (g=1) . In D=1 the results are equivalent to those of the Calogero-Sutherland model. Emphasis is given to the crossover between bosonlike and fermionlike features, caused by aspects of the statistical interaction that mimic long-range attraction and short-range repulsion. A phase transition along the isobar occurs at a nonzero temperature in all dimensions. The T dependence of the velocity of sound is in simple relation to isochores and isobars. The effects of soft container walls are accounted for rigorously for the case of a pure power-law potential.

  11. On stability and symmetries in quantum statistical mechanics

    NARCIS (Netherlands)

    Hoekman, Frank

    1977-01-01

    In deze studie wordt de aard van toestanden van systemen in de quantum statistische mechanica onderzocht vanuit het gezichtspunt van stabiliteit voor kleine storingen van de dynamica en vanuit het gezichtspunt van invariantie voor een geschikte ondergroep van de symmetrieën van de dynamica. Systemen

  12. Counting statistics of non-markovian quantum stochastic processes

    DEFF Research Database (Denmark)

    Flindt, Christian; Novotny, T.; Braggio, A.

    2008-01-01

    We derive a general expression for the cumulant generating function (CGF) of non-Markovian quantum stochastic transport processes. The long-time limit of the CGF is determined by a single dominating pole of the resolvent of the memory kernel from which we extract the zero-frequency cumulants...

  13. Topological and statistical properties of quantum control transition landscapes

    International Nuclear Information System (INIS)

    Hsieh, Michael; Wu Rebing; Rabitz, Herschel; Rosenthal, Carey

    2008-01-01

    A puzzle arising in the control of quantum dynamics is to explain the relative ease with which high-quality control solutions can be found in the laboratory and in simulations. The emerging explanation appears to lie in the nature of the quantum control landscape, which is an observable as a function of the control variables. This work considers the common case of the observable being the transition probability between an initial and a target state. For any controllable quantum system, this landscape contains only global maxima and minima, and no local extrema traps. The probability distribution function for the landscape value is used to calculate the relative volume of the region of the landscape corresponding to good control solutions. The topology of the global optima of the landscape is analysed and the optima are shown to have inherent robustness to variations in the controls. Although the relative landscape volume of good control solutions is found to shrink rapidly as the system Hilbert space dimension increases, the highly favourable landscape topology at and away from the global optima provides a rationale for understanding the relative ease of finding high-quality, stable quantum optimal control solutions

  14. Philosophical perspectives on quantum chaos: Models and interpretations

    Science.gov (United States)

    Bokulich, Alisa Nicole

    2001-09-01

    The problem of quantum chaos is a special case of the larger problem of understanding how the classical world emerges from quantum mechanics. While we have learned that chaos is pervasive in classical systems, it appears to be almost entirely absent in quantum systems. The aim of this dissertation is to determine what implications the interpretation of quantum mechanics has for attempts to explain the emergence of classical chaos. There are three interpretations of quantum mechanics that have set out programs for solving the problem of quantum chaos: the standard interpretation, the statistical interpretation, and the deBroglie-Bohm causal interpretation. One of the main conclusions of this dissertation is that an interpretation alone is insufficient for solving the problem of quantum chaos and that the phenomenon of decoherence must be taken into account. Although a completely satisfactory solution of the problem of quantum chaos is still outstanding, I argue that the deBroglie-Bohm interpretation with the help of decoherence outlines the most promising research program to pursue. In addition to making a contribution to the debate in the philosophy of physics concerning the interpretation of quantum mechanics, this dissertation reveals two important methodological lessons for the philosophy of science. First, issues of reductionism and intertheoretic relations cannot be divorced from questions concerning the interpretation of the theories involved. Not only is the exploration of intertheoretic relations a central part of the articulation and interpretation of an individual theory, but the very terms used to discuss intertheoretic relations, such as `state' and `classical limit', are themselves defined by particular interpretations of the theory. The second lesson that emerges is that, when it comes to characterizing the relationship between classical chaos and quantum mechanics, the traditional approaches to intertheoretic relations, namely reductionism and

  15. Some connections between relativistic classical mechanics, statistical mechanics, and quantum field theory

    International Nuclear Information System (INIS)

    Remler, E.A.

    1977-01-01

    A gauge-invariant version of the Wigner representation is used to relate relativistic mechanics, statistical mechanics, and quantum field theory in the context of the electrodynamics of scalar particles. A unified formulation of quantum field theory and statistical mechanics is developed which clarifies the physics interpretation of the single-particle Wigner function. A covariant form of Ehrenfest's theorem is derived. Classical electrodynamics is derived from quantum field theory after making a random-phase approximation. The validity of this approximation is discussed

  16. Statistics, synergy, and mechanism of multiple photogeneration of excitons in quantum dots: Fundamental and applied aspects

    International Nuclear Information System (INIS)

    Oksengendler, B. L.; Turaeva, N. N.; Uralov, I.; Marasulov, M. B.

    2012-01-01

    The effect of multiple exciton generation is analyzed based on statistical physics, quantum mechanics, and synergetics. Statistical problems of the effect of multiple exciton generation (MEG) are broadened and take into account not only exciton generation, but also background excitation. The study of the role of surface states of quantum dots is based on the synergy of self-catalyzed electronic reactions. An analysis of the MEG mechanism is based on the idea of electronic shaking using the sudden perturbation method in quantum mechanics. All of the above-mentioned results are applied to the problem of calculating the limiting efficiency to transform solar energy into electric energy. (authors)

  17. Statistical interpretation of transient current power-law decay in colloidal quantum dot arrays

    Energy Technology Data Exchange (ETDEWEB)

    Sibatov, R T, E-mail: ren_sib@bk.ru [Ulyanovsk State University, 432000, 42 Leo Tolstoy Street, Ulyanovsk (Russian Federation)

    2011-08-01

    A new statistical model of the charge transport in colloidal quantum dot arrays is proposed. It takes into account Coulomb blockade forbidding multiple occupancy of nanocrystals and the influence of energetic disorder of interdot space. The model explains power-law current transients and the presence of the memory effect. The fractional differential analogue of the Ohm law is found phenomenologically for nanocrystal arrays. The model combines ideas that were considered as conflicting by other authors: the Scher-Montroll idea about the power-law distribution of waiting times in localized states for disordered semiconductors is applied taking into account Coulomb blockade; Novikov's condition about the asymptotic power-law distribution of time intervals between successful current pulses in conduction channels is fulfilled; and the carrier injection blocking predicted by Ginger and Greenham (2000 J. Appl. Phys. 87 1361) takes place.

  18. Statistical interpretation of transient current power-law decay in colloidal quantum dot arrays

    International Nuclear Information System (INIS)

    Sibatov, R T

    2011-01-01

    A new statistical model of the charge transport in colloidal quantum dot arrays is proposed. It takes into account Coulomb blockade forbidding multiple occupancy of nanocrystals and the influence of energetic disorder of interdot space. The model explains power-law current transients and the presence of the memory effect. The fractional differential analogue of the Ohm law is found phenomenologically for nanocrystal arrays. The model combines ideas that were considered as conflicting by other authors: the Scher-Montroll idea about the power-law distribution of waiting times in localized states for disordered semiconductors is applied taking into account Coulomb blockade; Novikov's condition about the asymptotic power-law distribution of time intervals between successful current pulses in conduction channels is fulfilled; and the carrier injection blocking predicted by Ginger and Greenham (2000 J. Appl. Phys. 87 1361) takes place.

  19. Quantum mechanics as classical statistical mechanics with an ontic extension and an epistemic restriction.

    Science.gov (United States)

    Budiyono, Agung; Rohrlich, Daniel

    2017-11-03

    Where does quantum mechanics part ways with classical mechanics? How does quantum randomness differ fundamentally from classical randomness? We cannot fully explain how the theories differ until we can derive them within a single axiomatic framework, allowing an unambiguous account of how one theory is the limit of the other. Here we derive non-relativistic quantum mechanics and classical statistical mechanics within a common framework. The common axioms include conservation of average energy and conservation of probability current. But two axioms distinguish quantum mechanics from classical statistical mechanics: an "ontic extension" defines a nonseparable (global) random variable that generates physical correlations, and an "epistemic restriction" constrains allowed phase space distributions. The ontic extension and epistemic restriction, with strength on the order of Planck's constant, imply quantum entanglement and uncertainty relations. This framework suggests that the wave function is epistemic, yet it does not provide an ontic dynamics for individual systems.

  20. Shell model in large spaces and statistical spectroscopy

    International Nuclear Information System (INIS)

    Kota, V.K.B.

    1996-01-01

    For many nuclear structure problems of current interest it is essential to deal with shell model in large spaces. For this, three different approaches are now in use and two of them are: (i) the conventional shell model diagonalization approach but taking into account new advances in computer technology; (ii) the shell model Monte Carlo method. A brief overview of these two methods is given. Large space shell model studies raise fundamental questions regarding the information content of the shell model spectrum of complex nuclei. This led to the third approach- the statistical spectroscopy methods. The principles of statistical spectroscopy have their basis in nuclear quantum chaos and they are described (which are substantiated by large scale shell model calculations) in some detail. (author)

  1. Statistical distribution of the local purity in a large quantum system

    International Nuclear Information System (INIS)

    De Pasquale, A; Pascazio, S; Facchi, P; Giovannetti, V; Parisi, G; Scardicchio, A

    2012-01-01

    The local purity of large many-body quantum systems can be studied by following a statistical mechanical approach based on a random matrix model. Restricting the analysis to the case of global pure states, this method proved to be successful, and a full characterization of the statistical properties of the local purity was obtained by computing the partition function of the problem. Here we generalize these techniques to the case of global mixed states. In this context, by uniformly sampling the phase space of states with assigned global mixedness, we determine the exact expression of the first two moments of the local purity and a general expression for the moments of higher order. This generalizes previous results obtained for globally pure configurations. Furthermore, through the introduction of a partition function for a suitable canonical ensemble, we compute the approximate expression of the first moment of the marginal purity in the high-temperature regime. In the process, we establish a formal connection with the theory of quantum twirling maps that provides an alternative, possibly fruitful, way of performing the calculation. (paper)

  2. No information flow using statistical fluctuations and quantum cryptography

    Science.gov (United States)

    Larsson, Jan-Åke

    2004-04-01

    The communication protocol of Home and Whitaker [Phys. Rev. A 67, 022306 (2003)] is examined in some detail, and found to work equally well using a separable state. The protocol is in fact completely classical, based on postselection of suitable experimental runs. The quantum-cryptography protocol proposed in the same publication is also examined, and this protocol uses entanglement, a strictly quantum property of the system. An individual eavesdropping attack on each qubit pair would be detected by the security test proposed in the mentioned paper. However, the key is provided by groups of qubits, and there exists a coherent attack, internal to these groups, that will go unnoticed in that security test. A modified test is proposed here that will ensure security, even against such a coherent attack.

  3. No information flow using statistical fluctuations and quantum cryptography

    International Nuclear Information System (INIS)

    Larsson, Jan-Aake

    2004-01-01

    The communication protocol of Home and Whitaker [Phys. Rev. A 67, 022306 (2003)] is examined in some detail, and found to work equally well using a separable state. The protocol is in fact completely classical, based on postselection of suitable experimental runs. The quantum-cryptography protocol proposed in the same publication is also examined, and this protocol uses entanglement, a strictly quantum property of the system. An individual eavesdropping attack on each qubit pair would be detected by the security test proposed in the mentioned paper. However, the key is provided by groups of qubits, and there exists a coherent attack, internal to these groups, that will go unnoticed in that security test. A modified test is proposed here that will ensure security, even against such a coherent attack

  4. Statistical modelling of fish stocks

    DEFF Research Database (Denmark)

    Kvist, Trine

    1999-01-01

    for modelling the dynamics of a fish population is suggested. A new approach is introduced to analyse the sources of variation in age composition data, which is one of the most important sources of information in the cohort based models for estimation of stock abundancies and mortalities. The approach combines...... and it is argued that an approach utilising stochastic differential equations might be advantagous in fish stoch assessments....

  5. Application of nonequilibrium quantum statistical mechanics to homogeneous nucleation

    International Nuclear Information System (INIS)

    Larson, A.R.; Cantrell, C.D.

    1978-01-01

    The master equation for cluster growth and evaporation is derived from many-body quantum mechanics and from a modified version of quantum damping theory used in laser physics. For application to nucleation theory, the quantum damping theory has been generalized to include system and reservoir states that are not separate entities. Formulae for rate constants are obtained. Solutions of the master equation yield equations of state and system-averaged quantities recognized as thermodynamic variables. Formulae for Helmholtz free energies of clusters in a Debye approximation are derived. Coexistence-line equations for pressure volume, and number of clusters are obtained from equations-of-state analysis. Coexistence-line and surface-tension data are used to obtain values of parameters for the Debye approximation. These data are employed in calculating both the nucleation current in diffusion cloud chamber experiments and the onset of condensation in expansion nozzle experiments. Theoretical and experimental results are similar for both cloud-chamber and nozzle experiments, which measure water

  6. Homogeneous nucleation: a problem in nonequilibrium quantum statistical mechanics

    International Nuclear Information System (INIS)

    1978-08-01

    The master equation for cluster growth and evaporation is derived for many-body quantum mechanics and from a modified version of quantum damping theory used in laser physics. For application to nucleation theory, the quantum damping theory is generalized to include system and reservoir states that are not separate entities. Formulas for rate constants are obtained. Solutions of the master equation yield equations of state and system-averaged quantities recognized as thermodynamic variables. Formulas for Helmholtz free energies of clusters in a Debye approximation are derived. Coexistence-line equations for pressure, volume, and number of clusters are obtained from equations-of-state analysis. Coexistence-line and surface-tension data are used to obtain values of parameters for the Debye approximation. These data are employed in calculating both the nucleation current in diffusion cloud chamber experiments and the onset of condensation in expansion nozzle experiments. Theoretical and experimental results are similar for both cloud chamber and nozzle experiments, which measure water. Comparison with other theories reveals that classical theory only accidently agrees with experiment and that the Helmholtz free-energy formula used in the Lothe--Pound theory is incomplete. 27 figures, 3 tables, 149 references

  7. Integrable models of quantum optics

    Directory of Open Access Journals (Sweden)

    Yudson Vladimir

    2017-01-01

    Full Text Available We give an overview of exactly solvable many-body models of quantum optics. Among them is a system of two-level atoms which interact with photons propagating in a one-dimensional (1D chiral waveguide; exact eigenstates of this system can be explicitly constructed. This approach is used also for a system of closely located atoms in the usual (non-chiral waveguide or in 3D space. Moreover, it is shown that for an arbitrary atomic system with a cascade spontaneous radiative decay, the fluorescence spectrum can be described by an exact analytic expression which accounts for interference of emitted photons. Open questions related with broken integrability are discussed.

  8. Statistical lung model for microdosimetry

    International Nuclear Information System (INIS)

    Fisher, D.R.; Hadley, R.T.

    1984-03-01

    To calculate the microdosimetry of plutonium in the lung, a mathematical description is needed of lung tissue microstructure that defines source-site parameters. Beagle lungs were expanded using a glutaraldehyde fixative at 30 cm water pressure. Tissue specimens, five microns thick, were stained with hematoxylin and eosin then studied using an image analyzer. Measurements were made along horizontal lines through the magnified tissue image. The distribution of air space and tissue chord lengths and locations of epithelial cell nuclei were recorded from about 10,000 line scans. The distribution parameters constituted a model of lung microstructure for predicting the paths of random alpha particle tracks in the lung and the probability of traversing biologically sensitive sites. This lung model may be used in conjunction with established deposition and retention models for determining the microdosimetry in the pulmonary lung for a wide variety of inhaled radioactive materials

  9. Statistical modelling for ship propulsion efficiency

    DEFF Research Database (Denmark)

    Petersen, Jóan Petur; Jacobsen, Daniel J.; Winther, Ole

    2012-01-01

    This paper presents a state-of-the-art systems approach to statistical modelling of fuel efficiency in ship propulsion, and also a novel and publicly available data set of high quality sensory data. Two statistical model approaches are investigated and compared: artificial neural networks...

  10. Actuarial statistics with generalized linear mixed models

    NARCIS (Netherlands)

    Antonio, K.; Beirlant, J.

    2007-01-01

    Over the last decade the use of generalized linear models (GLMs) in actuarial statistics has received a lot of attention, starting from the actuarial illustrations in the standard text by McCullagh and Nelder [McCullagh, P., Nelder, J.A., 1989. Generalized linear models. In: Monographs on Statistics

  11. Spin chain model for correlated quantum channels

    Energy Technology Data Exchange (ETDEWEB)

    Rossini, Davide [International School for Advanced Studies SISSA/ISAS, via Beirut 2-4, I-34014 Trieste (Italy); Giovannetti, Vittorio; Montangero, Simone [NEST-CNR-INFM and Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa (Italy)], E-mail: monta@sns.it

    2008-11-15

    We analyze the quality of the quantum information transmission along a correlated quantum channel by studying the average fidelity between input and output states and the average output purity, giving bounds for the entropy of the channel. Noise correlations in the channel are modeled by the coupling of each channel use with an element of a one-dimensional interacting quantum spin chain. Criticality of the environment chain is seen to emerge in the changes of the fidelity and of the purity.

  12. Spherical Process Models for Global Spatial Statistics

    KAUST Repository

    Jeong, Jaehong; Jun, Mikyoung; Genton, Marc G.

    2017-01-01

    Statistical models used in geophysical, environmental, and climate science applications must reflect the curvature of the spatial domain in global data. Over the past few decades, statisticians have developed covariance models that capture

  13. A statistical mechanical model for equilibrium ionization

    International Nuclear Information System (INIS)

    Macris, N.; Martin, P.A.; Pule, J.

    1990-01-01

    A quantum electron interacts with a classical gas of hard spheres and is in thermal equilibrium with it. The interaction is attractive and the electron can form a bound state with the classical particles. It is rigorously shown that in a well defined low density and low temperature limit, the ionization probability for the electron tends to the value predicted by the Saha formula for thermal ionization. In this regime, the electron is found to be in a statistical mixture of a bound and a free state. (orig.)

  14. Quantum Models of Classical World

    Directory of Open Access Journals (Sweden)

    Petr Hájíček

    2013-02-01

    Full Text Available This paper is a review of our recent work on three notorious problems of non-relativistic quantum mechanics: realist interpretation, quantum theory of classical properties, and the problem of quantum measurement. A considerable progress has been achieved, based on four distinct new ideas. First, objective properties are associated with states rather than with values of observables. Second, all classical properties are selected properties of certain high entropy quantum states of macroscopic systems. Third, registration of a quantum system is strongly disturbed by systems of the same type in the environment. Fourth, detectors must be distinguished from ancillas and the states of registered systems are partially dissipated and lost in the detectors. The paper has two aims: a clear explanation of all new results and a coherent and contradiction-free account of the whole quantum mechanics including all necessary changes of its current textbook version.

  15. Statistical Models and Methods for Lifetime Data

    CERN Document Server

    Lawless, Jerald F

    2011-01-01

    Praise for the First Edition"An indispensable addition to any serious collection on lifetime data analysis and . . . a valuable contribution to the statistical literature. Highly recommended . . ."-Choice"This is an important book, which will appeal to statisticians working on survival analysis problems."-Biometrics"A thorough, unified treatment of statistical models and methods used in the analysis of lifetime data . . . this is a highly competent and agreeable statistical textbook."-Statistics in MedicineThe statistical analysis of lifetime or response time data is a key tool in engineering,

  16. Quantum decoration transformation for spin models

    Energy Technology Data Exchange (ETDEWEB)

    Braz, F.F.; Rodrigues, F.C.; Souza, S.M. de; Rojas, Onofre, E-mail: ors@dfi.ufla.br

    2016-09-15

    It is quite relevant the extension of decoration transformation for quantum spin models since most of the real materials could be well described by Heisenberg type models. Here we propose an exact quantum decoration transformation and also showing interesting properties such as the persistence of symmetry and the symmetry breaking during this transformation. Although the proposed transformation, in principle, cannot be used to map exactly a quantum spin lattice model into another quantum spin lattice model, since the operators are non-commutative. However, it is possible the mapping in the “classical” limit, establishing an equivalence between both quantum spin lattice models. To study the validity of this approach for quantum spin lattice model, we use the Zassenhaus formula, and we verify how the correction could influence the decoration transformation. But this correction could be useless to improve the quantum decoration transformation because it involves the second-nearest-neighbor and further nearest neighbor couplings, which leads into a cumbersome task to establish the equivalence between both lattice models. This correction also gives us valuable information about its contribution, for most of the Heisenberg type models, this correction could be irrelevant at least up to the third order term of Zassenhaus formula. This transformation is applied to a finite size Heisenberg chain, comparing with the exact numerical results, our result is consistent for weak xy-anisotropy coupling. We also apply to bond-alternating Ising–Heisenberg chain model, obtaining an accurate result in the limit of the quasi-Ising chain.

  17. Quantum decoration transformation for spin models

    International Nuclear Information System (INIS)

    Braz, F.F.; Rodrigues, F.C.; Souza, S.M. de; Rojas, Onofre

    2016-01-01

    It is quite relevant the extension of decoration transformation for quantum spin models since most of the real materials could be well described by Heisenberg type models. Here we propose an exact quantum decoration transformation and also showing interesting properties such as the persistence of symmetry and the symmetry breaking during this transformation. Although the proposed transformation, in principle, cannot be used to map exactly a quantum spin lattice model into another quantum spin lattice model, since the operators are non-commutative. However, it is possible the mapping in the “classical” limit, establishing an equivalence between both quantum spin lattice models. To study the validity of this approach for quantum spin lattice model, we use the Zassenhaus formula, and we verify how the correction could influence the decoration transformation. But this correction could be useless to improve the quantum decoration transformation because it involves the second-nearest-neighbor and further nearest neighbor couplings, which leads into a cumbersome task to establish the equivalence between both lattice models. This correction also gives us valuable information about its contribution, for most of the Heisenberg type models, this correction could be irrelevant at least up to the third order term of Zassenhaus formula. This transformation is applied to a finite size Heisenberg chain, comparing with the exact numerical results, our result is consistent for weak xy-anisotropy coupling. We also apply to bond-alternating Ising–Heisenberg chain model, obtaining an accurate result in the limit of the quasi-Ising chain.

  18. Statistics and the shell model

    International Nuclear Information System (INIS)

    Weidenmueller, H.A.

    1985-01-01

    Starting with N. Bohr's paper on compound-nucleus reactions, we confront regular dynamical features and chaotic motion in nuclei. The shell-model and, more generally, mean-field theories describe average nuclear properties which are thus identified as regular features. The fluctuations about the average show chaotic behaviour of the same type as found in classical chaotic systems upon quantisation. These features are therefore generic and quite independent of the specific dynamics of the nucleus. A novel method to calculate fluctuations is discussed, and the results of this method are described. (orig.)

  19. Quantum statistical entropy corresponding to cosmic horizon in five-dimensional spacetime

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    The generalized uncertainty relation is introduced to calculate the quantum statis-tical entropy corresponding to cosmic horizon. By using the new equation of state density motivated by the generalized uncertainty relation, we discuss entropies of Bose field and Fermi field on the background of five-dimensional spacetime. In our calculation, we need not introduce cutoff. There is no divergent logarithmic term in the original brick-wall method. And it is obtained that the quantum statistical en-tropy corresponding to cosmic horizon is proportional to the area of the horizon. Further it is shown that the entropy corresponding to cosmic horizon is the entropy of quantum state on the surface of horizon. The black hole’s entropy is the intrinsic property of the black hole. The entropy is a quantum effect. In our calculation, by using the quantum statistical method, we obtain the partition function of Bose field and Fermi field on the background of five-dimensional spacetime. We provide a way to study the quantum statistical entropy corresponding to cosmic horizon in the higher-dimensional spacetime.

  20. Quantum integrable models of field theory

    International Nuclear Information System (INIS)

    Faddeev, L.D.

    1979-01-01

    Fundamental features of the classical method of the inverse problem have been formulated in the form which is convenient for its quantum reformulation. Typical examples are studied which may help to formulate the quantum method of the inverse problem. Examples are considered for interaction with both attraction and repulsion at a final density. The sine-Gordon model and the XYZ model from the quantum theory of magnetics are examined in short. It is noted that all the achievements of the one-dimensional mathematical physics as applied to exactly solvable quantum models may be put to an extent within the framework of the quantum method of the inverse problem. Unsolved questions are enumerated and perspectives of applying the inverse problem method are shown

  1. Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems.

    Science.gov (United States)

    Gogolin, Christian; Eisert, Jens

    2016-05-01

    We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics. We cover topics such as equilibration and thermalisation in pure state statistical mechanics, the eigenstate thermalisation hypothesis, the equivalence of ensembles, non-equilibration dynamics following global and local quenches as well as ramps. We also address initial state independence, absence of thermalisation, and many-body localisation. We elucidate the role played by key concepts for these phenomena, such as Lieb-Robinson bounds, entanglement growth, typicality arguments, quantum maximum entropy principles and the generalised Gibbs ensembles, and quantum (non-)integrability. We put emphasis on rigorous approaches and present the most important results in a unified language.

  2. Bayesian models: A statistical primer for ecologists

    Science.gov (United States)

    Hobbs, N. Thompson; Hooten, Mevin B.

    2015-01-01

    Bayesian modeling has become an indispensable tool for ecological research because it is uniquely suited to deal with complexity in a statistically coherent way. This textbook provides a comprehensive and accessible introduction to the latest Bayesian methods—in language ecologists can understand. Unlike other books on the subject, this one emphasizes the principles behind the computations, giving ecologists a big-picture understanding of how to implement this powerful statistical approach.Bayesian Models is an essential primer for non-statisticians. It begins with a definition of probability and develops a step-by-step sequence of connected ideas, including basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and inference from single and multiple models. This unique book places less emphasis on computer coding, favoring instead a concise presentation of the mathematical statistics needed to understand how and why Bayesian analysis works. It also explains how to write out properly formulated hierarchical Bayesian models and use them in computing, research papers, and proposals.This primer enables ecologists to understand the statistical principles behind Bayesian modeling and apply them to research, teaching, policy, and management.Presents the mathematical and statistical foundations of Bayesian modeling in language accessible to non-statisticiansCovers basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and moreDeemphasizes computer coding in favor of basic principlesExplains how to write out properly factored statistical expressions representing Bayesian models

  3. Statistical Model-Based Face Pose Estimation

    Institute of Scientific and Technical Information of China (English)

    GE Xinliang; YANG Jie; LI Feng; WANG Huahua

    2007-01-01

    A robust face pose estimation approach is proposed by using face shape statistical model approach and pose parameters are represented by trigonometric functions. The face shape statistical model is firstly built by analyzing the face shapes from different people under varying poses. The shape alignment is vital in the process of building the statistical model. Then, six trigonometric functions are employed to represent the face pose parameters. Lastly, the mapping function is constructed between face image and face pose by linearly relating different parameters. The proposed approach is able to estimate different face poses using a few face training samples. Experimental results are provided to demonstrate its efficiency and accuracy.

  4. Uncertainty the soul of modeling, probability & statistics

    CERN Document Server

    Briggs, William

    2016-01-01

    This book presents a philosophical approach to probability and probabilistic thinking, considering the underpinnings of probabilistic reasoning and modeling, which effectively underlie everything in data science. The ultimate goal is to call into question many standard tenets and lay the philosophical and probabilistic groundwork and infrastructure for statistical modeling. It is the first book devoted to the philosophy of data aimed at working scientists and calls for a new consideration in the practice of probability and statistics to eliminate what has been referred to as the "Cult of Statistical Significance". The book explains the philosophy of these ideas and not the mathematics, though there are a handful of mathematical examples. The topics are logically laid out, starting with basic philosophy as related to probability, statistics, and science, and stepping through the key probabilistic ideas and concepts, and ending with statistical models. Its jargon-free approach asserts that standard methods, suc...

  5. Automated statistical modeling of analytical measurement systems

    International Nuclear Information System (INIS)

    Jacobson, J.J.

    1992-01-01

    The statistical modeling of analytical measurement systems at the Idaho Chemical Processing Plant (ICPP) has been completely automated through computer software. The statistical modeling of analytical measurement systems is one part of a complete quality control program used by the Remote Analytical Laboratory (RAL) at the ICPP. The quality control program is an integration of automated data input, measurement system calibration, database management, and statistical process control. The quality control program and statistical modeling program meet the guidelines set forth by the American Society for Testing Materials and American National Standards Institute. A statistical model is a set of mathematical equations describing any systematic bias inherent in a measurement system and the precision of a measurement system. A statistical model is developed from data generated from the analysis of control standards. Control standards are samples which are made up at precise known levels by an independent laboratory and submitted to the RAL. The RAL analysts who process control standards do not know the values of those control standards. The object behind statistical modeling is to describe real process samples in terms of their bias and precision and, to verify that a measurement system is operating satisfactorily. The processing of control standards gives us this ability

  6. Multiscale Monte Carlo algorithms in statistical mechanics and quantum field theory

    Energy Technology Data Exchange (ETDEWEB)

    Lauwers, P G

    1990-12-01

    Conventional Monte Carlo simulation algorithms for models in statistical mechanics and quantum field theory are afflicted by problems caused by their locality. They become highly inefficient if investigations of critical or nearly-critical systems, i.e., systems with important large scale phenomena, are undertaken. We present two types of multiscale approaches that alleveate problems of this kind: Stochastic cluster algorithms and multigrid Monte Carlo simulation algorithms. Another formidable computational problem in simulations of phenomenologically relevant field theories with fermions is the need for frequently inverting the Dirac operator. This inversion can be accelerated considerably by means of deterministic multigrid methods, very similar to the ones used for the numerical solution of differential equations. (orig.).

  7. Quantum Graphical Models and Belief Propagation

    International Nuclear Information System (INIS)

    Leifer, M.S.; Poulin, D.

    2008-01-01

    Belief Propagation algorithms acting on Graphical Models of classical probability distributions, such as Markov Networks, Factor Graphs and Bayesian Networks, are amongst the most powerful known methods for deriving probabilistic inferences amongst large numbers of random variables. This paper presents a generalization of these concepts and methods to the quantum case, based on the idea that quantum theory can be thought of as a noncommutative, operator-valued, generalization of classical probability theory. Some novel characterizations of quantum conditional independence are derived, and definitions of Quantum n-Bifactor Networks, Markov Networks, Factor Graphs and Bayesian Networks are proposed. The structure of Quantum Markov Networks is investigated and some partial characterization results are obtained, along the lines of the Hammersley-Clifford theorem. A Quantum Belief Propagation algorithm is presented and is shown to converge on 1-Bifactor Networks and Markov Networks when the underlying graph is a tree. The use of Quantum Belief Propagation as a heuristic algorithm in cases where it is not known to converge is discussed. Applications to decoding quantum error correcting codes and to the simulation of many-body quantum systems are described

  8. Topology for statistical modeling of petascale data.

    Energy Technology Data Exchange (ETDEWEB)

    Pascucci, Valerio (University of Utah, Salt Lake City, UT); Mascarenhas, Ajith Arthur; Rusek, Korben (Texas A& M University, College Station, TX); Bennett, Janine Camille; Levine, Joshua (University of Utah, Salt Lake City, UT); Pebay, Philippe Pierre; Gyulassy, Attila (University of Utah, Salt Lake City, UT); Thompson, David C.; Rojas, Joseph Maurice (Texas A& M University, College Station, TX)

    2011-07-01

    This document presents current technical progress and dissemination of results for the Mathematics for Analysis of Petascale Data (MAPD) project titled 'Topology for Statistical Modeling of Petascale Data', funded by the Office of Science Advanced Scientific Computing Research (ASCR) Applied Math program. Many commonly used algorithms for mathematical analysis do not scale well enough to accommodate the size or complexity of petascale data produced by computational simulations. The primary goal of this project is thus to develop new mathematical tools that address both the petascale size and uncertain nature of current data. At a high level, our approach is based on the complementary techniques of combinatorial topology and statistical modeling. In particular, we use combinatorial topology to filter out spurious data that would otherwise skew statistical modeling techniques, and we employ advanced algorithms from algebraic statistics to efficiently find globally optimal fits to statistical models. This document summarizes the technical advances we have made to date that were made possible in whole or in part by MAPD funding. These technical contributions can be divided loosely into three categories: (1) advances in the field of combinatorial topology, (2) advances in statistical modeling, and (3) new integrated topological and statistical methods.

  9. Statistical modelling of citation exchange between statistics journals.

    Science.gov (United States)

    Varin, Cristiano; Cattelan, Manuela; Firth, David

    2016-01-01

    Rankings of scholarly journals based on citation data are often met with scepticism by the scientific community. Part of the scepticism is due to disparity between the common perception of journals' prestige and their ranking based on citation counts. A more serious concern is the inappropriate use of journal rankings to evaluate the scientific influence of researchers. The paper focuses on analysis of the table of cross-citations among a selection of statistics journals. Data are collected from the Web of Science database published by Thomson Reuters. Our results suggest that modelling the exchange of citations between journals is useful to highlight the most prestigious journals, but also that journal citation data are characterized by considerable heterogeneity, which needs to be properly summarized. Inferential conclusions require care to avoid potential overinterpretation of insignificant differences between journal ratings. Comparison with published ratings of institutions from the UK's research assessment exercise shows strong correlation at aggregate level between assessed research quality and journal citation 'export scores' within the discipline of statistics.

  10. Representation of the contextual statistical model by hyperbolic amplitudes

    International Nuclear Information System (INIS)

    Khrennikov, Andrei

    2005-01-01

    We continue the development of a so-called contextual statistical model (here context has the meaning of a complex of physical conditions). It is shown that, besides contexts producing the conventional trigonometric cos-interference, there exist contexts producing the hyperbolic cos-interference. Starting with the corresponding interference formula of total probability we represent such contexts by hyperbolic probabilistic amplitudes or in the abstract formalism by normalized vectors of a hyperbolic analogue of the Hilbert space. There is obtained a hyperbolic Born's rule. Incompatible observables are represented by noncommutative operators. This paper can be considered as the first step towards hyperbolic quantum probability. We also discuss possibilities of experimental verification of hyperbolic quantum mechanics: in physics of elementary particles, string theory as well as in experiments with nonphysical systems, e.g., in psychology, cognitive sciences, and economy

  11. Statistical mechanics of the cluster Ising model

    International Nuclear Information System (INIS)

    Smacchia, Pietro; Amico, Luigi; Facchi, Paolo; Fazio, Rosario; Florio, Giuseppe; Pascazio, Saverio; Vedral, Vlatko

    2011-01-01

    We study a Hamiltonian system describing a three-spin-1/2 clusterlike interaction competing with an Ising-like antiferromagnetic interaction. We compute free energy, spin-correlation functions, and entanglement both in the ground and in thermal states. The model undergoes a quantum phase transition between an Ising phase with a nonvanishing magnetization and a cluster phase characterized by a string order. Any two-spin entanglement is found to vanish in both quantum phases because of a nontrivial correlation pattern. Nevertheless, the residual multipartite entanglement is maximal in the cluster phase and dependent on the magnetization in the Ising phase. We study the block entropy at the critical point and calculate the central charge of the system, showing that the criticality of the system is beyond the Ising universality class.

  12. Statistical mechanics of the cluster Ising model

    Energy Technology Data Exchange (ETDEWEB)

    Smacchia, Pietro [SISSA - via Bonomea 265, I-34136, Trieste (Italy); Amico, Luigi [CNR-MATIS-IMM and Dipartimento di Fisica e Astronomia Universita di Catania, C/O ed. 10, viale Andrea Doria 6, I-95125 Catania (Italy); Facchi, Paolo [Dipartimento di Matematica and MECENAS, Universita di Bari, I-70125 Bari (Italy); INFN, Sezione di Bari, I-70126 Bari (Italy); Fazio, Rosario [NEST, Scuola Normale Superiore and Istituto Nanoscienze - CNR, 56126 Pisa (Italy); Center for Quantum Technology, National University of Singapore, 117542 Singapore (Singapore); Florio, Giuseppe; Pascazio, Saverio [Dipartimento di Fisica and MECENAS, Universita di Bari, I-70126 Bari (Italy); INFN, Sezione di Bari, I-70126 Bari (Italy); Vedral, Vlatko [Center for Quantum Technology, National University of Singapore, 117542 Singapore (Singapore); Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542 (Singapore); Department of Physics, University of Oxford, Clarendon Laboratory, Oxford, OX1 3PU (United Kingdom)

    2011-08-15

    We study a Hamiltonian system describing a three-spin-1/2 clusterlike interaction competing with an Ising-like antiferromagnetic interaction. We compute free energy, spin-correlation functions, and entanglement both in the ground and in thermal states. The model undergoes a quantum phase transition between an Ising phase with a nonvanishing magnetization and a cluster phase characterized by a string order. Any two-spin entanglement is found to vanish in both quantum phases because of a nontrivial correlation pattern. Nevertheless, the residual multipartite entanglement is maximal in the cluster phase and dependent on the magnetization in the Ising phase. We study the block entropy at the critical point and calculate the central charge of the system, showing that the criticality of the system is beyond the Ising universality class.

  13. On the one variational principle in quantum statistical mechanics

    International Nuclear Information System (INIS)

    Kurbatov, A.M.; Sankovich, D.P.

    1980-01-01

    Essential features of the approximating Hamiltonian method are reviewed. The free energy of a system can be calculated with the help of the approximating Hamiltonian, which possesses a simpler operator form than the initial model Hamiltonian. The method is applied to the following cases: model system of BCS type, model system with positive and negative coupling constants, model with nonpolynomial interaction, and model of nonideal Bose gas

  14. Electromagnetic phenomena in matter statistical and quantum approaches

    CERN Document Server

    Toptygin, Igor N

    2015-01-01

    Modern electrodynamics in different media is a wide branch of electrodynamics which combines the exact theory of electromagnetic fields in the presence of electric charges and currents with statistical description of these fields in gases, plasmas, liquids and solids; dielectrics, conductors and superconductors. It is widely used in physics and in other natural sciences (such as astrophysics and geophysics, biophysics, ecology and evolution of terrestrial climate), and in various technological applications (radio electronics, technology of artificial materials, laser-based technological proces

  15. Daily precipitation statistics in regional climate models

    DEFF Research Database (Denmark)

    Frei, Christoph; Christensen, Jens Hesselbjerg; Déqué, Michel

    2003-01-01

    An evaluation is undertaken of the statistics of daily precipitation as simulated by five regional climate models using comprehensive observations in the region of the European Alps. Four limited area models and one variable-resolution global model are considered, all with a grid spacing of 50 km...

  16. Parallelism in computations in quantum and statistical mechanics

    International Nuclear Information System (INIS)

    Clementi, E.; Corongiu, G.; Detrich, J.H.

    1985-01-01

    Often very fundamental biochemical and biophysical problems defy simulations because of limitations in today's computers. We present and discuss a distributed system composed of two IBM 4341 s and/or an IBM 4381 as front-end processors and ten FPS-164 attached array processors. This parallel system - called LCAP - has presently a peak performance of about 110 Mflops; extensions to higher performance are discussed. Presently, the system applications use a modified version of VM/SP as the operating system: description of the modifications is given. Three applications programs have been migrated from sequential to parallel: a molecular quantum mechanical, a Metropolis-Monte Carlo and a molecular dynamics program. Descriptions of the parallel codes are briefly outlined. Use of these parallel codes has already opened up new capabilities for our research. The very positive performance comparisons with today's supercomputers allow us to conclude that parallel computers and programming, of the type we have considered, represent a pragmatic answer to many computationally intensive problems. (orig.)

  17. Matrix Tricks for Linear Statistical Models

    CERN Document Server

    Puntanen, Simo; Styan, George PH

    2011-01-01

    In teaching linear statistical models to first-year graduate students or to final-year undergraduate students there is no way to proceed smoothly without matrices and related concepts of linear algebra; their use is really essential. Our experience is that making some particular matrix tricks very familiar to students can substantially increase their insight into linear statistical models (and also multivariate statistical analysis). In matrix algebra, there are handy, sometimes even very simple "tricks" which simplify and clarify the treatment of a problem - both for the student and

  18. Modeling techniques for quantum cascade lasers

    Energy Technology Data Exchange (ETDEWEB)

    Jirauschek, Christian [Institute for Nanoelectronics, Technische Universität München, D-80333 Munich (Germany); Kubis, Tillmann [Network for Computational Nanotechnology, Purdue University, 207 S Martin Jischke Drive, West Lafayette, Indiana 47907 (United States)

    2014-03-15

    Quantum cascade lasers are unipolar semiconductor lasers covering a wide range of the infrared and terahertz spectrum. Lasing action is achieved by using optical intersubband transitions between quantized states in specifically designed multiple-quantum-well heterostructures. A systematic improvement of quantum cascade lasers with respect to operating temperature, efficiency, and spectral range requires detailed modeling of the underlying physical processes in these structures. Moreover, the quantum cascade laser constitutes a versatile model device for the development and improvement of simulation techniques in nano- and optoelectronics. This review provides a comprehensive survey and discussion of the modeling techniques used for the simulation of quantum cascade lasers. The main focus is on the modeling of carrier transport in the nanostructured gain medium, while the simulation of the optical cavity is covered at a more basic level. Specifically, the transfer matrix and finite difference methods for solving the one-dimensional Schrödinger equation and Schrödinger-Poisson system are discussed, providing the quantized states in the multiple-quantum-well active region. The modeling of the optical cavity is covered with a focus on basic waveguide resonator structures. Furthermore, various carrier transport simulation methods are discussed, ranging from basic empirical approaches to advanced self-consistent techniques. The methods include empirical rate equation and related Maxwell-Bloch equation approaches, self-consistent rate equation and ensemble Monte Carlo methods, as well as quantum transport approaches, in particular the density matrix and non-equilibrium Green's function formalism. The derived scattering rates and self-energies are generally valid for n-type devices based on one-dimensional quantum confinement, such as quantum well structures.

  19. Modeling techniques for quantum cascade lasers

    Science.gov (United States)

    Jirauschek, Christian; Kubis, Tillmann

    2014-03-01

    Quantum cascade lasers are unipolar semiconductor lasers covering a wide range of the infrared and terahertz spectrum. Lasing action is achieved by using optical intersubband transitions between quantized states in specifically designed multiple-quantum-well heterostructures. A systematic improvement of quantum cascade lasers with respect to operating temperature, efficiency, and spectral range requires detailed modeling of the underlying physical processes in these structures. Moreover, the quantum cascade laser constitutes a versatile model device for the development and improvement of simulation techniques in nano- and optoelectronics. This review provides a comprehensive survey and discussion of the modeling techniques used for the simulation of quantum cascade lasers. The main focus is on the modeling of carrier transport in the nanostructured gain medium, while the simulation of the optical cavity is covered at a more basic level. Specifically, the transfer matrix and finite difference methods for solving the one-dimensional Schrödinger equation and Schrödinger-Poisson system are discussed, providing the quantized states in the multiple-quantum-well active region. The modeling of the optical cavity is covered with a focus on basic waveguide resonator structures. Furthermore, various carrier transport simulation methods are discussed, ranging from basic empirical approaches to advanced self-consistent techniques. The methods include empirical rate equation and related Maxwell-Bloch equation approaches, self-consistent rate equation and ensemble Monte Carlo methods, as well as quantum transport approaches, in particular the density matrix and non-equilibrium Green's function formalism. The derived scattering rates and self-energies are generally valid for n-type devices based on one-dimensional quantum confinement, such as quantum well structures.

  20. Statistical physics of pairwise probability models

    DEFF Research Database (Denmark)

    Roudi, Yasser; Aurell, Erik; Hertz, John

    2009-01-01

    (dansk abstrakt findes ikke) Statistical models for describing the probability distribution over the states of biological systems are commonly used for dimensional reduction. Among these models, pairwise models are very attractive in part because they can be fit using a reasonable amount of  data......: knowledge of the means and correlations between pairs of elements in the system is sufficient. Not surprisingly, then, using pairwise models for studying neural data has been the focus of many studies in recent years. In this paper, we describe how tools from statistical physics can be employed for studying...

  1. Statistical inference with quantum measurements: methodologies for nitrogen vacancy centers in diamond

    Science.gov (United States)

    Hincks, Ian; Granade, Christopher; Cory, David G.

    2018-01-01

    The analysis of photon count data from the standard nitrogen vacancy (NV) measurement process is treated as a statistical inference problem. This has applications toward gaining better and more rigorous error bars for tasks such as parameter estimation (e.g. magnetometry), tomography, and randomized benchmarking. We start by providing a summary of the standard phenomenological model of the NV optical process in terms of Lindblad jump operators. This model is used to derive random variables describing emitted photons during measurement, to which finite visibility, dark counts, and imperfect state preparation are added. NV spin-state measurement is then stated as an abstract statistical inference problem consisting of an underlying biased coin obstructed by three Poisson rates. Relevant frequentist and Bayesian estimators are provided, discussed, and quantitatively compared. We show numerically that the risk of the maximum likelihood estimator is well approximated by the Cramér-Rao bound, for which we provide a simple formula. Of the estimators, we in particular promote the Bayes estimator, owing to its slightly better risk performance, and straightforward error propagation into more complex experiments. This is illustrated on experimental data, where quantum Hamiltonian learning is performed and cross-validated in a fully Bayesian setting, and compared to a more traditional weighted least squares fit.

  2. Distributions with given marginals and statistical modelling

    CERN Document Server

    Fortiana, Josep; Rodriguez-Lallena, José

    2002-01-01

    This book contains a selection of the papers presented at the meeting `Distributions with given marginals and statistical modelling', held in Barcelona (Spain), July 17-20, 2000. In 24 chapters, this book covers topics such as the theory of copulas and quasi-copulas, the theory and compatibility of distributions, models for survival distributions and other well-known distributions, time series, categorical models, definition and estimation of measures of dependence, monotonicity and stochastic ordering, shape and separability of distributions, hidden truncation models, diagonal families, orthogonal expansions, tests of independence, and goodness of fit assessment. These topics share the use and properties of distributions with given marginals, this being the fourth specialised text on this theme. The innovative aspect of the book is the inclusion of statistical aspects such as modelling, Bayesian statistics, estimation, and tests.

  3. Aspects of statistical model for multifragmentation

    International Nuclear Information System (INIS)

    Bhattacharyya, P.; Das Gupta, S.; Mekjian, A. Z.

    1999-01-01

    We deal with two different aspects of an exactly soluble statistical model of fragmentation. First we show, using zero range force and finite temperature Thomas-Fermi theory, that a common link can be found between finite temperature mean field theory and the statistical fragmentation model. We show the latter naturally arises in the spinodal region. Next we show that although the exact statistical model is a canonical model and uses temperature, microcanonical results which use constant energy rather than constant temperature can also be obtained from the canonical model using saddle-point approximation. The methodology is extremely simple to implement and at least in all the examples studied in this work is very accurate. (c) 1999 The American Physical Society

  4. Probing the exchange statistics of one-dimensional anyon models

    Science.gov (United States)

    Greschner, Sebastian; Cardarelli, Lorenzo; Santos, Luis

    2018-05-01

    We propose feasible scenarios for revealing the modified exchange statistics in one-dimensional anyon models in optical lattices based on an extension of the multicolor lattice-depth modulation scheme introduced in [Phys. Rev. A 94, 023615 (2016), 10.1103/PhysRevA.94.023615]. We show that the fast modulation of a two-component fermionic lattice gas in the presence a magnetic field gradient, in combination with additional resonant microwave fields, allows for the quantum simulation of hardcore anyon models with periodic boundary conditions. Such a semisynthetic ring setup allows for realizing an interferometric arrangement sensitive to the anyonic statistics. Moreover, we show as well that simple expansion experiments may reveal the formation of anomalously bound pairs resulting from the anyonic exchange.

  5. Quantum mechanics model on a Kaehler conifold

    International Nuclear Information System (INIS)

    Bellucci, Stefano; Nersessian, Armen; Yeranyan, Armen

    2004-01-01

    We propose an exactly solvable model of the quantum oscillator on the class of Kaehler spaces (with conic singularities), connected with two-dimensional complex projective spaces. Its energy spectrum is nondegenerate in the orbital quantum number, when the space has nonconstant curvature. We reduce the model to a three-dimensional system interacting with the Dirac monopole. Owing to noncommutativity of the reduction and quantization procedures, the Hamiltonian of the reduced system gets nontrivial quantum corrections. We transform the reduced system into a MIC-Kepler-like one and find that quantum corrections arise only in its energy and coupling constant. We present the exact spectrum of the generalized MIC-Kepler system. The one-(complex) dimensional analog of the suggested model is formulated on the Riemann surface over the complex projective plane and could be interpreted as a system with fractional spin

  6. Two point function for a simple general relativistic quantum model

    OpenAIRE

    Colosi, Daniele

    2007-01-01

    We study the quantum theory of a simple general relativistic quantum model of two coupled harmonic oscillators and compute the two-point function following a proposal first introduced in the context of loop quantum gravity.

  7. Statistical Compression for Climate Model Output

    Science.gov (United States)

    Hammerling, D.; Guinness, J.; Soh, Y. J.

    2017-12-01

    Numerical climate model simulations run at high spatial and temporal resolutions generate massive quantities of data. As our computing capabilities continue to increase, storing all of the data is not sustainable, and thus is it important to develop methods for representing the full datasets by smaller compressed versions. We propose a statistical compression and decompression algorithm based on storing a set of summary statistics as well as a statistical model describing the conditional distribution of the full dataset given the summary statistics. We decompress the data by computing conditional expectations and conditional simulations from the model given the summary statistics. Conditional expectations represent our best estimate of the original data but are subject to oversmoothing in space and time. Conditional simulations introduce realistic small-scale noise so that the decompressed fields are neither too smooth nor too rough compared with the original data. Considerable attention is paid to accurately modeling the original dataset-one year of daily mean temperature data-particularly with regard to the inherent spatial nonstationarity in global fields, and to determining the statistics to be stored, so that the variation in the original data can be closely captured, while allowing for fast decompression and conditional emulation on modest computers.

  8. Structural characterization and condition for measurement statistics preservation of a unital quantum operation

    International Nuclear Information System (INIS)

    Lee, Kai-Yan; Fung, Chi-Hang Fred; Chau, H F

    2013-01-01

    We investigate the necessary and sufficient condition for a convex cone of positive semidefinite operators to be fixed by a unital quantum operation ϕ acting on finite-dimensional quantum states. By reducing this problem to the problem of simultaneous diagonalization of the Kraus operators associated with ϕ, we can completely characterize the kinds of quantum states that are fixed by ϕ. Our work has several applications. It gives a simple proof of the structural characterization of a unital quantum operation that acts on finite-dimensional quantum states—a result not explicitly mentioned in earlier studies. It also provides a necessary and sufficient condition for determining what kind of measurement statistics is preserved by a unital quantum operation. Finally, our result clarifies and extends the work of Størmer by giving a proof of a reduction theorem on the unassisted and entanglement-assisted classical capacities, coherent information, and minimal output Renyi entropy of a unital channel acting on a finite-dimensional quantum state. (paper)

  9. Exactly solvable models of 2D-quantum gravity on the lattice. Course 5

    International Nuclear Information System (INIS)

    Kazakov, V.A.

    1990-01-01

    It is shown that statistical mechanical models defined on randomly triangulated surfaces can be solved exactly and that thereby the results on 2-D quantum gravity can be confirmed. (author). 32 refs.; 4 figs.; 2 tabs

  10. Quantum billiards in multidimensional models with branes

    Energy Technology Data Exchange (ETDEWEB)

    Ivashchuk, V.D.; Melnikov, V.N. [VNIIMS, Center for Gravitation and Fundamental Metrology, Moscow (Russian Federation); Peoples' Friendship University of Russia, Institute of Gravitation and Cosmology, Moscow (Russian Federation)

    2014-03-15

    gravitational D-dimensional model with l scalar fields and several forms is considered. When a cosmological-type diagonal metric is chosen, an electromagnetic composite brane ansatz is adopted and certain restrictions on the branes are imposed; the conformally covariant Wheeler-DeWitt (WDW) equation for the model is studied. Under certain restrictions asymptotic solutions to WDW equation are found in the limit of the formation of the billiard walls which reduce the problem to the so-called quantum billiard on the (D+l-2)-dimensional Lobachevsky space. Two examples of quantum billiards are considered. The first one deals with 9-dimensional quantum billiard for D = 11 model with 330 four-forms which mimic space-like M2- and M5-branes of D = 11 supergravity. The second one deals with the 9-dimensional quantum billiard for D = 10 gravitational model with one scalar field, 210 four-forms and 120 three-forms which mimic space-like D2-, D4-, FS1- and NS5-branes in D = 10 IIA supergravity. It is shown that in both examples wave functions vanish in the limit of the formation of the billiard walls (i.e. we get a quantum resolution of the singularity for 11D model) but magnetic branes could not be neglected in calculations of quantum asymptotic solutions while they are irrelevant for classical oscillating behavior when all 120 electric branes are present. (orig.)

  11. A new quantum statistical evaluation method for time correlation functions

    International Nuclear Information System (INIS)

    Loss, D.; Schoeller, H.

    1989-01-01

    Considering a system of N identical interacting particles, which obey Fermi-Dirac or Bose-Einstein statistics, the authors derive new formulas for correlation functions of the type C(t) = i= 1 N A i (t) Σ j=1 N B j > (where B j is diagonal in the free-particle states) in the thermodynamic limit. Thereby they apply and extend a superoperator formalism, recently developed for the derivation of long-time tails in semiclassical systems. As an illustrative application, the Boltzmann equation value of the time-integrated correlation function C(t) is derived in a straight-forward manner. Due to exchange effects, the obtained t-matrix and the resulting scattering cross section, which occurs in the Boltzmann collision operator, are now functionals of the Fermi-Dirac or Bose-Einstein distribution

  12. Performance modeling, loss networks, and statistical multiplexing

    CERN Document Server

    Mazumdar, Ravi

    2009-01-01

    This monograph presents a concise mathematical approach for modeling and analyzing the performance of communication networks with the aim of understanding the phenomenon of statistical multiplexing. The novelty of the monograph is the fresh approach and insights provided by a sample-path methodology for queueing models that highlights the important ideas of Palm distributions associated with traffic models and their role in performance measures. Also presented are recent ideas of large buffer, and many sources asymptotics that play an important role in understanding statistical multiplexing. I

  13. Simple statistical model for branched aggregates

    DEFF Research Database (Denmark)

    Lemarchand, Claire; Hansen, Jesper Schmidt

    2015-01-01

    , given that it already has bonds with others. The model is applied here to asphaltene nanoaggregates observed in molecular dynamics simulations of Cooee bitumen. The variation with temperature of the probabilities deduced from this model is discussed in terms of statistical mechanics arguments....... The relevance of the statistical model in the case of asphaltene nanoaggregates is checked by comparing the predicted value of the probability for one molecule to have exactly i bonds with the same probability directly measured in the molecular dynamics simulations. The agreement is satisfactory......We propose a statistical model that can reproduce the size distribution of any branched aggregate, including amylopectin, dendrimers, molecular clusters of monoalcohols, and asphaltene nanoaggregates. It is based on the conditional probability for one molecule to form a new bond with a molecule...

  14. Advances in statistical models for data analysis

    CERN Document Server

    Minerva, Tommaso; Vichi, Maurizio

    2015-01-01

    This edited volume focuses on recent research results in classification, multivariate statistics and machine learning and highlights advances in statistical models for data analysis. The volume provides both methodological developments and contributions to a wide range of application areas such as economics, marketing, education, social sciences and environment. The papers in this volume were first presented at the 9th biannual meeting of the Classification and Data Analysis Group (CLADAG) of the Italian Statistical Society, held in September 2013 at the University of Modena and Reggio Emilia, Italy.

  15. New Spin Foam Models of Quantum Gravity

    Science.gov (United States)

    Miković, A.

    We give a brief and a critical review of the Barret-Crane spin foam models of quantum gravity. Then we describe two new spin foam models which are obtained by direct quantization of General Relativity and do not have some of the drawbacks of the Barret-Crane models. These are the model of spin foam invariants for the embedded spin networks in loop quantum gravity and the spin foam model based on the integration of the tetrads in the path integral for the Palatini action.

  16. Structured statistical models of inductive reasoning.

    Science.gov (United States)

    Kemp, Charles; Tenenbaum, Joshua B

    2009-01-01

    Everyday inductive inferences are often guided by rich background knowledge. Formal models of induction should aim to incorporate this knowledge and should explain how different kinds of knowledge lead to the distinctive patterns of reasoning found in different inductive contexts. This article presents a Bayesian framework that attempts to meet both goals and describes [corrected] 4 applications of the framework: a taxonomic model, a spatial model, a threshold model, and a causal model. Each model makes probabilistic inferences about the extensions of novel properties, but the priors for the 4 models are defined over different kinds of structures that capture different relationships between the categories in a domain. The framework therefore shows how statistical inference can operate over structured background knowledge, and the authors argue that this interaction between structure and statistics is critical for explaining the power and flexibility of human reasoning.

  17. Model for neural signaling leap statistics

    International Nuclear Information System (INIS)

    Chevrollier, Martine; Oria, Marcos

    2011-01-01

    We present a simple model for neural signaling leaps in the brain considering only the thermodynamic (Nernst) potential in neuron cells and brain temperature. We numerically simulated connections between arbitrarily localized neurons and analyzed the frequency distribution of the distances reached. We observed qualitative change between Normal statistics (with T 37.5 0 C, awaken regime) and Levy statistics (T = 35.5 0 C, sleeping period), characterized by rare events of long range connections.

  18. Statistical models based on conditional probability distributions

    International Nuclear Information System (INIS)

    Narayanan, R.S.

    1991-10-01

    We present a formulation of statistical mechanics models based on conditional probability distribution rather than a Hamiltonian. We show that it is possible to realize critical phenomena through this procedure. Closely linked with this formulation is a Monte Carlo algorithm, in which a configuration generated is guaranteed to be statistically independent from any other configuration for all values of the parameters, in particular near the critical point. (orig.)

  19. Model for neural signaling leap statistics

    Science.gov (United States)

    Chevrollier, Martine; Oriá, Marcos

    2011-03-01

    We present a simple model for neural signaling leaps in the brain considering only the thermodynamic (Nernst) potential in neuron cells and brain temperature. We numerically simulated connections between arbitrarily localized neurons and analyzed the frequency distribution of the distances reached. We observed qualitative change between Normal statistics (with T = 37.5°C, awaken regime) and Lévy statistics (T = 35.5°C, sleeping period), characterized by rare events of long range connections.

  20. Model for neural signaling leap statistics

    Energy Technology Data Exchange (ETDEWEB)

    Chevrollier, Martine; Oria, Marcos, E-mail: oria@otica.ufpb.br [Laboratorio de Fisica Atomica e Lasers Departamento de Fisica, Universidade Federal da ParaIba Caixa Postal 5086 58051-900 Joao Pessoa, Paraiba (Brazil)

    2011-03-01

    We present a simple model for neural signaling leaps in the brain considering only the thermodynamic (Nernst) potential in neuron cells and brain temperature. We numerically simulated connections between arbitrarily localized neurons and analyzed the frequency distribution of the distances reached. We observed qualitative change between Normal statistics (with T 37.5{sup 0}C, awaken regime) and Levy statistics (T = 35.5{sup 0}C, sleeping period), characterized by rare events of long range connections.

  1. Modeling experiments using quantum and Kolmogorov probability

    International Nuclear Information System (INIS)

    Hess, Karl

    2008-01-01

    Criteria are presented that permit a straightforward partition of experiments into sets that can be modeled using both quantum probability and the classical probability framework of Kolmogorov. These new criteria concentrate on the operational aspects of the experiments and lead beyond the commonly appreciated partition by relating experiments to commuting and non-commuting quantum operators as well as non-entangled and entangled wavefunctions. In other words the space of experiments that can be understood using classical probability is larger than usually assumed. This knowledge provides advantages for areas such as nanoscience and engineering or quantum computation.

  2. Quantum protocols within Spekkens' toy model

    Science.gov (United States)

    Disilvestro, Leonardo; Markham, Damian

    2017-05-01

    Quantum mechanics is known to provide significant improvements in information processing tasks when compared to classical models. These advantages range from computational speedups to security improvements. A key question is where these advantages come from. The toy model developed by Spekkens [R. W. Spekkens, Phys. Rev. A 75, 032110 (2007), 10.1103/PhysRevA.75.032110] mimics many of the features of quantum mechanics, such as entanglement and no cloning, regarded as being important in this regard, despite being a local hidden variable theory. In this work, we study several protocols within Spekkens' toy model where we see it can also mimic the advantages and limitations shown in the quantum case. We first provide explicit proofs for the impossibility of toy bit commitment and the existence of a toy error correction protocol and consequent k -threshold secret sharing. Then, defining a toy computational model based on the quantum one-way computer, we prove the existence of blind and verified protocols. Importantly, these two last quantum protocols are known to achieve a better-than-classical security. Our results suggest that such quantum improvements need not arise from any Bell-type nonlocality or contextuality, but rather as a consequence of steering correlations.

  3. Quantum statistics of stimulated Raman and hyper-Raman scattering by master equation approach

    International Nuclear Information System (INIS)

    Gupta, P.S.; Dash, J.

    1991-01-01

    A quantum theoretical density matrix formalism of stimulated Raman and hyper-Raman scattering using master equation approach is presented. The atomic system is described by two energy levels. The effects of upper level population and the cavity loss are incorporated. The photon statistics, coherence characteristics and the building up of the Stokes field are investigated. (author). 8 figs., 5 refs

  4. An introduction to conformal invariance in quantum field theory and statistical mechanics

    International Nuclear Information System (INIS)

    Boyanovsky, D.; Naon, C.M.

    1990-01-01

    The subject of conformal invariance provides an extraordinarly successful and productive symbiosis between statistical mechanics and quantum field theory. The main goal of this paper, which is tailored to a wide audience, is to give an introduction to such vast subject (C.P.)

  5. Remarks on the choice of trial hamiltonians for the quantum statistical treatment of anharmonic systems

    International Nuclear Information System (INIS)

    Tsallis, C.; Valle, J.W.F.

    1979-01-01

    The use of the Variational Method to discuss Quantum Statistical Mechanics of anharmonic systems requires, in order to be able to obtain the correct classical limit, the allowance for renormalization of every operator whose definition depends on the harmonic coefficients. The point is exhibited for a single anharmonic oscillator. In this particular case there is no need for mass renormalization. (Author) [pt

  6. Quantum Statistical Mechanics, L-Series and Anabelian Geometry I: Partition Functions

    NARCIS (Netherlands)

    Marcolli, Matilde; Cornelissen, Gunther

    2014-01-01

    The zeta function of a number field can be interpreted as the partition function of an associated quantum statistical mechanical (QSM) system, built from abelian class field theory. We introduce a general notion of isomorphism of QSM-systems and prove that it preserves (extremal) KMS equilibrium

  7. Decoy-state quantum key distribution with both source errors and statistical fluctuations

    International Nuclear Information System (INIS)

    Wang Xiangbin; Yang Lin; Peng Chengzhi; Pan Jianwei

    2009-01-01

    We show how to calculate the fraction of single-photon counts of the 3-intensity decoy-state quantum cryptography faithfully with both statistical fluctuations and source errors. Our results rely only on the bound values of a few parameters of the states of pulses.

  8. A reciprocal of Coleman's theorem and the quantum statistics of systems with spontaneous symmetry breaking

    International Nuclear Information System (INIS)

    Chaichian, M.; Montonen, C.; Perez Rojas, H.

    1991-01-01

    The completely different conservation properties of charges associated to unbroken and broken symmetries are discussed. The impossibility of establishing a conservation law for nondegenerate Hilbert space representations in the broken case leads to a reciprocal of Coleman's theorem. The quantum statistical implication is that these charges cannot be introduced as conserved operators in the density matrix. (orig.)

  9. Numerical solutions of ideal quantum gas dynamical flows governed by semiclassical ellipsoidal-statistical distribution.

    Science.gov (United States)

    Yang, Jaw-Yen; Yan, Chih-Yuan; Diaz, Manuel; Huang, Juan-Chen; Li, Zhihui; Zhang, Hanxin

    2014-01-08

    The ideal quantum gas dynamics as manifested by the semiclassical ellipsoidal-statistical (ES) equilibrium distribution derived in Wu et al. (Wu et al . 2012 Proc. R. Soc. A 468 , 1799-1823 (doi:10.1098/rspa.2011.0673)) is numerically studied for particles of three statistics. This anisotropic ES equilibrium distribution was derived using the maximum entropy principle and conserves the mass, momentum and energy, but differs from the standard Fermi-Dirac or Bose-Einstein distribution. The present numerical method combines the discrete velocity (or momentum) ordinate method in momentum space and the high-resolution shock-capturing method in physical space. A decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. Computations of two-dimensional Riemann problems are presented, and various contours of the quantities unique to this ES model are illustrated. The main flow features, such as shock waves, expansion waves and slip lines and their complex nonlinear interactions, are depicted and found to be consistent with existing calculations for a classical gas.

  10. Numerical solutions of ideal quantum gas dynamical flows governed by semiclassical ellipsoidal-statistical distribution

    Science.gov (United States)

    Yang, Jaw-Yen; Yan, Chih-Yuan; Diaz, Manuel; Huang, Juan-Chen; Li, Zhihui; Zhang, Hanxin

    2014-01-01

    The ideal quantum gas dynamics as manifested by the semiclassical ellipsoidal-statistical (ES) equilibrium distribution derived in Wu et al. (Wu et al. 2012 Proc. R. Soc. A 468, 1799–1823 (doi:10.1098/rspa.2011.0673)) is numerically studied for particles of three statistics. This anisotropic ES equilibrium distribution was derived using the maximum entropy principle and conserves the mass, momentum and energy, but differs from the standard Fermi–Dirac or Bose–Einstein distribution. The present numerical method combines the discrete velocity (or momentum) ordinate method in momentum space and the high-resolution shock-capturing method in physical space. A decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. Computations of two-dimensional Riemann problems are presented, and various contours of the quantities unique to this ES model are illustrated. The main flow features, such as shock waves, expansion waves and slip lines and their complex nonlinear interactions, are depicted and found to be consistent with existing calculations for a classical gas. PMID:24399919

  11. Growth curve models and statistical diagnostics

    CERN Document Server

    Pan, Jian-Xin

    2002-01-01

    Growth-curve models are generalized multivariate analysis-of-variance models. These models are especially useful for investigating growth problems on short times in economics, biology, medical research, and epidemiology. This book systematically introduces the theory of the GCM with particular emphasis on their multivariate statistical diagnostics, which are based mainly on recent developments made by the authors and their collaborators. The authors provide complete proofs of theorems as well as practical data sets and MATLAB code.

  12. Topology for Statistical Modeling of Petascale Data

    Energy Technology Data Exchange (ETDEWEB)

    Pascucci, Valerio [Univ. of Utah, Salt Lake City, UT (United States); Levine, Joshua [Univ. of Utah, Salt Lake City, UT (United States); Gyulassy, Attila [Univ. of Utah, Salt Lake City, UT (United States); Bremer, P. -T. [Univ. of Utah, Salt Lake City, UT (United States)

    2013-10-31

    Many commonly used algorithms for mathematical analysis do not scale well enough to accommodate the size or complexity of petascale data produced by computational simulations. The primary goal of this project is to develop new mathematical tools that address both the petascale size and uncertain nature of current data. At a high level, the approach of the entire team involving all three institutions is based on the complementary techniques of combinatorial topology and statistical modelling. In particular, we use combinatorial topology to filter out spurious data that would otherwise skew statistical modelling techniques, and we employ advanced algorithms from algebraic statistics to efficiently find globally optimal fits to statistical models. The overall technical contributions can be divided loosely into three categories: (1) advances in the field of combinatorial topology, (2) advances in statistical modelling, and (3) new integrated topological and statistical methods. Roughly speaking, the division of labor between our 3 groups (Sandia Labs in Livermore, Texas A&M in College Station, and U Utah in Salt Lake City) is as follows: the Sandia group focuses on statistical methods and their formulation in algebraic terms, and finds the application problems (and data sets) most relevant to this project, the Texas A&M Group develops new algebraic geometry algorithms, in particular with fewnomial theory, and the Utah group develops new algorithms in computational topology via Discrete Morse Theory. However, we hasten to point out that our three groups stay in tight contact via videconference every 2 weeks, so there is much synergy of ideas between the groups. The following of this document is focused on the contributions that had grater direct involvement from the team at the University of Utah in Salt Lake City.

  13. Quantum mechanical analysis on faujasite-type molecular sieves by using fermi dirac statistics and quantum theory of dielectricity

    International Nuclear Information System (INIS)

    Jabeen, S.; Raza, S.M.; Ahmed, M.A.; Zai, M.Y.; Akbar, S.; Jafri, Y.Z.

    2012-01-01

    We studied Faujasite type molecular sieves by using Fermi Dirac statistics and the quantum theory of dielectricity. We developed an empirical relationship for quantum capacitance which follows an inverse Gaussian profile in the frequency range of 66 Hz - 3 MHz. We calculated quantum capacitance, sample crystal momentum, charge quantization and quantized energy of Faujasite type molecular sieves in the frequency range of 0.1 Hz - 10/sup 4/ MHz. Our calculations for diameter of sodalite and super-cages of Faujasite type molecular sieves are in agreement with experimental results reported in this manuscript. We also calculated quantum polarizability, quantized molecular field, orientational polarizability and deformation polarizability by using experimental results of Ligia Frunza etal. The phonons are over damped in the frequency range 0.1 Hz - 10 kHz and become a source for producing cages in the Faujasite type molecular sieves. Ion exchange recovery processes occur due to over damped phonon excitations in Faujasite type molecular sieves and with increasing temperatures. (author)

  14. Completeness of classical spin models and universal quantum computation

    International Nuclear Information System (INIS)

    De las Cuevas, Gemma; Dür, Wolfgang; Briegel, Hans J; Van den Nest, Maarten

    2009-01-01

    We study mappings between different classical spin systems that leave the partition function invariant. As recently shown in Van den Nest et al (2008 Phys. Rev. Lett. 100 110501), the partition function of the 2D square lattice Ising model in the presence of an inhomogeneous magnetic field can specialize to the partition function of any Ising system on an arbitrary graph. In this sense the 2D Ising model is said to be 'complete'. However, in order to obtain the above result, the coupling strengths on the 2D lattice must assume complex values, and thus do not allow for a physical interpretation. Here we show how a complete model with real—and, hence, 'physical'—couplings can be obtained if the 3D Ising model is considered. We furthermore show how to map general q-state systems with possibly many-body interactions to the 2D Ising model with complex parameters, and give completeness results for these models with real parameters. We also demonstrate that the computational overhead in these constructions is in all relevant cases polynomial. These results are proved by invoking a recently found cross-connection between statistical mechanics and quantum information theory, where partition functions are expressed as quantum mechanical amplitudes. Within this framework, there exists a natural correspondence between many-body quantum states that allow for universal quantum computation via local measurements only, and complete classical spin systems

  15. Modelling of multidimensional quantum systems by the numerical functional integration

    International Nuclear Information System (INIS)

    Lobanov, Yu.Yu.; Zhidkov, E.P.

    1990-01-01

    The employment of the numerical functional integration for the description of multidimensional systems in quantum and statistical physics is considered. For the multiple functional integrals with respect to Gaussian measures in the full separable metric spaces the new approximation formulas exact on a class of polynomial functionals of a given summary degree are constructed. The use of the formulas is demonstrated on example of computation of the Green function and the ground state energy in multidimensional Calogero model. 15 refs.; 2 tabs

  16. Bayesian models a statistical primer for ecologists

    CERN Document Server

    Hobbs, N Thompson

    2015-01-01

    Bayesian modeling has become an indispensable tool for ecological research because it is uniquely suited to deal with complexity in a statistically coherent way. This textbook provides a comprehensive and accessible introduction to the latest Bayesian methods-in language ecologists can understand. Unlike other books on the subject, this one emphasizes the principles behind the computations, giving ecologists a big-picture understanding of how to implement this powerful statistical approach. Bayesian Models is an essential primer for non-statisticians. It begins with a definition of probabili

  17. Quantum chromodynamics, chiral symmetry and bag models

    International Nuclear Information System (INIS)

    Soyeur, M.

    1983-08-01

    This course deals with the following subjects: quarks; quantum chromodynamics (the classical Lagrangian of QCD, quark masses, the classical equations of motion of QCD, general properties, lattices); chiral symmetry (massless free Dirac theory, realizations, the σ-model); the M.I.T. bag model (basic assumptions and equations of motion, spherical cavity approximation, properties of hadrons); the chiral bag models (basic assumptions, the cloudy bag model, the little bag model); non-topological soliton bag models

  18. On the role of complex phases in the quantum statistics of weak measurements

    International Nuclear Information System (INIS)

    Hofmann, Holger F

    2011-01-01

    Weak measurements carried out between quantum state preparation and post-selection result in complex values for self-adjoint operators, corresponding to complex conditional probabilities for the projections on specific eigenstates. In this paper it is shown that the complex phases of these weak conditional probabilities describe the dynamic response of the system to unitary transformations. Quantum mechanics thus unifies the statistical overlap of different states with the dynamical structure of transformations between these states. Specifically, it is possible to identify the phase of weak conditional probabilities directly with the action of a unitary transform that maximizes the overlap of initial and final states. This action provides a quantitative measure of how much quantum correlations can diverge from the deterministic relations between physical properties expected from classical physics or hidden variable theories. In terms of quantum information, the phases of weak conditional probabilities thus represent the logical tension between sets of three quantum states that is at the heart of quantum paradoxes. (paper)

  19. Quantum statistical entropy for Kerr-de Sitter black hole

    Institute of Scientific and Technical Information of China (English)

    Zhang Li-Chun; Wu Yue-Qin; Zhao Ren

    2004-01-01

    Improving the membrane model by which the entropy of the black hole is studied, we study the entropy of the black hole in the non-thermal equilibrium state. To give the problem stated here widespread meaning, we discuss the (n+2)-dimensional de Sitter spacetime. Through discussion, we obtain that the black hole's entropy which contains two horizons (a black hole's horizon and a cosmological horizon) in the non-thermal equilibrium state comprises the entropy corresponding to the black hole's horizon and the entropy corresponding to the cosmological horizon. Furthermore, the entropy of the black hole is a natural property of the black hole. The entropy is irrelevant to the radiation field out of the horizon. This deepens the understanding of the relationship between black hole's entropy and horizon's area. A way to study the bosonic and fermionic entropy of the black hole in high non-thermal equilibrium spacetime is given.

  20. Models of Quantum Space Time: Quantum Field Planes

    OpenAIRE

    Mack, G.; Schomerus, V.

    1994-01-01

    Quantum field planes furnish a noncommutative differential algebra $\\Omega$ which substitutes for the commutative algebra of functions and forms on a contractible manifold. The data required in their construction come from a quantum field theory. The basic idea is to replace the ground field ${\\bf C}$ of quantum planes by the noncommutative algebra ${\\cal A}$ of observables of the quantum field theory.

  1. Quantum field theory and the standard model

    CERN Document Server

    Schwartz, Matthew D

    2014-01-01

    Providing a comprehensive introduction to quantum field theory, this textbook covers the development of particle physics from its foundations to the discovery of the Higgs boson. Its combination of clear physical explanations, with direct connections to experimental data, and mathematical rigor make the subject accessible to students with a wide variety of backgrounds and interests. Assuming only an undergraduate-level understanding of quantum mechanics, the book steadily develops the Standard Model and state-of-the-art calculation techniques. It includes multiple derivations of many important results, with modern methods such as effective field theory and the renormalization group playing a prominent role. Numerous worked examples and end-of-chapter problems enable students to reproduce classic results and to master quantum field theory as it is used today. Based on a course taught by the author over many years, this book is ideal for an introductory to advanced quantum field theory sequence or for independe...

  2. Projected Dipole Model for Quantum Plasmonics

    DEFF Research Database (Denmark)

    Yan, Wei; Wubs, Martijn; Mortensen, N. Asger

    2015-01-01

    of classical electrodynamics, while quantum properties are described accurately through an infinitely thin layer of dipoles oriented normally to the metal surface. The nonlocal polarizability of the dipole layer-the only introduced parameter-is mapped from the free-electron distribution near the metal surface...... as obtained with 1D quantum calculations, such as time-dependent density-functional theory (TDDFT), and is determined once and for all. The model can be applied in two and three dimensions to any system size that is tractable within classical electrodynamics, while capturing quantum plasmonic aspects......Quantum effects of plasmonic phenomena have been explored through ab initio studies, but only for exceedingly small metallic nanostructures, leaving most experimentally relevant structures too large to handle. We propose instead an effective description with the computationally appealing features...

  3. STATISTICAL MODELS OF REPRESENTING INTELLECTUAL CAPITAL

    Directory of Open Access Journals (Sweden)

    Andreea Feraru

    2016-06-01

    Full Text Available This article entitled Statistical Models of Representing Intellectual Capital approaches and analyses the concept of intellectual capital, as well as the main models which can support enterprisers/managers in evaluating and quantifying the advantages of intellectual capital. Most authors examine intellectual capital from a static perspective and focus on the development of its various evaluation models. In this chapter we surveyed the classical static models: Sveiby, Edvisson, Balanced Scorecard, as well as the canonical model of intellectual capital. Among the group of static models for evaluating organisational intellectual capital the canonical model stands out. This model enables the structuring of organisational intellectual capital in: human capital, structural capital and relational capital. Although the model is widely spread, it is a static one and can thus create a series of errors in the process of evaluation, because all the three entities mentioned above are not independent from the viewpoint of their contents, as any logic of structuring complex entities requires.

  4. Effects of quantum statistics in cold-atom gases

    International Nuclear Information System (INIS)

    Villain, Pierre

    2000-01-01

    The first part of this research thesis recalls the main properties of Bose-Einstein condensates as they have been experimentally produced since 1995 in diluted alkaline gases and as they have been magnetically trapped. The author discusses the standard theoretical approach of Bogoliubov which relies on an hypothesis of symmetry breakage. Then, the author addresses the dynamic consequences of this hypothesis, in particularly on the existence of a condensate phase jamming which results in a loss of coherence properties for the system. The third part addresses the dynamic study of a condensate within a pattern-type potential. A numerical integration of the Gross-Pitaevskii equation is performed. Through variations of the non-linear parameter (which expresses interactions between atoms), the influence of non-linearities on the system behaviour is analysed. Notably, the author shows how, by increasing this parameter, the macroscopic wave function passes from a regular dynamics to a stochastic dynamics. In the fourth part, the author reports the modelling of an experiment of mixing with five waves within the context of matter waves. He shows how to adapt this experiment for fermions/bosons mixing where an incident fermion wave is sent towards a network of condensed bosons [fr

  5. Reason of method of density functional in classical and quantum statistical mechanisms

    International Nuclear Information System (INIS)

    Dinariev, O.Yu.

    2000-01-01

    Interaction between phenomenological description of a multi-component mixture on the basis of entropy functional with members, square in terms of component density gradients and temperature, on the one hand, and description in the framework of classical and quantum statistical mechanics, on the other hand, was investigated. Explicit expressions for the entropy functional in the classical and quantum theory were derived. Then a square approximation for the case of minor disturbances of uniform state was calculated. In the approximation the addends square in reference to the gradient were singlet out. It permits calculation of the relevant phenomenological coefficients from the leading principles [ru

  6. Non-extensive statistical mechanics and black hole entropy from quantum geometry

    Directory of Open Access Journals (Sweden)

    Abhishek Majhi

    2017-12-01

    Full Text Available Using non-extensive statistical mechanics, the Bekenstein–Hawking area law is obtained from microstates of black holes in loop quantum gravity, for arbitrary real positive values of the Barbero–Immirzi parameter (γ. The arbitrariness of γ is encoded in the strength of the “bias” created in the horizon microstates through the coupling with the quantum geometric fields exterior to the horizon. An experimental determination of γ will fix this coupling, leaving out the macroscopic area of the black hole to be the only free quantity of the theory.

  7. (ajst) statistical mechanics model for orientational

    African Journals Online (AJOL)

    Science and Engineering Series Vol. 6, No. 2, pp. 94 - 101. STATISTICAL MECHANICS MODEL FOR ORIENTATIONAL. MOTION OF TWO-DIMENSIONAL RIGID ROTATOR. Malo, J.O. ... there is no translational motion and that they are well separated so .... constant and I is the moment of inertia of a linear rotator. Thus, the ...

  8. Statistical Model Checking for Biological Systems

    DEFF Research Database (Denmark)

    David, Alexandre; Larsen, Kim Guldstrand; Legay, Axel

    2014-01-01

    Statistical Model Checking (SMC) is a highly scalable simulation-based verification approach for testing and estimating the probability that a stochastic system satisfies a given linear temporal property. The technique has been applied to (discrete and continuous time) Markov chains, stochastic...

  9. Topology for Statistical Modeling of Petascale Data

    Energy Technology Data Exchange (ETDEWEB)

    Bennett, Janine Camille [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Pebay, Philippe Pierre [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Pascucci, Valerio [Univ. of Utah, Salt Lake City, UT (United States); Levine, Joshua [Univ. of Utah, Salt Lake City, UT (United States); Gyulassy, Attila [Univ. of Utah, Salt Lake City, UT (United States); Rojas, Maurice [Texas A & M Univ., College Station, TX (United States)

    2014-07-01

    This document presents current technical progress and dissemination of results for the Mathematics for Analysis of Petascale Data (MAPD) project titled "Topology for Statistical Modeling of Petascale Data", funded by the Office of Science Advanced Scientific Computing Research (ASCR) Applied Math program.

  10. Establishing statistical models of manufacturing parameters

    International Nuclear Information System (INIS)

    Senevat, J.; Pape, J.L.; Deshayes, J.F.

    1991-01-01

    This paper reports on the effect of pilgering and cold-work parameters on contractile strain ratio and mechanical properties that were investigated using a large population of Zircaloy tubes. Statistical models were established between: contractile strain ratio and tooling parameters, mechanical properties (tensile test, creep test) and cold-work parameters, and mechanical properties and stress-relieving temperature

  11. Statistical models for optimizing mineral exploration

    International Nuclear Information System (INIS)

    Wignall, T.K.; DeGeoffroy, J.

    1987-01-01

    The primary purpose of mineral exploration is to discover ore deposits. The emphasis of this volume is on the mathematical and computational aspects of optimizing mineral exploration. The seven chapters that make up the main body of the book are devoted to the description and application of various types of computerized geomathematical models. These chapters include: (1) the optimal selection of ore deposit types and regions of search, as well as prospecting selected areas, (2) designing airborne and ground field programs for the optimal coverage of prospecting areas, and (3) delineating and evaluating exploration targets within prospecting areas by means of statistical modeling. Many of these statistical programs are innovative and are designed to be useful for mineral exploration modeling. Examples of geomathematical models are applied to exploring for six main types of base and precious metal deposits, as well as other mineral resources (such as bauxite and uranium)

  12. A statistical model for mapping morphological shape

    Directory of Open Access Journals (Sweden)

    Li Jiahan

    2010-07-01

    Full Text Available Abstract Background Living things come in all shapes and sizes, from bacteria, plants, and animals to humans. Knowledge about the genetic mechanisms for biological shape has far-reaching implications for a range spectrum of scientific disciplines including anthropology, agriculture, developmental biology, evolution and biomedicine. Results We derived a statistical model for mapping specific genes or quantitative trait loci (QTLs that control morphological shape. The model was formulated within the mixture framework, in which different types of shape are thought to result from genotypic discrepancies at a QTL. The EM algorithm was implemented to estimate QTL genotype-specific shapes based on a shape correspondence analysis. Computer simulation was used to investigate the statistical property of the model. Conclusion By identifying specific QTLs for morphological shape, the model developed will help to ask, disseminate and address many major integrative biological and genetic questions and challenges in the genetic control of biological shape and function.

  13. Performance modeling, stochastic networks, and statistical multiplexing

    CERN Document Server

    Mazumdar, Ravi R

    2013-01-01

    This monograph presents a concise mathematical approach for modeling and analyzing the performance of communication networks with the aim of introducing an appropriate mathematical framework for modeling and analysis as well as understanding the phenomenon of statistical multiplexing. The models, techniques, and results presented form the core of traffic engineering methods used to design, control and allocate resources in communication networks.The novelty of the monograph is the fresh approach and insights provided by a sample-path methodology for queueing models that highlights the importan

  14. Statistical models for competing risk analysis

    International Nuclear Information System (INIS)

    Sather, H.N.

    1976-08-01

    Research results on three new models for potential applications in competing risks problems. One section covers the basic statistical relationships underlying the subsequent competing risks model development. Another discusses the problem of comparing cause-specific risk structure by competing risks theory in two homogeneous populations, P1 and P2. Weibull models which allow more generality than the Berkson and Elveback models are studied for the effect of time on the hazard function. The use of concomitant information for modeling single-risk survival is extended to the multiple failure mode domain of competing risks. The model used to illustrate the use of this methodology is a life table model which has constant hazards within pre-designated intervals of the time scale. Two parametric models for bivariate dependent competing risks, which provide interesting alternatives, are proposed and examined

  15. Statistical physics of pairwise probability models

    Directory of Open Access Journals (Sweden)

    Yasser Roudi

    2009-11-01

    Full Text Available Statistical models for describing the probability distribution over the states of biological systems are commonly used for dimensional reduction. Among these models, pairwise models are very attractive in part because they can be fit using a reasonable amount of data: knowledge of the means and correlations between pairs of elements in the system is sufficient. Not surprisingly, then, using pairwise models for studying neural data has been the focus of many studies in recent years. In this paper, we describe how tools from statistical physics can be employed for studying and using pairwise models. We build on our previous work on the subject and study the relation between different methods for fitting these models and evaluating their quality. In particular, using data from simulated cortical networks we study how the quality of various approximate methods for inferring the parameters in a pairwise model depends on the time bin chosen for binning the data. We also study the effect of the size of the time bin on the model quality itself, again using simulated data. We show that using finer time bins increases the quality of the pairwise model. We offer new ways of deriving the expressions reported in our previous work for assessing the quality of pairwise models.

  16. Scrambling in the quantum Lifshitz model

    Science.gov (United States)

    Plamadeala, Eugeniu; Fradkin, Eduardo

    2018-06-01

    We study signatures of chaos in the quantum Lifshitz model through out-of-time ordered correlators (OTOC) of current operators. This model is a free scalar field theory with dynamical critical exponent z  =  2. It describes the quantum phase transition in 2D systems, such as quantum dimer models, between a phase with a uniform ground state to another one with spontaneously broken translation invariance. At the lowest temperatures the chaotic dynamics are dominated by a marginally irrelevant operator which induces a temperature dependent stiffness term. The numerical computations of OTOC exhibit a non-zero Lyapunov exponent (LE) in a wide range of temperatures and interaction strengths. The LE (in units of temperature) is a weakly temperature-dependent function; it vanishes at weak interaction and saturates for strong interaction. The Butterfly velocity increases monotonically with interaction strength in the studied region while remaining smaller than the interaction-induced velocity/stiffness.

  17. On the geometry of the spin-statistics connection in quantum mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Reyes, A.

    2006-07-01

    The Spin-Statistics theorem states that the statistics of a system of identical particles is determined by their spin: Particles of integer spin are Bosons (i.e. obey Bose-Einstein statistics), whereas particles of half-integer spin are Fermions (i.e. obey Fermi-Dirac statistics). Since the original proof by Fierz and Pauli, it has been known that the connection between Spin and Statistics follows from the general principles of relativistic Quantum Field Theory. In spite of this, there are different approaches to Spin-Statistics and it is not clear whether the theorem holds under assumptions that are different, and even less restrictive, than the usual ones (e.g. Lorentz-covariance). Additionally, in Quantum Mechanics there is a deep relation between indistinguishability and the geometry of the configuration space. This is clearly illustrated by Gibbs' paradox. Therefore, for many years efforts have been made in order to find a geometric proof of the connection between Spin and Statistics. Recently, various proposals have been put forward, in which an attempt is made to derive the Spin-Statistics connection from assumptions different from the ones used in the relativistic, quantum field theoretic proofs. Among these, there is the one due to Berry and Robbins (BR), based on the postulation of a certain single-valuedness condition, that has caused a renewed interest in the problem. In the present thesis, we consider the problem of indistinguishability in Quantum Mechanics from a geometric-algebraic point of view. An approach is developed to study configuration spaces Q having a finite fundamental group, that allows us to describe different geometric structures of Q in terms of spaces of functions on the universal cover of Q. In particular, it is shown that the space of complex continuous functions over the universal cover of Q admits a decomposition into C(Q)-submodules, labelled by the irreducible representations of the fundamental group of Q, that can be

  18. Effects of quantum statistics of phonons on the thermal conductivity of silicon and germanium nanoribbons

    Science.gov (United States)

    Kosevich, Yuriy A.; Savin, Alexander V.; Cantarero, Andrés

    2013-01-01

    We present molecular dynamics simulation of phonon thermal conductivity of semiconductor nanoribbons with an account for phonon quantum statistics. In our semiquantum molecular dynamics simulation, dynamics of the system is described with the use of classical Newtonian equations of motion where the effect of phonon quantum statistics is introduced through random Langevin-like forces with a specific power spectral density (color noise). The color noise describes interaction of the molecular system with the thermostat. The thermal transport of silicon and germanium nanoribbons with atomically smooth (perfect) and rough (porous) edges are studied. We show that the existence of rough (porous) edges and the quantum statistics of phonon change drastically the low-temperature thermal conductivity of the nanoribbon in comparison with that of the perfect nanoribbon with atomically smooth edges and classical phonon dynamics and statistics. The rough-edge phonon scattering and weak anharmonicity of the considered lattice produce a weakly pronounced maximum of thermal conductivity of the nanoribbon at low temperature.

  19. Introduction to the basic concepts of modern physics special relativity, quantum and statistical physics

    CERN Document Server

    Becchi, Carlo Maria

    2016-01-01

    This is the third edition of a well-received textbook on modern physics theory. This book provides an elementary but rigorous and self-contained presentation of the simplest theoretical framework that will meet the needs of undergraduate students. In addition, a number of examples of relevant applications and an appropriate list of solved problems are provided.Apart from a substantial extension of the proposed problems, the new edition provides more detailed discussion on Lorentz transformations and their group properties, a deeper treatment of quantum mechanics in a central potential, and a closer comparison of statistical mechanics in classical and in quantum physics. The first part of the book is devoted to special relativity, with a particular focus on space-time relativity and relativistic kinematics. The second part deals with Schrödinger's formulation of quantum mechanics. The presentation concerns mainly one-dimensional problems, but some three-dimensional examples are discussed in detail. The third...

  20. Statistical models of petrol engines vehicles dynamics

    Science.gov (United States)

    Ilie, C. O.; Marinescu, M.; Alexa, O.; Vilău, R.; Grosu, D.

    2017-10-01

    This paper focuses on studying statistical models of vehicles dynamics. It was design and perform a one year testing program. There were used many same type cars with gasoline engines and different mileage. Experimental data were collected of onboard sensors and those on the engine test stand. A database containing data of 64th tests was created. Several mathematical modelling were developed using database and the system identification method. Each modelling is a SISO or a MISO linear predictive ARMAX (AutoRegressive-Moving-Average with eXogenous inputs) model. It represents a differential equation with constant coefficients. It were made 64th equations for each dependency like engine torque as output and engine’s load and intake manifold pressure, as inputs. There were obtained strings with 64 values for each type of model. The final models were obtained using average values of the coefficients. The accuracy of models was assessed.

  1. Equilibrium statistical mechanics of lattice models

    CERN Document Server

    Lavis, David A

    2015-01-01

    Most interesting and difficult problems in equilibrium statistical mechanics concern models which exhibit phase transitions. For graduate students and more experienced researchers this book provides an invaluable reference source of approximate and exact solutions for a comprehensive range of such models. Part I contains background material on classical thermodynamics and statistical mechanics, together with a classification and survey of lattice models. The geometry of phase transitions is described and scaling theory is used to introduce critical exponents and scaling laws. An introduction is given to finite-size scaling, conformal invariance and Schramm—Loewner evolution. Part II contains accounts of classical mean-field methods. The parallels between Landau expansions and catastrophe theory are discussed and Ginzburg—Landau theory is introduced. The extension of mean-field theory to higher-orders is explored using the Kikuchi—Hijmans—De Boer hierarchy of approximations. In Part III the use of alge...

  2. Statistical shape and appearance models of bones.

    Science.gov (United States)

    Sarkalkan, Nazli; Weinans, Harrie; Zadpoor, Amir A

    2014-03-01

    When applied to bones, statistical shape models (SSM) and statistical appearance models (SAM) respectively describe the mean shape and mean density distribution of bones within a certain population as well as the main modes of variations of shape and density distribution from their mean values. The availability of this quantitative information regarding the detailed anatomy of bones provides new opportunities for diagnosis, evaluation, and treatment of skeletal diseases. The potential of SSM and SAM has been recently recognized within the bone research community. For example, these models have been applied for studying the effects of bone shape on the etiology of osteoarthritis, improving the accuracy of clinical osteoporotic fracture prediction techniques, design of orthopedic implants, and surgery planning. This paper reviews the main concepts, methods, and applications of SSM and SAM as applied to bone. Copyright © 2013 Elsevier Inc. All rights reserved.

  3. Statistical Models of Adaptive Immune populations

    Science.gov (United States)

    Sethna, Zachary; Callan, Curtis; Walczak, Aleksandra; Mora, Thierry

    The availability of large (104-106 sequences) datasets of B or T cell populations from a single individual allows reliable fitting of complex statistical models for naïve generation, somatic selection, and hypermutation. It is crucial to utilize a probabilistic/informational approach when modeling these populations. The inferred probability distributions allow for population characterization, calculation of probability distributions of various hidden variables (e.g. number of insertions), as well as statistical properties of the distribution itself (e.g. entropy). In particular, the differences between the T cell populations of embryonic and mature mice will be examined as a case study. Comparing these populations, as well as proposed mixed populations, provides a concrete exercise in model creation, comparison, choice, and validation.

  4. Cellular automata and statistical mechanical models

    International Nuclear Information System (INIS)

    Rujan, P.

    1987-01-01

    The authors elaborate on the analogy between the transfer matrix of usual lattice models and the master equation describing the time development of cellular automata. Transient and stationary properties of probabilistic automata are linked to surface and bulk properties, respectively, of restricted statistical mechanical systems. It is demonstrated that methods of statistical physics can be successfully used to describe the dynamic and the stationary behavior of such automata. Some exact results are derived, including duality transformations, exact mappings, disorder, and linear solutions. Many examples are worked out in detail to demonstrate how to use statistical physics in order to construct cellular automata with desired properties. This approach is considered to be a first step toward the design of fully parallel, probabilistic systems whose computational abilities rely on the cooperative behavior of their components

  5. Many-body problem in quantum mechanics and quantum statistical mechanics

    International Nuclear Information System (INIS)

    Lee, T.D.; Yang, C.N.

    1983-01-01

    This is a progress report on some work concerning the quantum mechanical calculation of the fugacity coefficients b/sub l/ (which correspond to the classical cluster integrals) of a Bose, a Fermi, and a Boltzmann gas at low temperatures. A binary collision expansion method is developed which allows for the systematic calculation of b/sub l/ as expansions in powers of a/λ, where a represents the parameters of the dimensions of length that characterize the low-energy two-body collision and λ is the thermal wavelength. To any power of (a/λ) the calculation of any specific b/sub l/ is reduced to a finite number of quadratures. The method, therefore, is the low-temperature counterpart of the high-temperature expansion of b/sub l/

  6. Renormalization of boundary conditions for distribution functions of quasiparticles obeying quantum statistics at interfaces between crystalline grains

    International Nuclear Information System (INIS)

    Grendel, M.

    1981-01-01

    Boundary conditions for distribution functions of quasiparticles scattered by an interface between two crystalline grains are presented. Contrary to former formulations where Maxwell-Boltzmann statistics was considered, the present boundary conditions take into account the quantum statistics (Fermi-Dirac or Bose-Einstein) of quasiparticles. Provided that small deviations only from thermodynamic equilibrium are present, the boundary conditions are linearized, and then their ''renormalization'' is investigated in case of elastic scattering. The final results of the renormalization, which are obtained for a simplified model of an interface, sugo.est that the portion of the Fermi (Bose)-quasiparticles reflected or transmitted specularly is decreased (increased) in comparison with the case of quasiparticles obeying Maxwell-Boltzmann statistics. (author)

  7. A unified treatment of dynamics and scattering in classical and quantum statistical mechanics

    International Nuclear Information System (INIS)

    Prugovecki, E.

    1978-01-01

    The common formal features of classical and quantum statistical mechanics are investigated at three separate levels: at the level of L 2 spaces of wave-packets on GAMMA-space, of Liouville spaces B 2 consisting of density operators constructed from such wave-packets, and of phase-space representation spaces P of GAMMA distribution functions. It is shown that at the last level the formal similarities become so outstanding that all key quantities in P-space, such as Liouville operators, Hamiltonian functions, position and momentum observables, etc., are represented by expressions which to the zeroth order in (h/2π) coincide in the classical and quantum case, and in some instances coincide completely. Scattering theory on the B 2 Liouville spaces takes on the same formal appearance for classical and quantum statistical mechanics, and to the zeroth order in (h/2π) it coincides in both cases. This makes possible the formulation of a classical approximation to quantum scattering, and of a computational scheme for determining rhosup(out) from rhosup(in) for successive order of (h/2π). (Auth.)

  8. Fractionalizing Majorana Fermions: Non-Abelian Statistics on the Edges of Abelian Quantum Hall States

    Directory of Open Access Journals (Sweden)

    Netanel H. Lindner

    2012-10-01

    Full Text Available We study the non-Abelian statistics characterizing systems where counterpropagating gapless modes on the edges of fractional quantum Hall states are gapped by proximity coupling to superconductors and ferromagnets. The most transparent example is that of a fractional quantum spin Hall state, in which electrons of one spin direction occupy a fractional quantum Hall state of ν=1/m, while electrons of the opposite spin occupy a similar state with ν=-1/m. However, we also propose other examples of such systems, which are easier to realize experimentally. We find that each interface between a region on the edge coupled to a superconductor and a region coupled to a ferromagnet corresponds to a non-Abelian anyon of quantum dimension sqrt[2m]. We calculate the unitary transformations that are associated with the braiding of these anyons, and we show that they are able to realize a richer set of non-Abelian representations of the braid group than the set realized by non-Abelian anyons based on Majorana fermions. We carry out this calculation both explicitly and by applying general considerations. Finally, we show that topological manipulations with these anyons cannot realize universal quantum computation.

  9. Nonlinear unitary quantum collapse model with self-generated noise

    Science.gov (United States)

    Geszti, Tamás

    2018-04-01

    Collapse models including some external noise of unknown origin are routinely used to describe phenomena on the quantum-classical border; in particular, quantum measurement. Although containing nonlinear dynamics and thereby exposed to the possibility of superluminal signaling in individual events, such models are widely accepted on the basis of fully reproducing the non-signaling statistical predictions of quantum mechanics. Here we present a deterministic nonlinear model without any external noise, in which randomness—instead of being universally present—emerges in the measurement process, from deterministic irregular dynamics of the detectors. The treatment is based on a minimally nonlinear von Neumann equation for a Stern–Gerlach or Bell-type measuring setup, containing coordinate and momentum operators in a self-adjoint skew-symmetric, split scalar product structure over the configuration space. The microscopic states of the detectors act as a nonlocal set of hidden parameters, controlling individual outcomes. The model is shown to display pumping of weights between setup-defined basis states, with a single winner randomly selected and the rest collapsing to zero. Environmental decoherence has no role in the scenario. Through stochastic modelling, based on Pearle’s ‘gambler’s ruin’ scheme, outcome probabilities are shown to obey Born’s rule under a no-drift or ‘fair-game’ condition. This fully reproduces quantum statistical predictions, implying that the proposed non-linear deterministic model satisfies the non-signaling requirement. Our treatment is still vulnerable to hidden signaling in individual events, which remains to be handled by future research.

  10. Statistical Modelling of Wind Proles - Data Analysis and Modelling

    DEFF Research Database (Denmark)

    Jónsson, Tryggvi; Pinson, Pierre

    The aim of the analysis presented in this document is to investigate whether statistical models can be used to make very short-term predictions of wind profiles.......The aim of the analysis presented in this document is to investigate whether statistical models can be used to make very short-term predictions of wind profiles....

  11. Optimal evolution models for quantum tomography

    International Nuclear Information System (INIS)

    Czerwiński, Artur

    2016-01-01

    The research presented in this article concerns the stroboscopic approach to quantum tomography, which is an area of science where quantum physics and linear algebra overlap. In this article we introduce the algebraic structure of the parametric-dependent quantum channels for 2-level and 3-level systems such that the generator of evolution corresponding with the Kraus operators has no degenerate eigenvalues. In such cases the index of cyclicity of the generator is equal to 1, which physically means that there exists one observable the measurement of which performed a sufficient number of times at distinct instants provides enough data to reconstruct the initial density matrix and, consequently, the trajectory of the state. The necessary conditions for the parameters and relations between them are introduced. The results presented in this paper seem to have considerable potential applications in experiments due to the fact that one can perform quantum tomography by conducting only one kind of measurement. Therefore, the analyzed evolution models can be considered optimal in the context of quantum tomography. Finally, we introduce some remarks concerning optimal evolution models in the case of n-dimensional Hilbert space. (paper)

  12. Statistical modeling of geopressured geothermal reservoirs

    Science.gov (United States)

    Ansari, Esmail; Hughes, Richard; White, Christopher D.

    2017-06-01

    Identifying attractive candidate reservoirs for producing geothermal energy requires predictive models. In this work, inspectional analysis and statistical modeling are used to create simple predictive models for a line drive design. Inspectional analysis on the partial differential equations governing this design yields a minimum number of fifteen dimensionless groups required to describe the physics of the system. These dimensionless groups are explained and confirmed using models with similar dimensionless groups but different dimensional parameters. This study models dimensionless production temperature and thermal recovery factor as the responses of a numerical model. These responses are obtained by a Box-Behnken experimental design. An uncertainty plot is used to segment the dimensionless time and develop a model for each segment. The important dimensionless numbers for each segment of the dimensionless time are identified using the Boosting method. These selected numbers are used in the regression models. The developed models are reduced to have a minimum number of predictors and interactions. The reduced final models are then presented and assessed using testing runs. Finally, applications of these models are offered. The presented workflow is generic and can be used to translate the output of a numerical simulator into simple predictive models in other research areas involving numerical simulation.

  13. A statistical model for instable thermodynamical systems

    International Nuclear Information System (INIS)

    Sommer, Jens-Uwe

    2003-01-01

    A generic model is presented for statistical systems which display thermodynamic features in contrast to our everyday experience, such as infinite and negative heat capacities. Such system are instable in terms of classical equilibrium thermodynamics. Using our statistical model, we are able to investigate states of instable systems which are undefined in the framework of equilibrium thermodynamics. We show that a region of negative heat capacity in the adiabatic environment, leads to a first order like phase transition when the system is coupled to a heat reservoir. This phase transition takes place without a phase coexistence. Nevertheless, all intermediate states are stable due to fluctuations. When two instable system are brought in thermal contact, the temperature of the composed system is lower than the minimum temperature of the individual systems. Generally, the equilibrium states of instable system cannot be simply decomposed into equilibrium states of the individual systems. The properties of instable system depend on the environment, ensemble equivalence is broken

  14. Logarithmic transformed statistical models in calibration

    International Nuclear Information System (INIS)

    Zeis, C.D.

    1975-01-01

    A general type of statistical model used for calibration of instruments having the property that the standard deviations of the observed values increase as a function of the mean value is described. The application to the Helix Counter at the Rocky Flats Plant is primarily from a theoretical point of view. The Helix Counter measures the amount of plutonium in certain types of chemicals. The method described can be used also for other calibrations. (U.S.)

  15. ARSENIC CONTAMINATION IN GROUNDWATER: A STATISTICAL MODELING

    OpenAIRE

    Palas Roy; Naba Kumar Mondal; Biswajit Das; Kousik Das

    2013-01-01

    High arsenic in natural groundwater in most of the tubewells of the Purbasthali- Block II area of Burdwan district (W.B, India) has recently been focused as a serious environmental concern. This paper is intending to illustrate the statistical modeling of the arsenic contaminated groundwater to identify the interrelation of that arsenic contain with other participating groundwater parameters so that the arsenic contamination level can easily be predicted by analyzing only such parameters. Mul...

  16. Fractional statistics and quantum scaling properties of the integrable Penson-Kolb-Hubbard chain

    Science.gov (United States)

    Vitoriano, Carlindo; Coutinho-Filho, M. D.

    2010-09-01

    We investigate the ground-state and low-temperature properties of the integrable version of the Penson-Kolb-Hubbard chain. The model obeys fractional statistical properties, which give rise to fractional elementary excitations and manifest differently in the four regions of the phase diagram U/t versus n , where U is the Coulomb coupling, t is the correlated hopping amplitude, and n is the particle density. In fact, we can find local pair formation, fractionalization of the average occupation number per orbital k , or U - and n -dependent average electric charge per orbital k . We also study the scaling behavior near the U -driven quantum phase transitions and characterize their universality classes. Finally, it is shown that in the regime of parameters where local pair formation is energetically more favorable, the ground state exhibits power-law superconductivity; we also stress that above half filling the pair-hopping term stabilizes local Cooper pairs in the repulsive- U regime for U

  17. Full counting statistics of level renormalization in electron transport through double quantum dots

    International Nuclear Information System (INIS)

    Luo Junyan; Shen Yu; Cen Gang; He Xiaoling; Wang Changrong; Jiao Hujun

    2011-01-01

    We examine the full counting statistics of electron transport through double quantum dots coupled in series, with particular attention being paid to the unique features originating from level renormalization. It is clearly illustrated that the energy renormalization gives rise to a dynamic charge blockade mechanism, which eventually results in super-Poissonian noise. Coupling of the double dots to an external heat bath leads to dephasing and relaxation mechanisms, which are demonstrated to suppress the noise in a unique way.

  18. Quantum Statistics: Is there an effective fermion repulsion or boson attraction?

    OpenAIRE

    Mullin, W. J.; Blaylock, G.

    2003-01-01

    Physicists often claim that there is an effective repulsion between fermions, implied by the Pauli principle, and a corresponding effective attraction between bosons. We examine the origins of such exchange force ideas, the validity for them, and the areas where they are highly misleading. We propose that future explanations of quantum statistics should avoid the idea of a effective force completely and replace it with more appropriate physical insights, some of which are suggested here.

  19. Exact diagonalization library for quantum electron models

    Science.gov (United States)

    Iskakov, Sergei; Danilov, Michael

    2018-04-01

    We present an exact diagonalization C++ template library (EDLib) for solving quantum electron models, including the single-band finite Hubbard cluster and the multi-orbital impurity Anderson model. The observables that can be computed using EDLib are single particle Green's functions and spin-spin correlation functions. This code provides three different types of Hamiltonian matrix storage that can be chosen based on the model.

  20. A simple statistical model for geomagnetic reversals

    Science.gov (United States)

    Constable, Catherine

    1990-01-01

    The diversity of paleomagnetic records of geomagnetic reversals now available indicate that the field configuration during transitions cannot be adequately described by simple zonal or standing field models. A new model described here is based on statistical properties inferred from the present field and is capable of simulating field transitions like those observed. Some insight is obtained into what one can hope to learn from paleomagnetic records. In particular, it is crucial that the effects of smoothing in the remanence acquisition process be separated from true geomagnetic field behavior. This might enable us to determine the time constants associated with the dominant field configuration during a reversal.

  1. Hybrid quantum teleportation: A theoretical model

    Energy Technology Data Exchange (ETDEWEB)

    Takeda, Shuntaro; Mizuta, Takahiro; Fuwa, Maria; Yoshikawa, Jun-ichi; Yonezawa, Hidehiro; Furusawa, Akira [Department of Applied Physics, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656 (Japan)

    2014-12-04

    Hybrid quantum teleportation – continuous-variable teleportation of qubits – is a promising approach for deterministically teleporting photonic qubits. We propose how to implement it with current technology. Our theoretical model shows that faithful qubit transfer can be achieved for this teleportation by choosing an optimal gain for the teleporter’s classical channel.

  2. The quantum hydrodynamics of the Sutherland model

    International Nuclear Information System (INIS)

    Stone, Michael; Gutman, Dmitry

    2008-01-01

    We show that the form of the chiral condition found by Abanov et al in the quantum hydrodynamics of the Sutherland model arises because there are two distinct inner products with respect to which the chiral Hamiltonian is Hermitian, but only one with respect to which the full, non-chiral, Hamiltonian is Hermitian

  3. Non standard analysis, polymer models, quantum fields

    International Nuclear Information System (INIS)

    Albeverio, S.

    1984-01-01

    We give an elementary introduction to non standard analysis and its applications to the theory of stochastic processes. This is based on a joint book with J.E. Fenstad, R. Hoeegh-Krohn and T. Lindstroeem. In particular we give a discussion of an hyperfinite theory of Dirichlet forms with applications to the study of the Hamiltonian for a quantum mechanical particle in the potential created by a polymer. We also discuss new results on the existence of attractive polymer measures in dimension d 1 2 phi 2 2 )sub(d)-model of interacting quantum fields. (orig.)

  4. Quantum mechanical Hamiltonian models of discrete processes

    International Nuclear Information System (INIS)

    Benioff, P.

    1981-01-01

    Here the results of other work on quantum mechanical Hamiltonian models of Turing machines are extended to include any discrete process T on a countably infinite set A. The models are constructed here by use of scattering phase shifts from successive scatterers to turn on successive step interactions. Also a locality requirement is imposed. The construction is done by first associating with each process T a model quantum system M with associated Hilbert space H/sub M/ and step operator U/sub T/. Since U/sub T/ is not unitary in general, M, H/sub M/, and U/sub T/ are extended into a (continuous time) Hamiltonian model on a larger space which satisfies the locality requirement. The construction is compared with the minimal unitary dilation of U/sub T/. It is seen that the model constructed here is larger than the minimal one. However, the minimal one does not satisfy the locality requirement

  5. Parameter optimization in biased decoy-state quantum key distribution with both source errors and statistical fluctuations

    Science.gov (United States)

    Zhu, Jian-Rong; Li, Jian; Zhang, Chun-Mei; Wang, Qin

    2017-10-01

    The decoy-state method has been widely used in commercial quantum key distribution (QKD) systems. In view of the practical decoy-state QKD with both source errors and statistical fluctuations, we propose a universal model of full parameter optimization in biased decoy-state QKD with phase-randomized sources. Besides, we adopt this model to carry out simulations of two widely used sources: weak coherent source (WCS) and heralded single-photon source (HSPS). Results show that full parameter optimization can significantly improve not only the secure transmission distance but also the final key generation rate. And when taking source errors and statistical fluctuations into account, the performance of decoy-state QKD using HSPS suffered less than that of decoy-state QKD using WCS.

  6. Statistical Modelling of the Soil Dielectric Constant

    Science.gov (United States)

    Usowicz, Boguslaw; Marczewski, Wojciech; Bogdan Usowicz, Jerzy; Lipiec, Jerzy

    2010-05-01

    The dielectric constant of soil is the physical property being very sensitive on water content. It funds several electrical measurement techniques for determining the water content by means of direct (TDR, FDR, and others related to effects of electrical conductance and/or capacitance) and indirect RS (Remote Sensing) methods. The work is devoted to a particular statistical manner of modelling the dielectric constant as the property accounting a wide range of specific soil composition, porosity, and mass density, within the unsaturated water content. Usually, similar models are determined for few particular soil types, and changing the soil type one needs switching the model on another type or to adjust it by parametrization of soil compounds. Therefore, it is difficult comparing and referring results between models. The presented model was developed for a generic representation of soil being a hypothetical mixture of spheres, each representing a soil fraction, in its proper phase state. The model generates a serial-parallel mesh of conductive and capacitive paths, which is analysed for a total conductive or capacitive property. The model was firstly developed to determine the thermal conductivity property, and now it is extended on the dielectric constant by analysing the capacitive mesh. The analysis is provided by statistical means obeying physical laws related to the serial-parallel branching of the representative electrical mesh. Physical relevance of the analysis is established electrically, but the definition of the electrical mesh is controlled statistically by parametrization of compound fractions, by determining the number of representative spheres per unitary volume per fraction, and by determining the number of fractions. That way the model is capable covering properties of nearly all possible soil types, all phase states within recognition of the Lorenz and Knudsen conditions. In effect the model allows on generating a hypothetical representative of

  7. On Mathematical Modeling Of Quantum Systems

    International Nuclear Information System (INIS)

    Achuthan, P.; Narayanankutty, Karuppath

    2009-01-01

    The world of physical systems at the most fundamental levels is replete with efficient, interesting models possessing sufficient ability to represent the reality to a considerable extent. So far, quantum mechanics (QM) forming the basis of almost all natural phenomena, has found beyond doubt its intrinsic ingenuity, capacity and robustness to stand the rigorous tests of validity from and through appropriate calculations and experiments. No serious failures of quantum mechanical predictions have been reported, yet. However, Albert Einstein, the greatest theoretical physicist of the twentieth century and some other eminent men of science have stated firmly and categorically that QM, though successful by and large, is incomplete. There are classical and quantum reality models including those based on consciousness. Relativistic quantum theoretical approaches to clearly understand the ultimate nature of matter as well as radiation have still much to accomplish in order to qualify for a final theory of everything (TOE). Mathematical models of better, suitable character as also strength are needed to achieve satisfactory explanation of natural processes and phenomena. We, in this paper, discuss some of these matters with certain apt illustrations as well.

  8. Encoding Dissimilarity Data for Statistical Model Building.

    Science.gov (United States)

    Wahba, Grace

    2010-12-01

    We summarize, review and comment upon three papers which discuss the use of discrete, noisy, incomplete, scattered pairwise dissimilarity data in statistical model building. Convex cone optimization codes are used to embed the objects into a Euclidean space which respects the dissimilarity information while controlling the dimension of the space. A "newbie" algorithm is provided for embedding new objects into this space. This allows the dissimilarity information to be incorporated into a Smoothing Spline ANOVA penalized likelihood model, a Support Vector Machine, or any model that will admit Reproducing Kernel Hilbert Space components, for nonparametric regression, supervised learning, or semi-supervised learning. Future work and open questions are discussed. The papers are: F. Lu, S. Keles, S. Wright and G. Wahba 2005. A framework for kernel regularization with application to protein clustering. Proceedings of the National Academy of Sciences 102, 12332-1233.G. Corrada Bravo, G. Wahba, K. Lee, B. Klein, R. Klein and S. Iyengar 2009. Examining the relative influence of familial, genetic and environmental covariate information in flexible risk models. Proceedings of the National Academy of Sciences 106, 8128-8133F. Lu, Y. Lin and G. Wahba. Robust manifold unfolding with kernel regularization. TR 1008, Department of Statistics, University of Wisconsin-Madison.

  9. ARSENIC CONTAMINATION IN GROUNDWATER: A STATISTICAL MODELING

    Directory of Open Access Journals (Sweden)

    Palas Roy

    2013-01-01

    Full Text Available High arsenic in natural groundwater in most of the tubewells of the Purbasthali- Block II area of Burdwan district (W.B, India has recently been focused as a serious environmental concern. This paper is intending to illustrate the statistical modeling of the arsenic contaminated groundwater to identify the interrelation of that arsenic contain with other participating groundwater parameters so that the arsenic contamination level can easily be predicted by analyzing only such parameters. Multivariate data analysis was done with the collected groundwater samples from the 132 tubewells of this contaminated region shows that three variable parameters are significantly related with the arsenic. Based on these relationships, a multiple linear regression model has been developed that estimated the arsenic contamination by measuring such three predictor parameters of the groundwater variables in the contaminated aquifer. This model could also be a suggestive tool while designing the arsenic removal scheme for any affected groundwater.

  10. Quantum Dynamics in the HMF Model

    Science.gov (United States)

    Plestid, Ryan; O'Dell, Duncan

    2017-04-01

    The Hamiltonian Mean Field (HMF) model represents a paradigm in the study of long-range interactions but has never been realized in a lab. Recently Shutz and Morigi (PRL 113) have come close but ultimately fallen short. Their proposal relied on cavity-induced interactions between atoms. If a design using cold atoms is to be successful, an understanding of quantum effects is essential. I will outline the natural quantum generalization of the HMF assuming a BEC by using a generalized Gross-Pitaevskii equation (gGPE). I will show how quantum effects modify features which are well understood in the classical model. More specifically, by working in the semi-classical regime (strong interparticle interactions) we can identify the universal features predicted by catastrophe theory dressed with quantum interference effects. The stationary states of gGPE can be solved exactly and are found to be described by self-consistent Mathieu functions. Finally, I will discuss the connection between the classical description of the dynamics in terms of the Vlassov equation, and the gGPE. We would like to thank the Government of Ontario's OGS program, NSERC, and the Perimeter Institute of Theoretical Physics.

  11. Optimizing refiner operation with statistical modelling

    Energy Technology Data Exchange (ETDEWEB)

    Broderick, G [Noranda Research Centre, Pointe Claire, PQ (Canada)

    1997-02-01

    The impact of refining conditions on the energy efficiency of the process and on the handsheet quality of a chemi-mechanical pulp was studied as part of a series of pilot scale refining trials. Statistical models of refiner performance were constructed from these results and non-linear optimization of process conditions were conducted. Optimization results indicated that increasing the ratio of specific energy applied in the first stage led to a reduction of some 15 per cent in the total energy requirement. The strategy can also be used to obtain significant increases in pulp quality for a given energy input. 20 refs., 6 tabs.

  12. Average Nuclear properties based on statistical model

    International Nuclear Information System (INIS)

    El-Jaick, L.J.

    1974-01-01

    The rough properties of nuclei were investigated by statistical model, in systems with the same and different number of protons and neutrons, separately, considering the Coulomb energy in the last system. Some average nuclear properties were calculated based on the energy density of nuclear matter, from Weizsscker-Beth mass semiempiric formulae, generalized for compressible nuclei. In the study of a s surface energy coefficient, the great influence exercised by Coulomb energy and nuclear compressibility was verified. For a good adjust of beta stability lines and mass excess, the surface symmetry energy were established. (M.C.K.) [pt

  13. Statistical physics as an approximate method of many-body quantum mechanics in the representation of occupation numbers

    International Nuclear Information System (INIS)

    Kushnirenko, A.N.

    1989-01-01

    An attempt was made to substantiate statistical physics from the viewpoint of many-body quantum mechanics in the representation of occupation numbers. This approach enabled to develop the variation method for solution of stationary and nonstationary nonequilibrium problems

  14. Thermo-dynamical contours of electronic-vibrational spectra simulated using the statistical quantum-mechanical methods

    DEFF Research Database (Denmark)

    Pomogaev, Vladimir; Pomogaeva, Anna; Avramov, Pavel

    2011-01-01

    Three polycyclic organic molecules in various solvents focused on thermo-dynamical aspects were theoretically investigated using the recently developed statistical quantum mechanical/classical molecular dynamics method for simulating electronic-vibrational spectra. The absorption bands of estradiol...

  15. Statistical pairwise interaction model of stock market

    Science.gov (United States)

    Bury, Thomas

    2013-03-01

    Financial markets are a classical example of complex systems as they are compound by many interacting stocks. As such, we can obtain a surprisingly good description of their structure by making the rough simplification of binary daily returns. Spin glass models have been applied and gave some valuable results but at the price of restrictive assumptions on the market dynamics or they are agent-based models with rules designed in order to recover some empirical behaviors. Here we show that the pairwise model is actually a statistically consistent model with the observed first and second moments of the stocks orientation without making such restrictive assumptions. This is done with an approach only based on empirical data of price returns. Our data analysis of six major indices suggests that the actual interaction structure may be thought as an Ising model on a complex network with interaction strengths scaling as the inverse of the system size. This has potentially important implications since many properties of such a model are already known and some techniques of the spin glass theory can be straightforwardly applied. Typical behaviors, as multiple equilibria or metastable states, different characteristic time scales, spatial patterns, order-disorder, could find an explanation in this picture.

  16. Quantum chaos and holographic tensor models

    Energy Technology Data Exchange (ETDEWEB)

    Krishnan, Chethan [Center for High Energy Physics, Indian Institute of Science,Bangalore 560012 (India); Sanyal, Sambuddha [International Center for Theoretical Sciences, Tata Institute of Fundamental Research,Bangalore 560089 (India); Subramanian, P.N. Bala [Center for High Energy Physics, Indian Institute of Science,Bangalore 560012 (India)

    2017-03-10

    A class of tensor models were recently outlined as potentially calculable examples of holography: their perturbative large-N behavior is similar to the Sachdev-Ye-Kitaev (SYK) model, but they are fully quantum mechanical (in the sense that there is no quenched disorder averaging). These facts make them intriguing tentative models for quantum black holes. In this note, we explicitly diagonalize the simplest non-trivial Gurau-Witten tensor model and study its spectral and late-time properties. We find parallels to (a single sample of) SYK where some of these features were recently attributed to random matrix behavior and quantum chaos. In particular, the spectral form factor exhibits a dip-ramp-plateau structure after a running time average, in qualitative agreement with SYK. But we also observe that even though the spectrum has a unique ground state, it has a huge (quasi-?)degeneracy of intermediate energy states, not seen in SYK. If one ignores the delta function due to the degeneracies however, there is level repulsion in the unfolded spacing distribution hinting chaos. Furthermore, there are gaps in the spectrum. The system also has a spectral mirror symmetry which we trace back to the presence of a unitary operator with which the Hamiltonian anticommutes. We use it to argue that to the extent that the model exhibits random matrix behavior, it is controlled not by the Dyson ensembles, but by the BDI (chiral orthogonal) class in the Altland-Zirnbauer classification.

  17. Quantum chaos and holographic tensor models

    International Nuclear Information System (INIS)

    Krishnan, Chethan; Sanyal, Sambuddha; Subramanian, P.N. Bala

    2017-01-01

    A class of tensor models were recently outlined as potentially calculable examples of holography: their perturbative large-N behavior is similar to the Sachdev-Ye-Kitaev (SYK) model, but they are fully quantum mechanical (in the sense that there is no quenched disorder averaging). These facts make them intriguing tentative models for quantum black holes. In this note, we explicitly diagonalize the simplest non-trivial Gurau-Witten tensor model and study its spectral and late-time properties. We find parallels to (a single sample of) SYK where some of these features were recently attributed to random matrix behavior and quantum chaos. In particular, the spectral form factor exhibits a dip-ramp-plateau structure after a running time average, in qualitative agreement with SYK. But we also observe that even though the spectrum has a unique ground state, it has a huge (quasi-?)degeneracy of intermediate energy states, not seen in SYK. If one ignores the delta function due to the degeneracies however, there is level repulsion in the unfolded spacing distribution hinting chaos. Furthermore, there are gaps in the spectrum. The system also has a spectral mirror symmetry which we trace back to the presence of a unitary operator with which the Hamiltonian anticommutes. We use it to argue that to the extent that the model exhibits random matrix behavior, it is controlled not by the Dyson ensembles, but by the BDI (chiral orthogonal) class in the Altland-Zirnbauer classification.

  18. Quantum statistics and squeezing for a microwave-driven interacting magnon system.

    Science.gov (United States)

    Haghshenasfard, Zahra; Cottam, Michael G

    2017-02-01

    Theoretical studies are reported for the statistical properties of a microwave-driven interacting magnon system. Both the magnetic dipole-dipole and the exchange interactions are included and the theory is developed for the case of parallel pumping allowing for the inclusion of the nonlinear processes due to the four-magnon interactions. The method of second quantization is used to transform the total Hamiltonian from spin operators to boson creation and annihilation operators. By using the coherent magnon state representation we have studied the magnon occupation number and the statistical behavior of the system. In particular, it is shown that the nonlinearities introduced by the parallel pumping field and the four-magnon interactions lead to non-classical quantum statistical properties of the system, such as magnon squeezing. Also control of the collapse-and-revival phenomena for the time evolution of the average magnon number is demonstrated by varying the parallel pumping amplitude and the four-magnon coupling.

  19. Introduction to the basic concepts of modern physics special relativity, quantum and statistical physics

    CERN Document Server

    Becchi, Carlo Maria

    2007-01-01

    These notes are designed as a text book for a course on the Modern Physics Theory for undergraduate students. The purpose is providing a rigorous and self-contained presentation of the simplest theoretical framework using elementary mathematical tools. A number of examples of relevant applications and an appropriate list of exercises and answered questions are also given. The first part is devoted to Special Relativity concerning in particular space-time relativity and relativistic kinematics. The second part deals with Schroedinger's formulation of quantum mechanics. The presentation concerns mainly one dimensional problems, in particular tunnel effect, discrete energy levels and band spectra. The third part concerns the application of Gibbs statistical methods to quantum systems and in particular to Bose and Fermi gasses.

  20. Statistical modeling to support power system planning

    Science.gov (United States)

    Staid, Andrea

    This dissertation focuses on data-analytic approaches that improve our understanding of power system applications to promote better decision-making. It tackles issues of risk analysis, uncertainty management, resource estimation, and the impacts of climate change. Tools of data mining and statistical modeling are used to bring new insight to a variety of complex problems facing today's power system. The overarching goal of this research is to improve the understanding of the power system risk environment for improved operation, investment, and planning decisions. The first chapter introduces some challenges faced in planning for a sustainable power system. Chapter 2 analyzes the driving factors behind the disparity in wind energy investments among states with a goal of determining the impact that state-level policies have on incentivizing wind energy. Findings show that policy differences do not explain the disparities; physical and geographical factors are more important. Chapter 3 extends conventional wind forecasting to a risk-based focus of predicting maximum wind speeds, which are dangerous for offshore operations. Statistical models are presented that issue probabilistic predictions for the highest wind speed expected in a three-hour interval. These models achieve a high degree of accuracy and their use can improve safety and reliability in practice. Chapter 4 examines the challenges of wind power estimation for onshore wind farms. Several methods for wind power resource assessment are compared, and the weaknesses of the Jensen model are demonstrated. For two onshore farms, statistical models outperform other methods, even when very little information is known about the wind farm. Lastly, chapter 5 focuses on the power system more broadly in the context of the risks expected from tropical cyclones in a changing climate. Risks to U.S. power system infrastructure are simulated under different scenarios of tropical cyclone behavior that may result from climate

  1. Acceleration transforms and statistical kinetic models

    International Nuclear Information System (INIS)

    LuValle, M.J.; Welsher, T.L.; Svoboda, K.

    1988-01-01

    For a restricted class of problems a mathematical model of microscopic degradation processes, statistical kinetics, is developed and linked through acceleration transforms to the information which can be obtained from a system in which the only observable sign of degradation is sudden and catastrophic failure. The acceleration transforms were developed in accelerated life testing applications as a tool for extrapolating from the observable results of an accelerated life test to the dynamics of the underlying degradation processes. A particular concern of a physicist attempting to interpreted the results of an analysis based on acceleration transforms is determining the physical species involved in the degradation process. These species may be (a) relatively abundant or (b) relatively rare. The main results of this paper are a theorem showing that for an important subclass of statistical kinetic models, acceleration transforms cannot be used to distinguish between cases a and b, and an example showing that in some cases falling outside the restrictions of the theorem, cases a and b can be distinguished by their acceleration transforms

  2. Quantum Statistics of the Toda Oscillator in the Wigner Function Formalism

    Science.gov (United States)

    Vojta, Günter; Vojta, Matthias

    Classical and quantum mechanical Toda systems (Toda molecules, Toda lattices, Toda quantum fields) recently found growing interest as nonlinear systems showing solitons and chaos. In this paper the statistical thermodynamics of a system of quantum mechanical Toda oscillators characterized by a potential energy V(q) = Vo cos h q is treated within the Wigner function formalism (phase space formalism of quantum statistics). The partition function is given as a Wigner- Kirkwood series expansion in terms of powers of h2 (semiclassical expansion). The partition function and all thermodynamic functions are written, with considerable exactness, as simple closed expressions containing only the modified Hankel functions Ko and K1 of the purely imaginary argument i with = Vo/kT.Translated AbstractQuantenstatistik des Toda-Oszillators im Formalismus der Wigner-FunktionKlassische und quantenmechanische Toda-Systeme (Toda-Moleküle, Toda-Gitter, Toda-Quantenfelder) haben als nichtlineare Systeme mit Solitonen und Chaos in jüngster Zeit zunehmend an Interesse gewonnen. Wir untersuchen die statistische Thermodynamik eines Systems quantenmechanischer Toda-Oszillatoren, die durch eine potentielle Energie der Form V(q) = Vo cos h q charakterisiert sind, im Formalismus der Wigner-Funktion (Phasenraum-Formalismus der Quantenstatistik). Die Zustandssumme wird als Wigner-Kirkwood-Reihe nach Potenzen von h2 (semiklassische Entwicklung) dargestellt, und aus ihr werden die thermodynamischen Funktionen berechnet. Sämtliche Funktionen sind durch einfache geschlossene Formeln allein mit den modifizierten Hankel-Funktionen Ko und K1 des rein imaginären Arguments i mit = Vo/kT mit großer Genauigkeit darzustellen.

  3. Atmospheric corrosion: statistical validation of models

    International Nuclear Information System (INIS)

    Diaz, V.; Martinez-Luaces, V.; Guineo-Cobs, G.

    2003-01-01

    In this paper we discuss two different methods for validation of regression models, applied to corrosion data. One of them is based on the correlation coefficient and the other one is the statistical test of lack of fit. Both methods are used here to analyse fitting of bi logarithmic model in order to predict corrosion for very low carbon steel substrates in rural and urban-industrial atmospheres in Uruguay. Results for parameters A and n of the bi logarithmic model are reported here. For this purpose, all repeated values were used instead of using average values as usual. Modelling is carried out using experimental data corresponding to steel substrates under the same initial meteorological conditions ( in fact, they are put in the rack at the same time). Results of correlation coefficient are compared with the lack of it tested at two different signification levels (α=0.01 and α=0.05). Unexpected differences between them are explained and finally, it is possible to conclude, at least in the studied atmospheres, that the bi logarithmic model does not fit properly the experimental data. (Author) 18 refs

  4. Statistical analysis of AFM topographic images of self-assembled quantum dots

    Energy Technology Data Exchange (ETDEWEB)

    Sevriuk, V. A.; Brunkov, P. N., E-mail: brunkov@mail.ioffe.ru; Shalnev, I. V.; Gutkin, A. A.; Klimko, G. V.; Gronin, S. V.; Sorokin, S. V.; Konnikov, S. G. [Russian Academy of Sciences, Ioffe Physical-Technical Institute (Russian Federation)

    2013-07-15

    To obtain statistical data on quantum-dot sizes, AFM topographic images of the substrate on which the dots under study are grown are analyzed. Due to the nonideality of the substrate containing height differences on the order of the size of nanoparticles at distances of 1-10 {mu}m and the insufficient resolution of closely arranged dots due to the finite curvature radius of the AFM probe, automation of the statistical analysis of their large dot array requires special techniques for processing topographic images to eliminate the loss of a particle fraction during conventional processing. As such a technique, convolution of the initial matrix of the AFM image with a specially selected matrix is used. This makes it possible to determine the position of each nanoparticle and, using the initial matrix, to measure their geometrical parameters. The results of statistical analysis by this method of self-assembled InAs quantum dots formed on the surface of an AlGaAs epitaxial layer are presented. It is shown that their concentration, average size, and half-width of height distribution depend strongly on the In flow and total amount of deposited InAs which are varied within insignificant limits.

  5. Quantum tunneling in the adiabatic Dicke model

    International Nuclear Information System (INIS)

    Chen Gang; Chen Zidong; Liang Jiuqing

    2007-01-01

    The Dicke model describes N two-level atoms interacting with a single-mode bosonic field and exhibits a second-order phase transition from the normal to the superradiant phase. The energy levels are not degenerate in the normal phase but have degeneracy in the superradiant phase, where quantum tunneling occurs. By means of the Born-Oppenheimer approximation and the instanton method in quantum field theory, the tunneling splitting, inversely proportional to the tunneling rate for the adiabatic Dicke model, in the superradiant phase can be evaluated explicitly. It is shown that the tunneling splitting vanishes as exp(-N) for large N, whereas for small N it disappears as √(N)/exp(N). The dependence of the tunneling splitting on the relevant parameters, especially on the atom-field coupling strength, is also discussed

  6. Gauge invariant lattice quantum field theory: Implications for statistical properties of high frequency financial markets

    Science.gov (United States)

    Dupoyet, B.; Fiebig, H. R.; Musgrove, D. P.

    2010-01-01

    We report on initial studies of a quantum field theory defined on a lattice with multi-ladder geometry and the dilation group as a local gauge symmetry. The model is relevant in the cross-disciplinary area of econophysics. A corresponding proposal by Ilinski aimed at gauge modeling in non-equilibrium pricing is implemented in a numerical simulation. We arrive at a probability distribution of relative gains which matches the high frequency historical data of the NASDAQ stock exchange index.

  7. Universe before Planck time: A quantum gravity model

    International Nuclear Information System (INIS)

    Padmanabhan, T.

    1983-01-01

    A model for quantum gravity can be constructed by treating the conformal degree of freedom of spacetime as a quantum variable. An isotropic, homogeneous cosmological solution in this quantum gravity model is presented. The spacetime is nonsingular for all the three possible values of three-space curvature, and agrees with the classical solution for time scales larger than the Planck time scale. A possibility of quantum fluctuations creating the matter in the universe is suggested

  8. Spherical Process Models for Global Spatial Statistics

    KAUST Repository

    Jeong, Jaehong

    2017-11-28

    Statistical models used in geophysical, environmental, and climate science applications must reflect the curvature of the spatial domain in global data. Over the past few decades, statisticians have developed covariance models that capture the spatial and temporal behavior of these global data sets. Though the geodesic distance is the most natural metric for measuring distance on the surface of a sphere, mathematical limitations have compelled statisticians to use the chordal distance to compute the covariance matrix in many applications instead, which may cause physically unrealistic distortions. Therefore, covariance functions directly defined on a sphere using the geodesic distance are needed. We discuss the issues that arise when dealing with spherical data sets on a global scale and provide references to recent literature. We review the current approaches to building process models on spheres, including the differential operator, the stochastic partial differential equation, the kernel convolution, and the deformation approaches. We illustrate realizations obtained from Gaussian processes with different covariance structures and the use of isotropic and nonstationary covariance models through deformations and geographical indicators for global surface temperature data. To assess the suitability of each method, we compare their log-likelihood values and prediction scores, and we end with a discussion of related research problems.

  9. A statistical mechanical model of economics

    Science.gov (United States)

    Lubbers, Nicholas Edward Williams

    Statistical mechanics pursues low-dimensional descriptions of systems with a very large number of degrees of freedom. I explore this theme in two contexts. The main body of this dissertation explores and extends the Yard Sale Model (YSM) of economic transactions using a combination of simulations and theory. The YSM is a simple interacting model for wealth distributions which has the potential to explain the empirical observation of Pareto distributions of wealth. I develop the link between wealth condensation and the breakdown of ergodicity due to nonlinear diffusion effects which are analogous to the geometric random walk. Using this, I develop a deterministic effective theory of wealth transfer in the YSM that is useful for explaining many quantitative results. I introduce various forms of growth to the model, paying attention to the effect of growth on wealth condensation, inequality, and ergodicity. Arithmetic growth is found to partially break condensation, and geometric growth is found to completely break condensation. Further generalizations of geometric growth with growth in- equality show that the system is divided into two phases by a tipping point in the inequality parameter. The tipping point marks the line between systems which are ergodic and systems which exhibit wealth condensation. I explore generalizations of the YSM transaction scheme to arbitrary betting functions to develop notions of universality in YSM-like models. I find that wealth vi condensation is universal to a large class of models which can be divided into two phases. The first exhibits slow, power-law condensation dynamics, and the second exhibits fast, finite-time condensation dynamics. I find that the YSM, which exhibits exponential dynamics, is the critical, self-similar model which marks the dividing line between the two phases. The final chapter develops a low-dimensional approach to materials microstructure quantification. Modern materials design harnesses complex

  10. Statistical Exploration of Electronic Structure of Molecules from Quantum Monte-Carlo Simulations

    Energy Technology Data Exchange (ETDEWEB)

    Prabhat, Mr; Zubarev, Dmitry; Lester, Jr., William A.

    2010-12-22

    In this report, we present results from analysis of Quantum Monte Carlo (QMC) simulation data with the goal of determining internal structure of a 3N-dimensional phase space of an N-electron molecule. We are interested in mining the simulation data for patterns that might be indicative of the bond rearrangement as molecules change electronic states. We examined simulation output that tracks the positions of two coupled electrons in the singlet and triplet states of an H2 molecule. The electrons trace out a trajectory, which was analyzed with a number of statistical techniques. This project was intended to address the following scientific questions: (1) Do high-dimensional phase spaces characterizing electronic structure of molecules tend to cluster in any natural way? Do we see a change in clustering patterns as we explore different electronic states of the same molecule? (2) Since it is hard to understand the high-dimensional space of trajectories, can we project these trajectories to a lower dimensional subspace to gain a better understanding of patterns? (3) Do trajectories inherently lie in a lower-dimensional manifold? Can we recover that manifold? After extensive statistical analysis, we are now in a better position to respond to these questions. (1) We definitely see clustering patterns, and differences between the H2 and H2tri datasets. These are revealed by the pamk method in a fairly reliable manner and can potentially be used to distinguish bonded and non-bonded systems and get insight into the nature of bonding. (2) Projecting to a lower dimensional subspace ({approx}4-5) using PCA or Kernel PCA reveals interesting patterns in the distribution of scalar values, which can be related to the existing descriptors of electronic structure of molecules. Also, these results can be immediately used to develop robust tools for analysis of noisy data obtained during QMC simulations (3) All dimensionality reduction and estimation techniques that we tried seem to

  11. Topological quantum theories and integrable models

    International Nuclear Information System (INIS)

    Keski-Vakkuri, E.; Niemi, A.J.; Semenoff, G.; Tirkkonen, O.

    1991-01-01

    The path-integral generalization of the Duistermaat-Heckman integration formula is investigated for integrable models. It is shown that for models with periodic classical trajectories the path integral reduces to a form similar to the finite-dimensional Duistermaat-Heckman integration formula. This provides a relation between exactness of the stationary-phase approximation and Morse theory. It is also argued that certain integrable models can be related to topological quantum theories. Finally, it is found that in general the stationary-phase approximation presumes that the initial and final configurations are in different polarizations. This is exemplified by the quantization of the SU(2) coadjoint orbit

  12. Quantum mechanical models for the Fermi shuttle

    Science.gov (United States)

    Sternberg, James; Ovchinnikov, S. Yu.; Macek, J. H.

    2009-05-01

    Although the Fermi shuttle was originally proposed as an explanation for highly energetic cosmic rays, it is also a mechanism for the production of high energy electrons in atomic collisions [1]. The Fermi shuttle is usually thought of as a classical effect and most models of this process rely on classical or semi-classical approximations. In this work we explore several quantum mechanical models for ion-atom collisions and examine the evidence for the Fermi shuttle in these models. [4pt] [1] B. Sulik, Cs. Koncz, K. Tok'esi, A. Orb'an, and D. Ber'enyi, Phys Rev. Lett. 88 073201 (2002)

  13. Detection of beamsplitting attack in a quantum cryptographic channel based on photon number statistics monitoring

    International Nuclear Information System (INIS)

    Gaidash, A A; Egorov, V I; Gleim, A V

    2014-01-01

    Quantum cryptography in theory allows distributing secure keys between two users so that any performed eavesdropping attempt would be immediately discovered. However, in practice an eavesdropper can obtain key information from multi-photon states when attenuated laser radiation is used as a source. In order to overcome this possibility, it is generally suggested to implement special cryptographic protocols, like decoy states or SARG04. We present an alternative method based on monitoring photon number statistics after detection. This method can therefore be used with any existing protocol

  14. Quantum-statistical mechanics of an atom-dimer mixture: Lee-Yang cluster expansion approach

    International Nuclear Information System (INIS)

    Ohkuma, Takahiro; Ueda, Masahito

    2006-01-01

    We use the Lee-Yang cluster expansion method to study quantum-statistical properties of a mixture of interconvertible atoms and dimers, where the dimers form in a two-body bound state of the atoms. We point out an infinite series of cluster diagrams whose summation leads to the Bose-Einstein condensation of the dimers below a critical temperature. Our theory captures some important features of a cold atom-dimer mixture such as interconversion of atoms and dimers and properties of the mixture at the unitarity limit

  15. Understanding quantum measurement from the solution of dynamical models

    Energy Technology Data Exchange (ETDEWEB)

    Allahverdyan, Armen E. [Laboratoire de Physique Statistique et Systèmes Complexes, ISMANS, 44 Av. Bartholdi, 72000 Le Mans (France); Balian, Roger [Institut de Physique Théorique, CEA Saclay, 91191 Gif-sur-Yvette cedex (France); Nieuwenhuizen, Theo M., E-mail: T.M.Nieuwenhuizen@uva.nl [Center for Cosmology and Particle Physics, New York University, 4 Washington Place, New York, NY 10003 (United States)

    2013-04-15

    The quantum measurement problem, to wit, understanding why a unique outcome is obtained in each individual experiment, is currently tackled by solving models. After an introduction we review the many dynamical models proposed over the years for elucidating quantum measurements. The approaches range from standard quantum theory, relying for instance on quantum statistical mechanics or on decoherence, to quantum–classical methods, to consistent histories and to modifications of the theory. Next, a flexible and rather realistic quantum model is introduced, describing the measurement of the z-component of a spin through interaction with a magnetic memory simulated by a Curie–Weiss magnet, including N≫1 spins weakly coupled to a phonon bath. Initially prepared in a metastable paramagnetic state, it may transit to its up or down ferromagnetic state, triggered by its coupling with the tested spin, so that its magnetization acts as a pointer. A detailed solution of the dynamical equations is worked out, exhibiting several time scales. Conditions on the parameters of the model are found, which ensure that the process satisfies all the features of ideal measurements. Various imperfections of the measurement are discussed, as well as attempts of incompatible measurements. The first steps consist in the solution of the Hamiltonian dynamics for the spin-apparatus density matrix D{sup -hat} (t). Its off-diagonal blocks in a basis selected by the spin–pointer coupling, rapidly decay owing to the many degrees of freedom of the pointer. Recurrences are ruled out either by some randomness of that coupling, or by the interaction with the bath. On a longer time scale, the trend towards equilibrium of the magnet produces a final state D{sup -hat} (t{sub f}) that involves correlations between the system and the indications of the pointer, thus ensuring registration. Although D{sup -hat} (t{sub f}) has the form expected for ideal measurements, it only describes a large set of

  16. The Real and the Mathematical in Quantum Modeling: From Principles to Models and from Models to Principles

    Science.gov (United States)

    Plotnitsky, Arkady

    2017-06-01

    The history of mathematical modeling outside physics has been dominated by the use of classical mathematical models, C-models, primarily those of a probabilistic or statistical nature. More recently, however, quantum mathematical models, Q-models, based in the mathematical formalism of quantum theory have become more prominent in psychology, economics, and decision science. The use of Q-models in these fields remains controversial, in part because it is not entirely clear whether Q-models are necessary for dealing with the phenomena in question or whether C-models would still suffice. My aim, however, is not to assess the necessity of Q-models in these fields, but instead to reflect on what the possible applicability of Q-models may tell us about the corresponding phenomena there, vis-à-vis quantum phenomena in physics. In order to do so, I shall first discuss the key reasons for the use of Q-models in physics. In particular, I shall examine the fundamental principles that led to the development of quantum mechanics. Then I shall consider a possible role of similar principles in using Q-models outside physics. Psychology, economics, and decision science borrow already available Q-models from quantum theory, rather than derive them from their own internal principles, while quantum mechanics was derived from such principles, because there was no readily available mathematical model to handle quantum phenomena, although the mathematics ultimately used in quantum did in fact exist then. I shall argue, however, that the principle perspective on mathematical modeling outside physics might help us to understand better the role of Q-models in these fields and possibly to envision new models, conceptually analogous to but mathematically different from those of quantum theory, helpful or even necessary there or in physics itself. I shall suggest one possible type of such models, singularized probabilistic, SP, models, some of which are time-dependent, TDSP-models. The

  17. The Generalized Quantum Episodic Memory Model.

    Science.gov (United States)

    Trueblood, Jennifer S; Hemmer, Pernille

    2017-11-01

    Recent evidence suggests that experienced events are often mapped to too many episodic states, including those that are logically or experimentally incompatible with one another. For example, episodic over-distribution patterns show that the probability of accepting an item under different mutually exclusive conditions violates the disjunction rule. A related example, called subadditivity, occurs when the probability of accepting an item under mutually exclusive and exhaustive instruction conditions sums to a number >1. Both the over-distribution effect and subadditivity have been widely observed in item and source-memory paradigms. These phenomena are difficult to explain using standard memory frameworks, such as signal-detection theory. A dual-trace model called the over-distribution (OD) model (Brainerd & Reyna, 2008) can explain the episodic over-distribution effect, but not subadditivity. Our goal is to develop a model that can explain both effects. In this paper, we propose the Generalized Quantum Episodic Memory (GQEM) model, which extends the Quantum Episodic Memory (QEM) model developed by Brainerd, Wang, and Reyna (2013). We test GQEM by comparing it to the OD model using data from a novel item-memory experiment and a previously published source-memory experiment (Kellen, Singmann, & Klauer, 2014) examining the over-distribution effect. Using the best-fit parameters from the over-distribution experiments, we conclude by showing that the GQEM model can also account for subadditivity. Overall these results add to a growing body of evidence suggesting that quantum probability theory is a valuable tool in modeling recognition memory. Copyright © 2016 Cognitive Science Society, Inc.

  18. Statistical model for OCT image denoising

    KAUST Repository

    Li, Muxingzi

    2017-08-01

    Optical coherence tomography (OCT) is a non-invasive technique with a large array of applications in clinical imaging and biological tissue visualization. However, the presence of speckle noise affects the analysis of OCT images and their diagnostic utility. In this article, we introduce a new OCT denoising algorithm. The proposed method is founded on a numerical optimization framework based on maximum-a-posteriori estimate of the noise-free OCT image. It combines a novel speckle noise model, derived from local statistics of empirical spectral domain OCT (SD-OCT) data, with a Huber variant of total variation regularization for edge preservation. The proposed approach exhibits satisfying results in terms of speckle noise reduction as well as edge preservation, at reduced computational cost.

  19. Quantum Statistical Entropy of Non-extreme and Nearly Extreme Black Holes in Higher-Dimensional Space-Time

    Institute of Scientific and Technical Information of China (English)

    XU Dian-Yan

    2003-01-01

    The free energy and entropy of Reissner-Nordstrom black holes in higher-dimensional space-time are calculated by the quantum statistic method with a brick wall model. The space-time of the black holes is divided into three regions: region 1, (r > r0); region 2, (r0 > r > n); and region 3, (T-J > r > 0), where r0 is the radius of the outer event horizon, and r, is the radius of the inner event horizon. Detailed calculation shows that the entropy contributed by region 2 is zero, the entropy contributed by region 1 is positive and proportional to the outer event horizon area, the entropy contributed by region 3 is negative and proportional to the inner event horizon area. The total entropy contributed by all the three regions is positive and proportional to the area difference between the outer and inner event horizons. As rt approaches r0 in the nearly extreme case, the total quantum statistical entropy approaches zero.

  20. The determinants of bond angle variability in protein/peptide backbones: A comprehensive statistical/quantum mechanics analysis.

    Science.gov (United States)

    Improta, Roberto; Vitagliano, Luigi; Esposito, Luciana

    2015-11-01

    The elucidation of the mutual influence between peptide bond geometry and local conformation has important implications for protein structure refinement, validation, and prediction. To gain insights into the structural determinants and the energetic contributions associated with protein/peptide backbone plasticity, we here report an extensive analysis of the variability of the peptide bond angles by combining statistical analyses of protein structures and quantum mechanics calculations on small model peptide systems. Our analyses demonstrate that all the backbone bond angles strongly depend on the peptide conformation and unveil the existence of regular trends as function of ψ and/or φ. The excellent agreement of the quantum mechanics calculations with the statistical surveys of protein structures validates the computational scheme here employed and demonstrates that the valence geometry of protein/peptide backbone is primarily dictated by local interactions. Notably, for the first time we show that the position of the H(α) hydrogen atom, which is an important parameter in NMR structural studies, is also dependent on the local conformation. Most of the trends observed may be satisfactorily explained by invoking steric repulsive interactions; in some specific cases the valence bond variability is also influenced by hydrogen-bond like interactions. Moreover, we can provide a reliable estimate of the energies involved in the interplay between geometry and conformations. © 2015 Wiley Periodicals, Inc.

  1. Quantum statistics for a two-mode magnon system with microwave pumping: application to coupled ferromagnetic nanowires.

    Science.gov (United States)

    Haghshenasfard, Zahra; Cottam, M G

    2017-05-17

    A microscopic (Hamiltonian-based) method for the quantum statistics of bosonic excitations in a two-mode magnon system is developed. Both the exchange and the dipole-dipole interactions, as well as the Zeeman term for an external applied field, are included in the spin Hamiltonian, and the model also contains the nonlinear effects due to parallel pumping and four-magnon interactions. The quantization of spin operators is achieved through the Holstein-Primakoff formalism, and then a coherent magnon state representation is used to study the occupation magnon number and the quantum statistical behaviour of the system. Particular attention is given to the cross correlation between the two coupled magnon modes in a ferromagnetic nanowire geometry formed by two lines of spins. Manipulation of the collapse-and-revival phenomena for the temporal evolution of the magnon number as well as the control of the cross correlation between the two magnon modes is demonstrated by tuning the parallel pumping field amplitude. The role of the four-magnon interactions is particularly interesting and leads to anti-correlation in some cases with coherent states.

  2. Quantum statistics for a two-mode magnon system with microwave pumping: application to coupled ferromagnetic nanowires

    International Nuclear Information System (INIS)

    Haghshenasfard, Zahra; Cottam, M G

    2017-01-01

    A microscopic (Hamiltonian-based) method for the quantum statistics of bosonic excitations in a two-mode magnon system is developed. Both the exchange and the dipole–dipole interactions, as well as the Zeeman term for an external applied field, are included in the spin Hamiltonian, and the model also contains the nonlinear effects due to parallel pumping and four-magnon interactions. The quantization of spin operators is achieved through the Holstein–Primakoff formalism, and then a coherent magnon state representation is used to study the occupation magnon number and the quantum statistical behaviour of the system. Particular attention is given to the cross correlation between the two coupled magnon modes in a ferromagnetic nanowire geometry formed by two lines of spins. Manipulation of the collapse-and-revival phenomena for the temporal evolution of the magnon number as well as the control of the cross correlation between the two magnon modes is demonstrated by tuning the parallel pumping field amplitude. The role of the four-magnon interactions is particularly interesting and leads to anti-correlation in some cases with coherent states. (paper)

  3. Integrable models in 1+1 dimensional quantum field theory

    International Nuclear Information System (INIS)

    Faddeev, Ludvig.

    1982-09-01

    The goal of this lecture is to present a unifying view on the exactly soluble models. There exist several reasons arguing in favor of the 1+1 dimensional models: every exact solution of a field-theoretical model can teach about the ability of quantum field theory to describe spectrum and scattering; some 1+1 d models have physical applications in the solid state theory. There are several ways to become acquainted with the methods of exactly soluble models: via classical statistical mechanics, via Bethe Ansatz, via inverse scattering method. Fundamental Poisson bracket relation FPR and/or fundamental commutation relations FCR play fundamental role. General classification of FPR is given with promizing generalizations to FCR

  4. Modeling stock return distributions with a quantum harmonic oscillator

    Science.gov (United States)

    Ahn, K.; Choi, M. Y.; Dai, B.; Sohn, S.; Yang, B.

    2017-11-01

    We propose a quantum harmonic oscillator as a model for the market force which draws a stock return from short-run fluctuations to the long-run equilibrium. The stochastic equation governing our model is transformed into a Schrödinger equation, the solution of which features “quantized” eigenfunctions. Consequently, stock returns follow a mixed χ distribution, which describes Gaussian and non-Gaussian features. Analyzing the Financial Times Stock Exchange (FTSE) All Share Index, we demonstrate that our model outperforms traditional stochastic process models, e.g., the geometric Brownian motion and the Heston model, with smaller fitting errors and better goodness-of-fit statistics. In addition, making use of analogy, we provide an economic rationale of the physics concepts such as the eigenstate, eigenenergy, and angular frequency, which sheds light on the relationship between finance and econophysics literature.

  5. Information Graph Flow: A Geometric Approximation of Quantum and Statistical Systems

    Science.gov (United States)

    Vanchurin, Vitaly

    2018-05-01

    Given a quantum (or statistical) system with a very large number of degrees of freedom and a preferred tensor product factorization of the Hilbert space (or of a space of distributions) we describe how it can be approximated with a very low-dimensional field theory with geometric degrees of freedom. The geometric approximation procedure consists of three steps. The first step is to construct weighted graphs (we call information graphs) with vertices representing subsystems (e.g., qubits or random variables) and edges representing mutual information (or the flow of information) between subsystems. The second step is to deform the adjacency matrices of the information graphs to that of a (locally) low-dimensional lattice using the graph flow equations introduced in the paper. (Note that the graph flow produces very sparse adjacency matrices and thus might also be used, for example, in machine learning or network science where the task of graph sparsification is of a central importance.) The third step is to define an emergent metric and to derive an effective description of the metric and possibly other degrees of freedom. To illustrate the procedure we analyze (numerically and analytically) two information graph flows with geometric attractors (towards locally one- and two-dimensional lattices) and metric perturbations obeying a geometric flow equation. Our analysis also suggests a possible approach to (a non-perturbative) quantum gravity in which the geometry (a secondary object) emerges directly from a quantum state (a primary object) due to the flow of the information graphs.

  6. New advances in statistical modeling and applications

    CERN Document Server

    Santos, Rui; Oliveira, Maria; Paulino, Carlos

    2014-01-01

    This volume presents selected papers from the XIXth Congress of the Portuguese Statistical Society, held in the town of Nazaré, Portugal, from September 28 to October 1, 2011. All contributions were selected after a thorough peer-review process. It covers a broad range of papers in the areas of statistical science, probability and stochastic processes, extremes and statistical applications.

  7. Quantum Bohmian model for financial market

    Science.gov (United States)

    Choustova, Olga Al.

    2007-01-01

    We apply methods of quantum mechanics for mathematical modeling of price dynamics at the financial market. The Hamiltonian formalism on the price/price-change phase space describes the classical-like evolution of prices. This classical dynamics of prices is determined by “hard” conditions (natural resources, industrial production, services and so on). These conditions are mathematically described by the classical financial potential V(q), where q=(q1,…,qn) is the vector of prices of various shares. But the information exchange and market psychology play important (and sometimes determining) role in price dynamics. We propose to describe such behavioral financial factors by using the pilot wave (Bohmian) model of quantum mechanics. The theory of financial behavioral waves takes into account the market psychology. The real trajectories of prices are determined (through the financial analogue of the second Newton law) by two financial potentials: classical-like V(q) (“hard” market conditions) and quantum-like U(q) (behavioral market conditions).

  8. Coherent nonlinear quantum model for composite fermions

    Energy Technology Data Exchange (ETDEWEB)

    Reinisch, Gilbert [Science Institute, University of Iceland, Dunhaga 3, IS-107 Reykjavik (Iceland); Gudmundsson, Vidar, E-mail: vidar@hi.is [Science Institute, University of Iceland, Dunhaga 3, IS-107 Reykjavik (Iceland); Manolescu, Andrei [School of Science and Engineering, Reykjavik University, Menntavegur 1, IS-101 Reykjavik (Iceland)

    2014-04-01

    Originally proposed by Read [1] and Jain [2], the so-called “composite-fermion” is a phenomenological quasi-particle resulting from the attachment of two local flux quanta, seen as nonlocal vortices, to electrons situated on a two-dimensional (2D) surface embedded in a strong orthogonal magnetic field. In this Letter this phenomenon is described as a highly-nonlinear and coherent mean-field quantum process of the soliton type by use of a 2D stationary Schrödinger–Poisson differential model with only two Coulomb-interacting electrons. At filling factor ν=1/3 of the lowest Landau level the solution agrees with both the exact two-electron antisymmetric Schrödinger wavefunction and with Laughlin's Jastrow-type guess for the fractional quantum Hall effect, hence providing this latter with a tentative physical justification deduced from the experimental results and based on first principles.

  9. A probability space for quantum models

    Science.gov (United States)

    Lemmens, L. F.

    2017-06-01

    A probability space contains a set of outcomes, a collection of events formed by subsets of the set of outcomes and probabilities defined for all events. A reformulation in terms of propositions allows to use the maximum entropy method to assign the probabilities taking some constraints into account. The construction of a probability space for quantum models is determined by the choice of propositions, choosing the constraints and making the probability assignment by the maximum entropy method. This approach shows, how typical quantum distributions such as Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein are partly related with well-known classical distributions. The relation between the conditional probability density, given some averages as constraints and the appropriate ensemble is elucidated.

  10. Quantum ergodicity in the SYK model

    Science.gov (United States)

    Altland, Alexander; Bagrets, Dmitry

    2018-05-01

    We present a replica path integral approach describing the quantum chaotic dynamics of the SYK model at large time scales. The theory leads to the identification of non-ergodic collective modes which relax and eventually give way to an ergodic long time regime (describable by random matrix theory). These modes, which play a role conceptually similar to the diffusion modes of dirty metals, carry quantum numbers which we identify as the generators of the Clifford algebra: each of the 2N different products that can be formed from N Majorana operators defines one effective mode. The competition between a decay rate quickly growing in the order of the product and a density of modes exponentially growing in the same parameter explains the characteristics of the system's approach to the ergodic long time regime. We probe this dynamics through various spectral correlation functions and obtain favorable agreement with existing numerical data.

  11. A statistical model for predicting muscle performance

    Science.gov (United States)

    Byerly, Diane Leslie De Caix

    The objective of these studies was to develop a capability for predicting muscle performance and fatigue to be utilized for both space- and ground-based applications. To develop this predictive model, healthy test subjects performed a defined, repetitive dynamic exercise to failure using a Lordex spinal machine. Throughout the exercise, surface electromyography (SEMG) data were collected from the erector spinae using a Mega Electronics ME3000 muscle tester and surface electrodes placed on both sides of the back muscle. These data were analyzed using a 5th order Autoregressive (AR) model and statistical regression analysis. It was determined that an AR derived parameter, the mean average magnitude of AR poles, significantly correlated with the maximum number of repetitions (designated Rmax) that a test subject was able to perform. Using the mean average magnitude of AR poles, a test subject's performance to failure could be predicted as early as the sixth repetition of the exercise. This predictive model has the potential to provide a basis for improving post-space flight recovery, monitoring muscle atrophy in astronauts and assessing the effectiveness of countermeasures, monitoring astronaut performance and fatigue during Extravehicular Activity (EVA) operations, providing pre-flight assessment of the ability of an EVA crewmember to perform a given task, improving the design of training protocols and simulations for strenuous International Space Station assembly EVA, and enabling EVA work task sequences to be planned enhancing astronaut performance and safety. Potential ground-based, medical applications of the predictive model include monitoring muscle deterioration and performance resulting from illness, establishing safety guidelines in the industry for repetitive tasks, monitoring the stages of rehabilitation for muscle-related injuries sustained in sports and accidents, and enhancing athletic performance through improved training protocols while reducing

  12. Quantum interference vs. quantum chaos in the nuclear shell model

    International Nuclear Information System (INIS)

    Fernández, Gerardo; Hautefeuille, M; Velázquez, V; Hernández, Edna M; Landa, E; Morales, I O; Frank, A; Fossion, R; Vargas, C E

    2015-01-01

    In this paper we study the complexity of the nuclear states in terms of a two body quadupole-quadrupole interaction. Energy distributions and eigenvectors composition exhibit a visible interference pattern which is dependent on the intensity of the interaction. In analogy with optics, the visibility of the interference is related to the purity of the states, therefore, we show that the fluctuations associated with quantum chaos have as their origin the remaining quantum coherence with a visibility magnitude close to 5%

  13. Statistical Model Checking of Rich Models and Properties

    DEFF Research Database (Denmark)

    Poulsen, Danny Bøgsted

    in undecidability issues for the traditional model checking approaches. Statistical model checking has proven itself a valuable supplement to model checking and this thesis is concerned with extending this software validation technique to stochastic hybrid systems. The thesis consists of two parts: the first part...... motivates why existing model checking technology should be supplemented by new techniques. It also contains a brief introduction to probability theory and concepts covered by the six papers making up the second part. The first two papers are concerned with developing online monitoring techniques...... systems. The fifth paper shows how stochastic hybrid automata are useful for modelling biological systems and the final paper is concerned with showing how statistical model checking is efficiently distributed. In parallel with developing the theory contained in the papers, a substantial part of this work...

  14. Critical, statistical, and thermodynamical properties of lattice models

    Energy Technology Data Exchange (ETDEWEB)

    Varma, Vipin Kerala

    2013-10-15

    In this thesis we investigate zero temperature and low temperature properties - critical, statistical and thermodynamical - of lattice models in the contexts of bosonic cold atom systems, magnetic materials, and non-interacting particles on various lattice geometries. We study quantum phase transitions in the Bose-Hubbard model with higher body interactions, as relevant for optical lattice experiments of strongly interacting bosons, in one and two dimensions; the universality of the Mott insulator to superfluid transition is found to remain unchanged for even large three body interaction strengths. A systematic renormalization procedure is formulated to fully re-sum these higher (three and four) body interactions into the two body terms. In the strongly repulsive limit, we analyse the zero and low temperature physics of interacting hard-core bosons on the kagome lattice at various fillings. Evidence for a disordered phase in the Ising limit of the model is presented; in the strong coupling limit, the transition between the valence bond solid and the superfluid is argued to be first order at the tip of the solid lobe.

  15. Critical, statistical, and thermodynamical properties of lattice models

    International Nuclear Information System (INIS)

    Varma, Vipin Kerala

    2013-10-01

    In this thesis we investigate zero temperature and low temperature properties - critical, statistical and thermodynamical - of lattice models in the contexts of bosonic cold atom systems, magnetic materials, and non-interacting particles on various lattice geometries. We study quantum phase transitions in the Bose-Hubbard model with higher body interactions, as relevant for optical lattice experiments of strongly interacting bosons, in one and two dimensions; the universality of the Mott insulator to superfluid transition is found to remain unchanged for even large three body interaction strengths. A systematic renormalization procedure is formulated to fully re-sum these higher (three and four) body interactions into the two body terms. In the strongly repulsive limit, we analyse the zero and low temperature physics of interacting hard-core bosons on the kagome lattice at various fillings. Evidence for a disordered phase in the Ising limit of the model is presented; in the strong coupling limit, the transition between the valence bond solid and the superfluid is argued to be first order at the tip of the solid lobe.

  16. Are quantum-mechanical-like models possible, or necessary, outside quantum physics?

    International Nuclear Information System (INIS)

    Plotnitsky, Arkady

    2014-01-01

    This article examines some experimental conditions that invite and possibly require recourse to quantum-mechanical-like mathematical models (QMLMs), models based on the key mathematical features of quantum mechanics, in scientific fields outside physics, such as biology, cognitive psychology, or economics. In particular, I consider whether the following two correlative features of quantum phenomena that were decisive for establishing the mathematical formalism of quantum mechanics play similarly important roles in QMLMs elsewhere. The first is the individuality and discreteness of quantum phenomena, and the second is the irreducibly probabilistic nature of our predictions concerning them, coupled to the particular character of the probabilities involved, as different from the character of probabilities found in classical physics. I also argue that these features could be interpreted in terms of a particular form of epistemology that suspends and even precludes a causal and, in the first place, realist description of quantum objects and processes. This epistemology limits the descriptive capacity of quantum theory to the description, classical in nature, of the observed quantum phenomena manifested in measuring instruments. Quantum mechanics itself only provides descriptions, probabilistic in nature, concerning numerical data pertaining to such phenomena, without offering a physical description of quantum objects and processes. While QMLMs share their use of the quantum-mechanical or analogous mathematical formalism, they may differ by the roles, if any, the two features in question play in them and by different ways of interpreting the phenomena they considered and this formalism itself. This article will address those differences as well. (paper)

  17. Rank-based model selection for multiple ions quantum tomography

    International Nuclear Information System (INIS)

    Guţă, Mădălin; Kypraios, Theodore; Dryden, Ian

    2012-01-01

    The statistical analysis of measurement data has become a key component of many quantum engineering experiments. As standard full state tomography becomes unfeasible for large dimensional quantum systems, one needs to exploit prior information and the ‘sparsity’ properties of the experimental state in order to reduce the dimensionality of the estimation problem. In this paper we propose model selection as a general principle for finding the simplest, or most parsimonious explanation of the data, by fitting different models and choosing the estimator with the best trade-off between likelihood fit and model complexity. We apply two well established model selection methods—the Akaike information criterion (AIC) and the Bayesian information criterion (BIC)—two models consisting of states of fixed rank and datasets such as are currently produced in multiple ions experiments. We test the performance of AIC and BIC on randomly chosen low rank states of four ions, and study the dependence of the selected rank with the number of measurement repetitions for one ion states. We then apply the methods to real data from a four ions experiment aimed at creating a Smolin state of rank 4. By applying the two methods together with the Pearson χ 2 test we conclude that the data can be suitably described with a model whose rank is between 7 and 9. Additionally we find that the mean square error of the maximum likelihood estimator for pure states is close to that of the optimal over all possible measurements. (paper)

  18. Quantum modeling of ultrafast photoinduced charge separation

    Science.gov (United States)

    Rozzi, Carlo Andrea; Troiani, Filippo; Tavernelli, Ivano

    2018-01-01

    Phenomena involving electron transfer are ubiquitous in nature, photosynthesis and enzymes or protein activity being prominent examples. Their deep understanding thus represents a mandatory scientific goal. Moreover, controlling the separation of photogenerated charges is a crucial prerequisite in many applicative contexts, including quantum electronics, photo-electrochemical water splitting, photocatalytic dye degradation, and energy conversion. In particular, photoinduced charge separation is the pivotal step driving the storage of sun light into electrical or chemical energy. If properly mastered, these processes may also allow us to achieve a better command of information storage at the nanoscale, as required for the development of molecular electronics, optical switching, or quantum technologies, amongst others. In this Topical Review we survey recent progress in the understanding of ultrafast charge separation from photoexcited states. We report the state-of-the-art of the observation and theoretical description of charge separation phenomena in the ultrafast regime mainly focusing on molecular- and nano-sized solar energy conversion systems. In particular, we examine different proposed mechanisms driving ultrafast charge dynamics, with particular regard to the role of quantum coherence and electron-nuclear coupling, and link experimental observations to theoretical approaches based either on model Hamiltonians or on first principles simulations.

  19. Quantum measurement as a driven phase transition: An exactly solvable model

    NARCIS (Netherlands)

    Allahverdyan, A.; Balian, R.

    2001-01-01

    A model of quantum measurement is proposed, which aims to describe statistical mechanical aspects of this phenomenon, starting from a purely Hamiltonian formulation. The macroscopic measurement apparatus is modeled as an ideal Bose gas, the order parameter of which, that is, the amplitude of the

  20. Network Data: Statistical Theory and New Models

    Science.gov (United States)

    2016-02-17

    and with environmental scientists at JPL and Emory University to retrieval from NASA MISR remote sensing images aerosol index AOD for air pollution ...Beijing, May, 2013 Beijing Statistics Forum, Beijing, May, 2013 Statistics Seminar, CREST-ENSAE, Paris , March, 2013 Statistics Seminar, University...to retrieval from NASA MISR remote sensing images aerosol index AOD for air pollution monitoring and management. Satellite- retrieved Aerosol Optical

  1. Exact infinite-time statistics of the Loschmidt echo for a quantum quench.

    Science.gov (United States)

    Campos Venuti, Lorenzo; Jacobson, N Tobias; Santra, Siddhartha; Zanardi, Paolo

    2011-07-01

    The equilibration dynamics of a closed quantum system is encoded in the long-time distribution function of generic observables. In this Letter we consider the Loschmidt echo generalized to finite temperature, and show that we can obtain an exact expression for its long-time distribution for a closed system described by a quantum XY chain following a sudden quench. In the thermodynamic limit the logarithm of the Loschmidt echo becomes normally distributed, whereas for small quenches in the opposite, quasicritical regime, the distribution function acquires a universal double-peaked form indicating poor equilibration. These findings, obtained by a central limit theorem-type result, extend to completely general models in the small-quench regime.

  2. Statistical analysis of error rate of large-scale single flux quantum logic circuit by considering fluctuation of timing parameters

    International Nuclear Information System (INIS)

    Yamanashi, Yuki; Masubuchi, Kota; Yoshikawa, Nobuyuki

    2016-01-01

    The relationship between the timing margin and the error rate of the large-scale single flux quantum logic circuits is quantitatively investigated to establish a timing design guideline. We observed that the fluctuation in the set-up/hold time of single flux quantum logic gates caused by thermal noises is the most probable origin of the logical error of the large-scale single flux quantum circuit. The appropriate timing margin for stable operation of the large-scale logic circuit is discussed by taking the fluctuation of setup/hold time and the timing jitter in the single flux quantum circuits. As a case study, the dependence of the error rate of the 1-million-bit single flux quantum shift register on the timing margin is statistically analyzed. The result indicates that adjustment of timing margin and the bias voltage is important for stable operation of a large-scale SFQ logic circuit.

  3. Statistical analysis of error rate of large-scale single flux quantum logic circuit by considering fluctuation of timing parameters

    Energy Technology Data Exchange (ETDEWEB)

    Yamanashi, Yuki, E-mail: yamanasi@ynu.ac.jp [Department of Electrical and Computer Engineering, Yokohama National University, Tokiwadai 79-5, Hodogaya-ku, Yokohama 240-8501 (Japan); Masubuchi, Kota; Yoshikawa, Nobuyuki [Department of Electrical and Computer Engineering, Yokohama National University, Tokiwadai 79-5, Hodogaya-ku, Yokohama 240-8501 (Japan)

    2016-11-15

    The relationship between the timing margin and the error rate of the large-scale single flux quantum logic circuits is quantitatively investigated to establish a timing design guideline. We observed that the fluctuation in the set-up/hold time of single flux quantum logic gates caused by thermal noises is the most probable origin of the logical error of the large-scale single flux quantum circuit. The appropriate timing margin for stable operation of the large-scale logic circuit is discussed by taking the fluctuation of setup/hold time and the timing jitter in the single flux quantum circuits. As a case study, the dependence of the error rate of the 1-million-bit single flux quantum shift register on the timing margin is statistically analyzed. The result indicates that adjustment of timing margin and the bias voltage is important for stable operation of a large-scale SFQ logic circuit.

  4. Analytical eigenstates for the quantum Rabi model

    International Nuclear Information System (INIS)

    Zhong, Honghua; Xie, Qiongtao; Lee, Chaohong; Batchelor, Murray T

    2013-01-01

    We develop a method to find analytical solutions for the eigenstates of the quantum Rabi model. These include symmetric, anti-symmetric and asymmetric analytic solutions given in terms of the confluent Heun functions. Both regular and exceptional solutions are given in a unified form. In addition, the analytic conditions for determining the energy spectrum are obtained. Our results show that conditions proposed by Braak (2011 Phys. Rev. Lett. 107 100401) are a type of sufficiency condition for determining the regular solutions. The well-known Judd isolated exact solutions appear naturally as truncations of the confluent Heun functions. (paper)

  5. Rabi model as a quantum coherent heat engine: From quantum biology to superconducting circuits

    Science.gov (United States)

    Altintas, Ferdi; Hardal, Ali Ü. C.; Müstecaplıoǧlu, Özgür E.

    2015-02-01

    We propose a multilevel quantum heat engine with a working medium described by a generalized Rabi model which consists of a two-level system coupled to a single-mode bosonic field. The model is constructed to be a continuum limit of a quantum biological description of light-harvesting complexes so that it can amplify quantum coherence by a mechanism which is a quantum analog of classical Huygens clocks. The engine operates in a quantum Otto cycle where the working medium is coupled to classical heat baths in the isochoric processes of the four-stroke cycle, while either the coupling strength or the resonance frequency is changed in the adiabatic stages. We found that such an engine can produce work with an efficiency close to the Carnot bound when it operates at low temperatures and in the ultrastrong-coupling regime. The interplay of the effects of quantum coherence and quantum correlations on the engine performance is discussed in terms of second-order coherence, quantum mutual information, and the logarithmic negativity of entanglement. We point out that the proposed quantum Otto engine can be implemented experimentally with modern circuit quantum electrodynamic systems where flux qubits can be coupled ultrastrongly to superconducting transmission-line resonators.

  6. Modeling of the quantum dot filling and the dark current of quantum dot infrared photodetectors

    International Nuclear Information System (INIS)

    Ameen, Tarek A.; El-Batawy, Yasser M.; Abouelsaood, A. A.

    2014-01-01

    A generalized drift-diffusion model for the calculation of both the quantum dot filling profile and the dark current of quantum dot infrared photodetectors is proposed. The confined electrons inside the quantum dots produce a space-charge potential barrier between the two contacts, which controls the quantum dot filling and limits the dark current in the device. The results of the model reasonably agree with a published experimental work. It is found that increasing either the doping level or the temperature results in an exponential increase of the dark current. The quantum dot filling turns out to be nonuniform, with a dot near the contacts containing more electrons than one in the middle of the device where the dot occupation approximately equals the number of doping atoms per dot, which means that quantum dots away from contacts will be nearly unoccupied if the active region is undoped

  7. Thue-Morse quantum Ising model

    International Nuclear Information System (INIS)

    Doria, M.M.; Nori, F.; Satija, I.I.

    1989-01-01

    We study the one-dimensional quantum Ising model in a transverse magnetic field where the exchange couplings are ordered according to the Thue-Morse (TM) sequence. At zero temperature, this model is equivalent to a two-dimensional classical Ising model in a magnetic field with TM aperiodicity along one direction. We compute the order parameter (magnetization) of the chain and the scaling behavior of the energy spectrum when the system undergoes a phase transition. Analogous to the quasiperiodic (QP) quantum Ising chain, the onset of long-range order is signaled by a nonanaliticity in the exponent δ which describes the scaling of the total bandwidth with the size of the chain. The critical spin-coupling can be computed analytically and it is found to be lower than the QP case. Furthermore, the energy bands are found to be narrower than the corresponding QP chain. The former and latter results are consistent with the fact that the present structure has a degree of ordering intermediate between QP and random

  8. Quantum Simulation of the Quantum Rabi Model in a Trapped Ion

    Science.gov (United States)

    Lv, Dingshun; An, Shuoming; Liu, Zhenyu; Zhang, Jing-Ning; Pedernales, Julen S.; Lamata, Lucas; Solano, Enrique; Kim, Kihwan

    2018-04-01

    The quantum Rabi model, involving a two-level system and a bosonic field mode, is arguably the simplest and most fundamental model describing quantum light-matter interactions. Historically, due to the restricted parameter regimes of natural light-matter processes, the richness of this model has been elusive in the lab. Here, we experimentally realize a quantum simulation of the quantum Rabi model in a single trapped ion, where the coupling strength between the simulated light mode and atom can be tuned at will. The versatility of the demonstrated quantum simulator enables us to experimentally explore the quantum Rabi model in detail, including a wide range of otherwise unaccessible phenomena, as those happening in the ultrastrong and deep strong-coupling regimes. In this sense, we are able to adiabatically generate the ground state of the quantum Rabi model in the deep strong-coupling regime, where we are able to detect the nontrivial entanglement between the bosonic field mode and the two-level system. Moreover, we observe the breakdown of the rotating-wave approximation when the coupling strength is increased, and the generation of phonon wave packets that bounce back and forth when the coupling reaches the deep strong-coupling regime. Finally, we also measure the energy spectrum of the quantum Rabi model in the ultrastrong-coupling regime.

  9. Quantum Simulation of the Quantum Rabi Model in a Trapped Ion

    Directory of Open Access Journals (Sweden)

    Dingshun Lv

    2018-04-01

    Full Text Available The quantum Rabi model, involving a two-level system and a bosonic field mode, is arguably the simplest and most fundamental model describing quantum light-matter interactions. Historically, due to the restricted parameter regimes of natural light-matter processes, the richness of this model has been elusive in the lab. Here, we experimentally realize a quantum simulation of the quantum Rabi model in a single trapped ion, where the coupling strength between the simulated light mode and atom can be tuned at will. The versatility of the demonstrated quantum simulator enables us to experimentally explore the quantum Rabi model in detail, including a wide range of otherwise unaccessible phenomena, as those happening in the ultrastrong and deep strong-coupling regimes. In this sense, we are able to adiabatically generate the ground state of the quantum Rabi model in the deep strong-coupling regime, where we are able to detect the nontrivial entanglement between the bosonic field mode and the two-level system. Moreover, we observe the breakdown of the rotating-wave approximation when the coupling strength is increased, and the generation of phonon wave packets that bounce back and forth when the coupling reaches the deep strong-coupling regime. Finally, we also measure the energy spectrum of the quantum Rabi model in the ultrastrong-coupling regime.

  10. Quantum Brownian motion in a bath of parametric oscillators: A model for system-field interactions

    International Nuclear Information System (INIS)

    Hu, B.L.; Matacz, A.

    1994-01-01

    The quantum Brownian motion paradigm provides a unified framework where one can see the interconnection of some basic quantum statistical processes such as decoherence, dissipation, particle creation, noise, and fluctuation. The present paper continues the investigation begun in earlier papers on the quantum Brownian motion in a general environment via the influence functional formalism. Here, the Brownian particle is coupled linearly to a bath of the most general time-dependent quadratic oscillators. This bath of parametric oscillators minics a scalar field, while the motion of the Brownian particle modeled by a single oscillator could be used to depict the behavior of a particle detector, a quantum field mode, or the scale factor of the Universe. An important result of this paper is the derivation of the influence functional encompassing the noise and dissipation kernels in terms of the Bogolubov coefficients, thus setting the stage for the influence functional formalism treatment of problems in quantum field theory in curved spacetime. This method enables one to trace the source of statistical processes such as decoherence and dissipation to vacuum fluctuations and particle creation, and in turn impart a statistical mechanical interpretation of quantum field processes. With this result we discuss the statistical mechanical origin of quantum noise and thermal radiance from black holes and from uniformly accelerated observers in Minkowski space as well as from the de Sitter universe discovered by Hawking, Unruh, and Gibbons and Hawking. We also derive the exact evolution operator and master equation for the reduced density matrix of the system interacting with a parametric oscillator bath in an initial squeezed thermal state. These results are useful for decoherence and back reaction studies for systems and processes of interest in semiclassical cosmology and gravity. Our model and results are also expected to be useful for related problems in quantum optics

  11. Quantum Brownian motion model for the stock market

    Science.gov (United States)

    Meng, Xiangyi; Zhang, Jian-Wei; Guo, Hong

    2016-06-01

    It is believed by the majority today that the efficient market hypothesis is imperfect because of market irrationality. Using the physical concepts and mathematical structures of quantum mechanics, we construct an econophysical framework for the stock market, based on which we analogously map massive numbers of single stocks into a reservoir consisting of many quantum harmonic oscillators and their stock index into a typical quantum open system-a quantum Brownian particle. In particular, the irrationality of stock transactions is quantitatively considered as the Planck constant within Heisenberg's uncertainty relationship of quantum mechanics in an analogous manner. We analyze real stock data of Shanghai Stock Exchange of China and investigate fat-tail phenomena and non-Markovian behaviors of the stock index with the assistance of the quantum Brownian motion model, thereby interpreting and studying the limitations of the classical Brownian motion model for the efficient market hypothesis from a new perspective of quantum open system dynamics.

  12. A BRDF statistical model applying to space target materials modeling

    Science.gov (United States)

    Liu, Chenghao; Li, Zhi; Xu, Can; Tian, Qichen

    2017-10-01

    In order to solve the problem of poor effect in modeling the large density BRDF measured data with five-parameter semi-empirical model, a refined statistical model of BRDF which is suitable for multi-class space target material modeling were proposed. The refined model improved the Torrance-Sparrow model while having the modeling advantages of five-parameter model. Compared with the existing empirical model, the model contains six simple parameters, which can approximate the roughness distribution of the material surface, can approximate the intensity of the Fresnel reflectance phenomenon and the attenuation of the reflected light's brightness with the azimuth angle changes. The model is able to achieve parameter inversion quickly with no extra loss of accuracy. The genetic algorithm was used to invert the parameters of 11 different samples in the space target commonly used materials, and the fitting errors of all materials were below 6%, which were much lower than those of five-parameter model. The effect of the refined model is verified by comparing the fitting results of the three samples at different incident zenith angles in 0° azimuth angle. Finally, the three-dimensional modeling visualizations of these samples in the upper hemisphere space was given, in which the strength of the optical scattering of different materials could be clearly shown. It proved the good describing ability of the refined model at the material characterization as well.

  13. Statistical Challenges in Modeling Big Brain Signals

    KAUST Repository

    Yu, Zhaoxia

    2017-11-01

    Brain signal data are inherently big: massive in amount, complex in structure, and high in dimensions. These characteristics impose great challenges for statistical inference and learning. Here we review several key challenges, discuss possible solutions, and highlight future research directions.

  14. Statistical Challenges in Modeling Big Brain Signals

    KAUST Repository

    Yu, Zhaoxia; Pluta, Dustin; Shen, Tong; Chen, Chuansheng; Xue, Gui; Ombao, Hernando

    2017-01-01

    Brain signal data are inherently big: massive in amount, complex in structure, and high in dimensions. These characteristics impose great challenges for statistical inference and learning. Here we review several key challenges, discuss possible

  15. Statistical Learning Theory: Models, Concepts, and Results

    OpenAIRE

    von Luxburg, Ulrike; Schoelkopf, Bernhard

    2008-01-01

    Statistical learning theory provides the theoretical basis for many of today's machine learning algorithms. In this article we attempt to give a gentle, non-technical overview over the key ideas and insights of statistical learning theory. We target at a broad audience, not necessarily machine learning researchers. This paper can serve as a starting point for people who want to get an overview on the field before diving into technical details.

  16. Spin foam models for quantum gravity

    Science.gov (United States)

    Perez, Alejandro

    The definition of a quantum theory of gravity is explored following Feynman's path-integral approach. The aim is to construct a well defined version of the Wheeler-Misner- Hawking ``sum over four geometries'' formulation of quantum general relativity (GR). This is done by means of exploiting the similarities between the formulation of GR in terms of tetrad-connection variables (Palatini formulation) and a simpler theory called BF theory. One can go from BF theory to GR by imposing certain constraints on the BF-theory configurations. BF theory contains only global degrees of freedom (topological theory) and it can be exactly quantized á la Feynman introducing a discretization of the manifold. Using the path integral for BF theory we define a path integration for GR imposing the BF-to-GR constraints on the BF measure. The infinite degrees of freedom of gravity are restored in the process, and the restriction to a single discretization introduces a cut- off in the summed-over configurations. In order to capture all the degrees of freedom a sum over discretization is implemented. Both the implementation of the BF-to-GR constraints and the sum over discretizations are obtained by means of the introduction of an auxiliary field theory (AFT). 4-geometries in the path integral for GR are given by the Feynman diagrams of the AFT which is in this sense dual to GR. Feynman diagrams correspond to 2-complexes labeled by unitary irreducible representations of the internal gauge group (corresponding to tetrad rotation in the connection to GR). A model for 4-dimensional Euclidean quantum gravity (QG) is defined which corresponds to a different normalization of the Barrett-Crane model. The model is perturbatively finite; divergences appearing in the Barrett-Crane model are cured by the new normalization. We extend our techniques to the Lorentzian sector, where we define two models for four-dimensional QG. The first one contains only time-like representations and is shown to be

  17. Quantum 1/f noise in non-degerate semiconductors and emission statistics of alpha particles

    International Nuclear Information System (INIS)

    Kousik, G.S.

    1985-01-01

    Charged particle scattering is accompanied by the emission of soft photons. Handel's theory of 1/f noise, based on the infrared divergent coupling of the system to the electromagnetic field or other elementary excitations, states that the current associated with a beam of scattered particles will exhibit 1/f noise. The fraction of the particles scattered with an energy loss epsilon to soft photon emission is proportional to 1/epsilon and herein lies the origin of the quantum theory of 1/f noise. The 1/f noise caused by mobility fluctuations in semiconductors is related to the scattering cross section fluctuation given by Handel's theory, through the relaxation time. Chapters Two through Five of this dissertation presents the results of the detailed calculation of mobility fluctuation 1/f noise and Hooge parameter in nondegenerate semiconductors. Numerical results are given for silicon and gallium arsenide. Data obtained from extensive measurements on counting techniques for alpha-particles radioactive decay from a source containing 94 Pu 239 , 95 Am 241 and 96 Cm 244 are presented in Chapters Six and Seven of this dissertation. These data show that the statistics are non-Poissonian for large counting times (of the order of 1000 minutes) contrary to the popular belief that alpha-decay is an example of Poissonian statistics. Measurements of the Allan variance indicated the presence of a slow Lorentzian flicker noise and 1/f noise and the magnitude of the noise for large counting times is considerably larger than that predicted by Poissonian statistics

  18. Online Statistical Modeling (Regression Analysis) for Independent Responses

    Science.gov (United States)

    Made Tirta, I.; Anggraeni, Dian; Pandutama, Martinus

    2017-06-01

    Regression analysis (statistical analmodelling) are among statistical methods which are frequently needed in analyzing quantitative data, especially to model relationship between response and explanatory variables. Nowadays, statistical models have been developed into various directions to model various type and complex relationship of data. Rich varieties of advanced and recent statistical modelling are mostly available on open source software (one of them is R). However, these advanced statistical modelling, are not very friendly to novice R users, since they are based on programming script or command line interface. Our research aims to developed web interface (based on R and shiny), so that most recent and advanced statistical modelling are readily available, accessible and applicable on web. We have previously made interface in the form of e-tutorial for several modern and advanced statistical modelling on R especially for independent responses (including linear models/LM, generalized linier models/GLM, generalized additive model/GAM and generalized additive model for location scale and shape/GAMLSS). In this research we unified them in the form of data analysis, including model using Computer Intensive Statistics (Bootstrap and Markov Chain Monte Carlo/ MCMC). All are readily accessible on our online Virtual Statistics Laboratory. The web (interface) make the statistical modeling becomes easier to apply and easier to compare them in order to find the most appropriate model for the data.

  19. Physics colloquium: Single-electron counting in quantum metrology and in statistical mechanics

    CERN Multimedia

    Geneva University

    2011-01-01

    GENEVA UNIVERSITY Ecole de physique Département de physique nucléaire et corspusculaire 24, quai Ernest-Ansermet 1211 Genève 4 Tél.: (022) 379 62 73 Fax: (022) 379 69 92olé   Lundi 17 octobre 2011 17h00 - Ecole de Physique, Auditoire Stueckelberg PHYSICS COLLOQUIUM « Single-electron counting in quantum metrology and in statistical mechanics » Prof. Jukka Pekola Low Temperature Laboratory, Aalto University Helsinki, Finland   First I discuss the basics of single-electron tunneling and its potential applications in metrology. My main focus is in developing an accurate source of single-electron current for the realization of the unit ampere. I discuss the principle and the present status of the so-called single- electron turnstile. Investigation of errors in transporting electrons one by one has revealed a wealth of observations on fundamental phenomena in mesoscopic superconductivity, including individual Andreev...

  20. Random matrix model of adiabatic quantum computing

    International Nuclear Information System (INIS)

    Mitchell, David R.; Adami, Christoph; Lue, Waynn; Williams, Colin P.

    2005-01-01

    We present an analysis of the quantum adiabatic algorithm for solving hard instances of 3-SAT (an NP-complete problem) in terms of random matrix theory (RMT). We determine the global regularity of the spectral fluctuations of the instantaneous Hamiltonians encountered during the interpolation between the starting Hamiltonians and the ones whose ground states encode the solutions to the computational problems of interest. At each interpolation point, we quantify the degree of regularity of the average spectral distribution via its Brody parameter, a measure that distinguishes regular (i.e., Poissonian) from chaotic (i.e., Wigner-type) distributions of normalized nearest-neighbor spacings. We find that for hard problem instances - i.e., those having a critical ratio of clauses to variables - the spectral fluctuations typically become irregular across a contiguous region of the interpolation parameter, while the spectrum is regular for easy instances. Within the hard region, RMT may be applied to obtain a mathematical model of the probability of avoided level crossings and concomitant failure rate of the adiabatic algorithm due to nonadiabatic Landau-Zener-type transitions. Our model predicts that if the interpolation is performed at a uniform rate, the average failure rate of the quantum adiabatic algorithm, when averaged over hard problem instances, scales exponentially with increasing problem size

  1. Modeling quantum fluid dynamics at nonzero temperatures

    Science.gov (United States)

    Berloff, Natalia G.; Brachet, Marc; Proukakis, Nick P.

    2014-01-01

    The detailed understanding of the intricate dynamics of quantum fluids, in particular in the rapidly growing subfield of quantum turbulence which elucidates the evolution of a vortex tangle in a superfluid, requires an in-depth understanding of the role of finite temperature in such systems. The Landau two-fluid model is the most successful hydrodynamical theory of superfluid helium, but by the nature of the scale separations it cannot give an adequate description of the processes involving vortex dynamics and interactions. In our contribution we introduce a framework based on a nonlinear classical-field equation that is mathematically identical to the Landau model and provides a mechanism for severing and coalescence of vortex lines, so that the questions related to the behavior of quantized vortices can be addressed self-consistently. The correct equation of state as well as nonlocality of interactions that leads to the existence of the roton minimum can also be introduced in such description. We review and apply the ideas developed for finite-temperature description of weakly interacting Bose gases as possible extensions and numerical refinements of the proposed method. We apply this method to elucidate the behavior of the vortices during expansion and contraction following the change in applied pressure. We show that at low temperatures, during the contraction of the vortex core as the negative pressure grows back to positive values, the vortex line density grows through a mechanism of vortex multiplication. This mechanism is suppressed at high temperatures. PMID:24704874

  2. Fock representations of the superalgebra sl(n+1 vertical bar m), its quantum analogue Uq[sl(n+1 vertical bar m)] and related quantum statistics

    International Nuclear Information System (INIS)

    Palev, T.D.; Stoilova, N.I.; Jeugt, J. van der

    1999-12-01

    Fock space representations of the Lie superalgebra sl(n + 1 vertical bar m) and of its quantum analogue U q [sl(n + 1 vertical bar m)] are written down. The results are based on a description of these superalgebras via creation and annihilation operators. The properties of the underlying statistics are briefly discussed. (author)

  3. State sum models for quantum gravity

    OpenAIRE

    Barrett, John W.

    2000-01-01

    This paper reviews the construction of quantum field theory on a 4-dimensional spacetime by combinatorial methods, and discusses the recent developments in the direction of a combinatorial construction of quantum gravity.

  4. Statistical model of exotic rotational correlations in emergent space-time

    Energy Technology Data Exchange (ETDEWEB)

    Hogan, Craig; Kwon, Ohkyung; Richardson, Jonathan

    2017-06-06

    A statistical model is formulated to compute exotic rotational correlations that arise as inertial frames and causal structure emerge on large scales from entangled Planck scale quantum systems. Noncommutative quantum dynamics are represented by random transverse displacements that respect causal symmetry. Entanglement is represented by covariance of these displacements in Planck scale intervals defined by future null cones of events on an observer's world line. Light that propagates in a nonradial direction inherits a projected component of the exotic rotational correlation that accumulates as a random walk in phase. A calculation of the projection and accumulation leads to exact predictions for statistical properties of exotic Planck scale correlations in an interferometer of any configuration. The cross-covariance for two nearly co-located interferometers is shown to depart only slightly from the autocovariance. Specific examples are computed for configurations that approximate realistic experiments, and show that the model can be rigorously tested.

  5. On the structure of the quantum-mechanical probability models

    International Nuclear Information System (INIS)

    Cufaro-Petroni, N.

    1992-01-01

    In this paper the role of the mathematical probability models in the classical and quantum physics in shortly analyzed. In particular the formal structure of the quantum probability spaces (QPS) is contrasted with the usual Kolmogorovian models of probability by putting in evidence the connections between this structure and the fundamental principles of the quantum mechanics. The fact that there is no unique Kolmogorovian model reproducing a QPS is recognized as one of the main reasons of the paradoxical behaviors pointed out in the quantum theory from its early days. 8 refs

  6. Quantum phase transition of the transverse-field quantum Ising model on scale-free networks.

    Science.gov (United States)

    Yi, Hangmo

    2015-01-01

    I investigate the quantum phase transition of the transverse-field quantum Ising model in which nearest neighbors are defined according to the connectivity of scale-free networks. Using a continuous-time quantum Monte Carlo simulation method and the finite-size scaling analysis, I identify the quantum critical point and study its scaling characteristics. For the degree exponent λ=6, I obtain results that are consistent with the mean-field theory. For λ=4.5 and 4, however, the results suggest that the quantum critical point belongs to a non-mean-field universality class. Further simulations indicate that the quantum critical point remains mean-field-like if λ>5, but it continuously deviates from the mean-field theory as λ becomes smaller.

  7. Integer Set Compression and Statistical Modeling

    DEFF Research Database (Denmark)

    Larsson, N. Jesper

    2014-01-01

    enumeration of elements may be arbitrary or random, but where statistics is kept in order to estimate probabilities of elements. We present a recursive subset-size encoding method that is able to benefit from statistics, explore the effects of permuting the enumeration order based on element probabilities......Compression of integer sets and sequences has been extensively studied for settings where elements follow a uniform probability distribution. In addition, methods exist that exploit clustering of elements in order to achieve higher compression performance. In this work, we address the case where...

  8. Blinking in quantum dots: The origin of the grey state and power law statistics

    Science.gov (United States)

    Ye, Mao; Searson, Peter C.

    2011-09-01

    Quantum dot (QD) blinking is characterized by switching between an “on” state and an “off” state, and a power-law distribution of on and off times with exponents from 1.0 to 2.0. The origin of blinking behavior in QDs, however, has remained a mystery. Here we describe an energy-band model for QDs that captures the full range of blinking behavior reported in the literature and provides new insight into features such as the gray state, the power-law distribution of on and off times, and the power-law exponents.

  9. Quantum kinematics of spacetime. II. A model quantum cosmology with real clocks

    International Nuclear Information System (INIS)

    Hartle, J.B.

    1988-01-01

    Nonrelativistic model quantum cosmologies are studied in which the basic time variable is the position of a clock indicator and the time parameter of the Schroedinger equation is an unobservable label. Familiar Schroedinger-Heisenberg quantum mechanics emerges if the clock is ideal: arbitrarily accurate for arbitrarily long times. More realistically, however, the usual formulation emerges only as an approximation appropriate to states of this model universe in which part of the system functions approximately as an ideal clock. It is suggested that the quantum kinematics of spacetime theories such as general relativity may be analogous to those of this model. In particular it is suggested that our familiar notion of time in quantum mechanics is not an inevitable property of a general quantum framework but an approximate feature of specific initial conditions

  10. Three-dimensional simplicial quantum gravity and generalized matrix models

    International Nuclear Information System (INIS)

    Ambjoern, J.; Durhuus, B.; Jonsson, T.

    1990-11-01

    We consider a discrete model of Euclidean quantum gravity in three dimensions based on a summation over random simplicial manifolds. We derive some elementary properties of the model and discuss possible 'matrix' models for 3d gravity. (orig.)

  11. Super-quantum curves from super-eigenvalue models

    Energy Technology Data Exchange (ETDEWEB)

    Ciosmak, Paweł [Faculty of Mathematics, Informatics and Mechanics, University of Warsaw,ul. Banacha 2, 02-097 Warsaw (Poland); Hadasz, Leszek [M. Smoluchowski Institute of Physics, Jagiellonian University,ul. Łojasiewicza 11, 30-348 Kraków (Poland); Manabe, Masahide [Faculty of Physics, University of Warsaw,ul. Pasteura 5, 02-093 Warsaw (Poland); Sułkowski, Piotr [Faculty of Physics, University of Warsaw,ul. Pasteura 5, 02-093 Warsaw (Poland); Walter Burke Institute for Theoretical Physics, California Institute of Technology,1200 E. California Blvd, Pasadena, CA 91125 (United States)

    2016-10-10

    In modern mathematical and theoretical physics various generalizations, in particular supersymmetric or quantum, of Riemann surfaces and complex algebraic curves play a prominent role. We show that such supersymmetric and quantum generalizations can be combined together, and construct supersymmetric quantum curves, or super-quantum curves for short. Our analysis is conducted in the formalism of super-eigenvalue models: we introduce β-deformed version of those models, and derive differential equations for associated α/β-deformed super-matrix integrals. We show that for a given model there exists an infinite number of such differential equations, which we identify as super-quantum curves, and which are in one-to-one correspondence with, and have the structure of, super-Virasoro singular vectors. We discuss potential applications of super-quantum curves and prospects of other generalizations.

  12. Super-quantum curves from super-eigenvalue models

    International Nuclear Information System (INIS)

    Ciosmak, Paweł; Hadasz, Leszek; Manabe, Masahide; Sułkowski, Piotr

    2016-01-01

    In modern mathematical and theoretical physics various generalizations, in particular supersymmetric or quantum, of Riemann surfaces and complex algebraic curves play a prominent role. We show that such supersymmetric and quantum generalizations can be combined together, and construct supersymmetric quantum curves, or super-quantum curves for short. Our analysis is conducted in the formalism of super-eigenvalue models: we introduce β-deformed version of those models, and derive differential equations for associated α/β-deformed super-matrix integrals. We show that for a given model there exists an infinite number of such differential equations, which we identify as super-quantum curves, and which are in one-to-one correspondence with, and have the structure of, super-Virasoro singular vectors. We discuss potential applications of super-quantum curves and prospects of other generalizations.

  13. Super-quantum curves from super-eigenvalue models

    Science.gov (United States)

    Ciosmak, Paweł; Hadasz, Leszek; Manabe, Masahide; Sułkowski, Piotr

    2016-10-01

    In modern mathematical and theoretical physics various generalizations, in particular supersymmetric or quantum, of Riemann surfaces and complex algebraic curves play a prominent role. We show that such supersymmetric and quantum generalizations can be combined together, and construct supersymmetric quantum curves, or super-quantum curves for short. Our analysis is conducted in the formalism of super-eigenvalue models: we introduce β-deformed version of those models, and derive differential equations for associated α/ β-deformed super-matrix integrals. We show that for a given model there exists an infinite number of such differential equations, which we identify as super-quantum curves, and which are in one-to-one correspondence with, and have the structure of, super-Virasoro singular vectors. We discuss potential applications of super-quantum curves and prospects of other generalizations.

  14. Statistical modelling for social researchers principles and practice

    CERN Document Server

    Tarling, Roger

    2008-01-01

    This book explains the principles and theory of statistical modelling in an intelligible way for the non-mathematical social scientist looking to apply statistical modelling techniques in research. The book also serves as an introduction for those wishing to develop more detailed knowledge and skills in statistical modelling. Rather than present a limited number of statistical models in great depth, the aim is to provide a comprehensive overview of the statistical models currently adopted in social research, in order that the researcher can make appropriate choices and select the most suitable model for the research question to be addressed. To facilitate application, the book also offers practical guidance and instruction in fitting models using SPSS and Stata, the most popular statistical computer software which is available to most social researchers. Instruction in using MLwiN is also given. Models covered in the book include; multiple regression, binary, multinomial and ordered logistic regression, log-l...

  15. Linear Mixed Models in Statistical Genetics

    NARCIS (Netherlands)

    R. de Vlaming (Ronald)

    2017-01-01

    markdownabstractOne of the goals of statistical genetics is to elucidate the genetic architecture of phenotypes (i.e., observable individual characteristics) that are affected by many genetic variants (e.g., single-nucleotide polymorphisms; SNPs). A particular aim is to identify specific SNPs that

  16. Statistical models and methods for reliability and survival analysis

    CERN Document Server

    Couallier, Vincent; Huber-Carol, Catherine; Mesbah, Mounir; Huber -Carol, Catherine; Limnios, Nikolaos; Gerville-Reache, Leo

    2013-01-01

    Statistical Models and Methods for Reliability and Survival Analysis brings together contributions by specialists in statistical theory as they discuss their applications providing up-to-date developments in methods used in survival analysis, statistical goodness of fit, stochastic processes for system reliability, amongst others. Many of these are related to the work of Professor M. Nikulin in statistics over the past 30 years. The authors gather together various contributions with a broad array of techniques and results, divided into three parts - Statistical Models and Methods, Statistical

  17. The quantum HMF model: I. Fermions

    International Nuclear Information System (INIS)

    Chavanis, Pierre-Henri

    2011-01-01

    We study the thermodynamics of quantum particles with long-range interactions at T = 0. Specifically, we generalize the Hamiltonian mean-field (HMF) model to the case of fermions. We consider the Thomas–Fermi approximation that becomes exact in a proper thermodynamic limit N→+∞ with a coupling constant k ∼ N. The equilibrium configurations, described by the mean-field Fermi (or waterbag) distribution, are equivalent to polytropes of index n = 1/2. We show that the homogeneous phase, which is unstable in the classical regime, becomes stable in the quantum regime. The homogeneous phase is stabilized by the Pauli exclusion principle. This takes place through a first-order phase transition where the control parameter is the normalized Planck constant. The homogeneous phase is unstable for ℎ c ≡2/√(π), metastable for ℎ c t ≡1.16 and stable for ℎ>ℎ t . The inhomogeneous phase is stable for ℎ t , metastable for ℎ t * ≡1.18 and disappears for ℎ>ℎ * (for ℎ c * , there exists an unstable inhomogeneous phase with magnetization 0 * ≡ 0.37). We point out analogies between the fermionic HMF model and the concept of fermion stars in astrophysics. Finally, as a by-product of our analysis, we obtain new results concerning the Vlasov dynamical stability of the waterbag distribution which is the ground state of the Lynden-Bell distribution in the theory of violent relaxation of the classical HMF model. We show that spatially homogeneous waterbag distributions are Vlasov-stable iff ε ≥ ε c = 1/3 and spatially inhomogeneous waterbag distributions are Vlasov-stable iff ε ≤ ε * = 0.379 and b ≥ b * = 0.37, where ε and b are the normalized energy and magnetization. The magnetization curve displays a first-order phase transition at ε t = 0.352 and the domain of metastability ranges from ε c to ε *

  18. Geometric modeling in probability and statistics

    CERN Document Server

    Calin, Ovidiu

    2014-01-01

    This book covers topics of Informational Geometry, a field which deals with the differential geometric study of the manifold probability density functions. This is a field that is increasingly attracting the interest of researchers from many different areas of science, including mathematics, statistics, geometry, computer science, signal processing, physics and neuroscience. It is the authors’ hope that the present book will be a valuable reference for researchers and graduate students in one of the aforementioned fields. This textbook is a unified presentation of differential geometry and probability theory, and constitutes a text for a course directed at graduate or advanced undergraduate students interested in applications of differential geometry in probability and statistics. The book contains over 100 proposed exercises meant to help students deepen their understanding, and it is accompanied by software that is able to provide numerical computations of several information geometric objects. The reader...

  19. Challenges in dental statistics: data and modelling

    OpenAIRE

    Matranga, D.; Castiglia, P.; Solinas, G.

    2013-01-01

    The aim of this work is to present the reflections and proposals derived from the first Workshop of the SISMEC STATDENT working group on statistical methods and applications in dentistry, held in Ancona (Italy) on 28th September 2011. STATDENT began as a forum of comparison and discussion for statisticians working in the field of dental research in order to suggest new and improve existing biostatistical and clinical epidemiological methods. During the meeting, we dealt with very important to...

  20. Model of a programmable quantum processing unit based on a quantum transistor effect

    Science.gov (United States)

    Ablayev, Farid; Andrianov, Sergey; Fetisov, Danila; Moiseev, Sergey; Terentyev, Alexandr; Urmanchev, Andrey; Vasiliev, Alexander

    2018-02-01

    In this paper we propose a model of a programmable quantum processing device realizable with existing nano-photonic technologies. It can be viewed as a basis for new high performance hardware architectures. Protocols for physical implementation of device on the controlled photon transfer and atomic transitions are presented. These protocols are designed for executing basic single-qubit and multi-qubit gates forming a universal set. We analyze the possible operation of this quantum computer scheme. Then we formalize the physical architecture by a mathematical model of a Quantum Processing Unit (QPU), which we use as a basis for the Quantum Programming Framework. This framework makes it possible to perform universal quantum computations in a multitasking environment.

  1. A statistical model of future human actions

    International Nuclear Information System (INIS)

    Woo, G.

    1992-02-01

    A critical review has been carried out of models of future human actions during the long term post-closure period of a radioactive waste repository. Various Markov models have been considered as alternatives to the standard Poisson model, and the problems of parameterisation have been addressed. Where the simplistic Poisson model unduly exaggerates the intrusion risk, some form of Markov model may have to be introduced. This situation may well arise for shallow repositories, but it is less likely for deep repositories. Recommendations are made for a practical implementation of a computer based model and its associated database. (Author)

  2. Quantum simulation of transverse Ising models with Rydberg atoms

    Science.gov (United States)

    Schauss, Peter

    2018-04-01

    Quantum Ising models are canonical models for the study of quantum phase transitions (Sachdev 1999 Quantum Phase Transitions (Cambridge: Cambridge University Press)) and are the underlying concept for many analogue quantum computing and quantum annealing ideas (Tanaka et al Quantum Spin Glasses, Annealing and Computation (Cambridge: Cambridge University Press)). Here we focus on the implementation of finite-range interacting Ising spin models, which are barely tractable numerically. Recent experiments with cold atoms have reached the interaction-dominated regime in quantum Ising magnets via optical coupling of trapped neutral atoms to Rydberg states. This approach allows for the tunability of all relevant terms in an Ising spin Hamiltonian with 1/{r}6 interactions in transverse and longitudinal fields. This review summarizes the recent progress of these implementations in Rydberg lattices with site-resolved detection. Strong correlations in quantum Ising models have been observed in several experiments, starting from a single excitation in the superatom regime up to the point of crystallization. The rapid progress in this field makes spin systems based on Rydberg atoms a promising platform for quantum simulation because of the unmatched flexibility and strength of interactions combined with high control and good isolation from the environment.

  3. Enhanced surrogate models for statistical design exploiting space mapping technology

    DEFF Research Database (Denmark)

    Koziel, Slawek; Bandler, John W.; Mohamed, Achmed S.

    2005-01-01

    We present advances in microwave and RF device modeling exploiting Space Mapping (SM) technology. We propose new SM modeling formulations utilizing input mappings, output mappings, frequency scaling and quadratic approximations. Our aim is to enhance circuit models for statistical analysis...

  4. Statistical models of shape optimisation and evaluation

    CERN Document Server

    Davies, Rhodri; Taylor, Chris

    2014-01-01

    Deformable shape models have wide application in computer vision and biomedical image analysis. This book addresses a key issue in shape modelling: establishment of a meaningful correspondence between a set of shapes. Full implementation details are provided.

  5. Characterization of Strong Light-Matter Coupling in Semiconductor Quantum-Dot Microcavities via Photon-Statistics Spectroscopy

    Science.gov (United States)

    Schneebeli, L.; Kira, M.; Koch, S. W.

    2008-08-01

    It is shown that spectrally resolved photon-statistics measurements of the resonance fluorescence from realistic semiconductor quantum-dot systems allow for high contrast identification of the two-photon strong-coupling states. Using a microscopic theory, the second-rung resonance of Jaynes-Cummings ladder is analyzed and optimum excitation conditions are determined. The computed photon-statistics spectrum displays gigantic, experimentally robust resonances at the energetic positions of the second-rung emission.

  6. The implicit possibility of dualism in quantum probabilistic cognitive modeling.

    Science.gov (United States)

    Mender, Donald

    2013-06-01

    Pothos & Busemeyer (P&B) argue convincingly that quantum probability offers an improvement over classical Bayesian probability in modeling the empirical data of cognitive science. However, a weakness related to restrictions on the dimensionality of incompatible physical observables flows from the authors' "agnosticism" regarding quantum processes in neural substrates underlying cognition. Addressing this problem will require either future research findings validating quantum neurophysics or theoretical expansion of the uncertainty principle as a new, neurocognitively contextualized, "local" symmetry.

  7. How to practise Bayesian statistics outside the Bayesian church: What philosophy for Bayesian statistical modelling?

    NARCIS (Netherlands)

    Borsboom, D.; Haig, B.D.

    2013-01-01

    Unlike most other statistical frameworks, Bayesian statistical inference is wedded to a particular approach in the philosophy of science (see Howson & Urbach, 2006); this approach is called Bayesianism. Rather than being concerned with model fitting, this position in the philosophy of science

  8. Statistical Tests for Mixed Linear Models

    CERN Document Server

    Khuri, André I; Sinha, Bimal K

    2011-01-01

    An advanced discussion of linear models with mixed or random effects. In recent years a breakthrough has occurred in our ability to draw inferences from exact and optimum tests of variance component models, generating much research activity that relies on linear models with mixed and random effects. This volume covers the most important research of the past decade as well as the latest developments in hypothesis testing. It compiles all currently available results in the area of exact and optimum tests for variance component models and offers the only comprehensive treatment for these models a

  9. Quantum statistical description of transport of the quasi-particles in optic fibers

    International Nuclear Information System (INIS)

    Rasulova, M.Yu.; Hassan, T.; Mohamed Ridza bin Wahiddin; Umarov, B.

    2006-12-01

    On the basis of BBGKY hierarchy of quantum kinetic equations the quasi-quantum analogue of the linearized wave equation for one, two quasi-particles in optic fiber is obtained. The method which enables to obtain the quasi-quantum analogue of wave equations for any number of quasi- particles in fiber is suggested. (author)

  10. Statistical modelling of traffic safety development

    DEFF Research Database (Denmark)

    Christens, Peter

    2004-01-01

    there were 6861 injury trafficc accidents reported by the police, resulting in 4519 minor injuries, 3946 serious injuries, and 431 fatalities. The general purpose of the research was to improve the insight into aggregated road safety methodology in Denmark. The aim was to analyse advanced statistical methods......, that were designed to study developments over time, including effects of interventions. This aim has been achieved by investigating variations in aggregated Danish traffic accident series and by applying state of the art methodologies to specific case studies. The thesis comprises an introduction...

  11. Statistical image processing and multidimensional modeling

    CERN Document Server

    Fieguth, Paul

    2010-01-01

    Images are all around us! The proliferation of low-cost, high-quality imaging devices has led to an explosion in acquired images. When these images are acquired from a microscope, telescope, satellite, or medical imaging device, there is a statistical image processing task: the inference of something - an artery, a road, a DNA marker, an oil spill - from imagery, possibly noisy, blurry, or incomplete. A great many textbooks have been written on image processing. However this book does not so much focus on images, per se, but rather on spatial data sets, with one or more measurements taken over

  12. Quantum dynamics modeled by interacting trajectories

    Science.gov (United States)

    Cruz-Rodríguez, L.; Uranga-Piña, L.; Martínez-Mesa, A.; Meier, C.

    2018-03-01

    We present quantum dynamical simulations based on the propagation of interacting trajectories where the effect of the quantum potential is mimicked by effective pseudo-particle interactions. The method is applied to several quantum systems, both for bound and scattering problems. For the bound systems, the quantum ground state density and zero point energy are shown to be perfectly obtained by the interacting trajectories. In the case of time-dependent quantum scattering, the Eckart barrier and uphill ramp are considered, with transmission coefficients in very good agreement with standard quantum calculations. Finally, we show that via wave function synthesis along the trajectories, correlation functions and energy spectra can be obtained based on the dynamics of interacting trajectories.

  13. Quantum Gravity Mathematical Models and Experimental Bounds

    CERN Document Server

    Fauser, Bertfried; Zeidler, Eberhard

    2007-01-01

    The construction of a quantum theory of gravity is the most fundamental challenge confronting contemporary theoretical physics. The different physical ideas which evolved while developing a theory of quantum gravity require highly advanced mathematical methods. This book presents different mathematical approaches to formulate a theory of quantum gravity. It represents a carefully selected cross-section of lively discussions about the issue of quantum gravity which took place at the second workshop "Mathematical and Physical Aspects of Quantum Gravity" in Blaubeuren, Germany. This collection covers in a unique way aspects of various competing approaches. A unique feature of the book is the presentation of different approaches to quantum gravity making comparison feasible. This feature is supported by an extensive index. The book is mainly addressed to mathematicians and physicists who are interested in questions related to mathematical physics. It allows the reader to obtain a broad and up-to-date overview on ...

  14. Spin foam models for quantum gravity

    International Nuclear Information System (INIS)

    Perez, Alejandro

    2003-01-01

    In this topical review, we review the present status of the spin foam formulation of non-perturbative (background-independent) quantum gravity. The topical review is divided into two parts. In the first part, we present a general introduction to the main ideas emphasizing their motivation from various perspectives. Riemannian three-dimensional gravity is used as a simple example to illustrate conceptual issues and the main goals of the approach. The main features of the various existing models for four-dimensional gravity are also presented here. We conclude with a discussion of important questions to be addressed in four dimensions (gauge invariance, discretization independence, etc). In the second part, we concentrate on the definition of the Barrett-Crane model. We present the main results obtained in this framework from a critical perspective. Finally, we review the combinatorial formulation of spin foam models based on the dual group field theory technology. We present the Barrett-Crane model in this framework and review the finiteness results obtained for both its Riemannian and its Lorentzian variants. (topical review)

  15. Fluctuations and correlations in statistical models of hadron production

    International Nuclear Information System (INIS)

    Gorenstein, M. I.

    2012-01-01

    An extension of the standard concept of the statistical ensembles is suggested. Namely, the statistical ensembles with extensive quantities fluctuating according to an externally given distribution are introduced. Applications in the statistical models of multiple hadron production in high energy physics are discussed.

  16. Analysis and Evaluation of Statistical Models for Integrated Circuits Design

    Directory of Open Access Journals (Sweden)

    Sáenz-Noval J.J.

    2011-10-01

    Full Text Available Statistical models for integrated circuits (IC allow us to estimate the percentage of acceptable devices in the batch before fabrication. Actually, Pelgrom is the statistical model most accepted in the industry; however it was derived from a micrometer technology, which does not guarantee reliability in nanometric manufacturing processes. This work considers three of the most relevant statistical models in the industry and evaluates their limitations and advantages in analog design, so that the designer has a better criterion to make a choice. Moreover, it shows how several statistical models can be used for each one of the stages and design purposes.

  17. Modeling of uncertainties in statistical inverse problems

    International Nuclear Information System (INIS)

    Kaipio, Jari

    2008-01-01

    In all real world problems, the models that tie the measurements to the unknowns of interest, are at best only approximations for reality. While moderate modeling and approximation errors can be tolerated with stable problems, inverse problems are a notorious exception. Typical modeling errors include inaccurate geometry, unknown boundary and initial data, properties of noise and other disturbances, and simply the numerical approximations of the physical models. In principle, the Bayesian approach to inverse problems, in which all uncertainties are modeled as random variables, is capable of handling these uncertainties. Depending on the type of uncertainties, however, different strategies may be adopted. In this paper we give an overview of typical modeling errors and related strategies within the Bayesian framework.

  18. Equilibrium statistical mechanics

    CERN Document Server

    Jackson, E Atlee

    2000-01-01

    Ideal as an elementary introduction to equilibrium statistical mechanics, this volume covers both classical and quantum methodology for open and closed systems. Introductory chapters familiarize readers with probability and microscopic models of systems, while additional chapters describe the general derivation of the fundamental statistical mechanics relationships. The final chapter contains 16 sections, each dealing with a different application, ordered according to complexity, from classical through degenerate quantum statistical mechanics. Key features include an elementary introduction t

  19. Interpretation of commonly used statistical regression models.

    Science.gov (United States)

    Kasza, Jessica; Wolfe, Rory

    2014-01-01

    A review of some regression models commonly used in respiratory health applications is provided in this article. Simple linear regression, multiple linear regression, logistic regression and ordinal logistic regression are considered. The focus of this article is on the interpretation of the regression coefficients of each model, which are illustrated through the application of these models to a respiratory health research study. © 2013 The Authors. Respirology © 2013 Asian Pacific Society of Respirology.

  20. Statistical modeling and extrapolation of carcinogenesis data

    International Nuclear Information System (INIS)

    Krewski, D.; Murdoch, D.; Dewanji, A.

    1986-01-01

    Mathematical models of carcinogenesis are reviewed, including pharmacokinetic models for metabolic activation of carcinogenic substances. Maximum likelihood procedures for fitting these models to epidemiological data are discussed, including situations where the time to tumor occurrence is unobservable. The plausibility of different possible shapes of the dose response curve at low doses is examined, and a robust method for linear extrapolation to low doses is proposed and applied to epidemiological data on radiation carcinogenesis

  1. Plan Recognition using Statistical Relational Models

    Science.gov (United States)

    2014-08-25

    corresponding undirected model can be significantly more complex since there is no closed form solution for the maximum-likelihood set of parameters unlike in...algorithm did not scale to larger training sets, and the overall results are still not competitive with BALPs. 5In directed models, a closed form solution...opinions of ARO, DARPA, NSF or any other government agency. References Albrecht DW, Zukerman I, Nicholson AE. Bayesian models for keyhole plan

  2. Multivariate statistical modelling based on generalized linear models

    CERN Document Server

    Fahrmeir, Ludwig

    1994-01-01

    This book is concerned with the use of generalized linear models for univariate and multivariate regression analysis. Its emphasis is to provide a detailed introductory survey of the subject based on the analysis of real data drawn from a variety of subjects including the biological sciences, economics, and the social sciences. Where possible, technical details and proofs are deferred to an appendix in order to provide an accessible account for non-experts. Topics covered include: models for multi-categorical responses, model checking, time series and longitudinal data, random effects models, and state-space models. Throughout, the authors have taken great pains to discuss the underlying theoretical ideas in ways that relate well to the data at hand. As a result, numerous researchers whose work relies on the use of these models will find this an invaluable account to have on their desks. "The basic aim of the authors is to bring together and review a large part of recent advances in statistical modelling of m...

  3. Statistical Modelling of Extreme Rainfall in Taiwan

    NARCIS (Netherlands)

    L-F. Chu (Lan-Fen); M.J. McAleer (Michael); C-C. Chang (Ching-Chung)

    2012-01-01

    textabstractIn this paper, the annual maximum daily rainfall data from 1961 to 2010 are modelled for 18 stations in Taiwan. We fit the rainfall data with stationary and non-stationary generalized extreme value distributions (GEV), and estimate their future behaviour based on the best fitting model.

  4. Statistical Modelling of Extreme Rainfall in Taiwan

    NARCIS (Netherlands)

    L. Chu (LanFen); M.J. McAleer (Michael); C-H. Chang (Chu-Hsiang)

    2013-01-01

    textabstractIn this paper, the annual maximum daily rainfall data from 1961 to 2010 are modelled for 18 stations in Taiwan. We fit the rainfall data with stationary and non-stationary generalized extreme value distributions (GEV), and estimate their future behaviour based on the best fitting model.

  5. Quantum entanglement and quantum phase transitions in frustrated Majumdar-Ghosh model

    International Nuclear Information System (INIS)

    Liu Guanghua; Wang Chunhai; Deng Xiaoyan

    2011-01-01

    By using the density matrix renormalization group technique, the quantum phase transitions in the frustrated Majumdar-Ghosh model are investigated. The behaviors of the conventional order parameter and the quantum entanglement entropy are analyzed in detail. The order parameter is found to peak at J 2 ∼0.58, but not at the Majumdar-Ghosh point (J 2 =0.5). Although, the quantum entanglements calculated with different subsystems display dissimilarly, the extremes of their first derivatives approach to the same critical point. By finite size scaling, this quantum critical point J C 2 converges to around 0.301 in the thermodynamic limit, which is consistent with those predicted previously by some authors (Tonegawa and Harada, 1987 ; Kuboki and Fukuyama, 1987 ; Chitra et al., 1995 ). Across the J C 2 , the system undergoes a quantum phase transition from a gapless spin-fluid phase to a gapped dimerized phase.

  6. Quasilocal conservation laws in the quantum Hirota model

    International Nuclear Information System (INIS)

    Zadnik, Lenart; Prosen, Tomaž

    2017-01-01

    The extensivity of the quantum Hirota model’s conservation laws on a 1  +  1 dimensional lattice is considered. This model can be interpreted in terms of an integrable many-body quantum Floquet dynamics. We establish the procedure to generate a continuous family of quasilocal conservation laws from the conserved operators proposed by Faddeev and Volkov. The Hilbert–Schmidt kernel which allows the calculation of inner products of these new conservation laws is explicitly computed. This result has potential applications in quantum quench and transport problems in integrable quantum field theories. (paper)

  7. Quantum model of light transmission in array waveguide gratings.

    Science.gov (United States)

    Capmany, J; Mora, J; Fernández-Pousa, C R; Muñoz, P

    2013-06-17

    We develop, to the best of our knowledge, the first model for an array waveguide grating (AWG) device subject to quantum inputs and analyze its basic transformation functionalities for single-photon states. A commercial, cyclic AWG is experimentally characterized with weak input coherent states as a means of exploring its behaviour under realistic quantum detection. In particular it is shown the existence of a cutoff value of the average photon number below which quantum crosstalk between AWG ports is negligible with respect to dark counts. These results can be useful when considering the application of AWG devices to integrated quantum photonic systems.

  8. Modeling coherent errors in quantum error correction

    Science.gov (United States)

    Greenbaum, Daniel; Dutton, Zachary

    2018-01-01

    Analysis of quantum error correcting codes is typically done using a stochastic, Pauli channel error model for describing the noise on physical qubits. However, it was recently found that coherent errors (systematic rotations) on physical data qubits result in both physical and logical error rates that differ significantly from those predicted by a Pauli model. Here we examine the accuracy of the Pauli approximation for noise containing coherent errors (characterized by a rotation angle ɛ) under the repetition code. We derive an analytic expression for the logical error channel as a function of arbitrary code distance d and concatenation level n, in the small error limit. We find that coherent physical errors result in logical errors that are partially coherent and therefore non-Pauli. However, the coherent part of the logical error is negligible at fewer than {ε }-({dn-1)} error correction cycles when the decoder is optimized for independent Pauli errors, thus providing a regime of validity for the Pauli approximation. Above this number of correction cycles, the persistent coherent logical error will cause logical failure more quickly than the Pauli model would predict, and this may need to be combated with coherent suppression methods at the physical level or larger codes.

  9. Quantum Vertex Model for Reversible Classical Computing

    Science.gov (United States)

    Chamon, Claudio; Mucciolo, Eduardo; Ruckenstein, Andrei; Yang, Zhicheng

    We present a planar vertex model that encodes the result of a universal reversible classical computation in its ground state. The approach involves Boolean variables (spins) placed on links of a two-dimensional lattice, with vertices representing logic gates. Large short-ranged interactions between at most two spins implement the operation of each gate. The lattice is anisotropic with one direction corresponding to computational time, and with transverse boundaries storing the computation's input and output. The model displays no finite temperature phase transitions, including no glass transitions, independent of circuit. The computational complexity is encoded in the scaling of the relaxation rate into the ground state with the system size. We use thermal annealing and a novel and more efficient heuristic \\x9Dannealing with learning to study various computational problems. To explore faster relaxation routes, we construct an explicit mapping of the vertex model into the Chimera architecture of the D-Wave machine, initiating a novel approach to reversible classical computation based on quantum annealing.

  10. Disciplines, models, and computers: the path to computational quantum chemistry.

    Science.gov (United States)

    Lenhard, Johannes

    2014-12-01

    Many disciplines and scientific fields have undergone a computational turn in the past several decades. This paper analyzes this sort of turn by investigating the case of computational quantum chemistry. The main claim is that the transformation from quantum to computational quantum chemistry involved changes in three dimensions. First, on the side of instrumentation, small computers and a networked infrastructure took over the lead from centralized mainframe architecture. Second, a new conception of computational modeling became feasible and assumed a crucial role. And third, the field of computa- tional quantum chemistry became organized in a market-like fashion and this market is much bigger than the number of quantum theory experts. These claims will be substantiated by an investigation of the so-called density functional theory (DFT), the arguably pivotal theory in the turn to computational quantum chemistry around 1990.

  11. On the Logical Development of Statistical Models.

    Science.gov (United States)

    1983-12-01

    1978). "Modelos con parametros variables en el analisis de series temporales " Questiio, 4, 2, 75-87. [25] Seal, H. L. (1967). "The historical...example, a classical state-space representation of a simple time series model is: yt = it + ut Ut = *It-I + Ct (2.2) ut and et are independent normal...on its past values is displayed in the structural equation. This approach has been particularly useful in time series models. For example, model (2.2

  12. A Noise Robust Statistical Texture Model

    DEFF Research Database (Denmark)

    Hilger, Klaus Baggesen; Stegmann, Mikkel Bille; Larsen, Rasmus

    2002-01-01

    Appearance Models segmentation framework. This is accomplished by augmenting the model with an estimate of the covariance of the noise present in the training data. This results in a more compact model maximising the signal-to-noise ratio, thus favouring subspaces rich on signal, but low on noise......This paper presents a novel approach to the problem of obtaining a low dimensional representation of texture (pixel intensity) variation present in a training set after alignment using a Generalised Procrustes analysis.We extend the conventional analysis of training textures in the Active...

  13. Model for calorimetric measurements in an open quantum system

    Science.gov (United States)

    Donvil, Brecht; Muratore-Ginanneschi, Paolo; Pekola, Jukka P.; Schwieger, Kay

    2018-05-01

    We investigate the experimental setup proposed in New J. Phys. 15, 115006 (2013), 10.1088/1367-2630/15/11/115006 for calorimetric measurements of thermodynamic indicators in an open quantum system. As a theoretical model we consider a periodically driven qubit coupled with a large yet finite electron reservoir, the calorimeter. The calorimeter is initially at equilibrium with an infinite phonon bath. As time elapses, the temperature of the calorimeter varies in consequence of energy exchanges with the qubit and the phonon bath. We show how under weak-coupling assumptions, the evolution of the qubit-calorimeter system can be described by a generalized quantum jump process including as dynamical variable the temperature of the calorimeter. We study the jump process by numeric and analytic methods. Asymptotically with the duration of the drive, the qubit-calorimeter attains a steady state. In this same limit, we use multiscale perturbation theory to derive a Fokker-Planck equation governing the calorimeter temperature distribution. We inquire the properties of the temperature probability distribution close and at the steady state. In particular, we predict the behavior of measurable statistical indicators versus the qubit-calorimeter coupling constant.

  14. Statistics

    CERN Document Server

    Hayslett, H T

    1991-01-01

    Statistics covers the basic principles of Statistics. The book starts by tackling the importance and the two kinds of statistics; the presentation of sample data; the definition, illustration and explanation of several measures of location; and the measures of variation. The text then discusses elementary probability, the normal distribution and the normal approximation to the binomial. Testing of statistical hypotheses and tests of hypotheses about the theoretical proportion of successes in a binomial population and about the theoretical mean of a normal population are explained. The text the

  15. 12th Workshop on Stochastic Models, Statistics and Their Applications

    CERN Document Server

    Rafajłowicz, Ewaryst; Szajowski, Krzysztof

    2015-01-01

    This volume presents the latest advances and trends in stochastic models and related statistical procedures. Selected peer-reviewed contributions focus on statistical inference, quality control, change-point analysis and detection, empirical processes, time series analysis, survival analysis and reliability, statistics for stochastic processes, big data in technology and the sciences, statistical genetics, experiment design, and stochastic models in engineering. Stochastic models and related statistical procedures play an important part in furthering our understanding of the challenging problems currently arising in areas of application such as the natural sciences, information technology, engineering, image analysis, genetics, energy and finance, to name but a few. This collection arises from the 12th Workshop on Stochastic Models, Statistics and Their Applications, Wroclaw, Poland.

  16. The quantum mechanics of the supersymmetric nonlinear sigma-model

    International Nuclear Information System (INIS)

    Davis, A.C.; Macfarlane, A.J.; Popat, P.C.; Holten, J.W. van

    1984-01-01

    The classical and quantum mechanical formalisms of the models are developed. The quantisation is done in such a way that the quantum theory can be represented explicitly in as simple a form as possible, and the problem of ordering of operators is resolved so as to maintain the supersymmetry algebra of the classical theory. (author)

  17. Fragments of reminiscences and exactly solvable nonrelativistic quantum models

    International Nuclear Information System (INIS)

    Zakhariev, B.N.

    1994-01-01

    Some exactly solvable nonrelativistic quantum models are discussed. Special attention is paid to the quantum inverse problem. It is pointed out that by analyzing the inverse problem pictures one can get a deeper insight into the laws of the microworld and acquire the ability to make the qualitative predictions without computers and formulae. 5 refs

  18. Self-organized quantum rings : Physical characterization and theoretical modeling

    NARCIS (Netherlands)

    Fomin, V.M.; Gladilin, V.N.; Devreese, J.T.; Koenraad, P.M.; Fomin, V.M.

    2014-01-01

    An adequate modeling of the self-organized quantum rings is possible only on the basis of the modern characterization of those nanostructures.We discuss an atomic-scale analysis of the indium distribution of self-organized InGaAs quantum rings (QRs). The analysis of the shape, size and composition

  19. Cryptography In The Bounded Quantum-Storage Model

    DEFF Research Database (Denmark)

    Damgård, Ivan Bjerre; Salvail, Louis; Schaffner, Christian

    2005-01-01

    We initiate the study of two-party cryptographic primitives with unconditional security, assuming that the adversary's quantum memory is of bounded size. We show that oblivious transfer and bit commitment can be implemented in this model using protocols where honest parties need no quantum memory...

  20. Cryptography in the Bounded Quantum-Storage Model

    DEFF Research Database (Denmark)

    Damgård, Ivan Bjerre; Serge, Fehr; Schaffner, Christian

    2008-01-01

    We initiate the study of two-party cryptographic primitives with unconditional security, assuming that the adversary's quantum memory is of bounded size. We show that oblivious transfer and bit commitment can be implemented in this model using protocols where honest parties need no quantum memory...