Statistical transmutation in doped quantum dimer models.
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.
Harrison, JM; Robbins, JM; 10.1098/rspa.2010.0254
2011-01-01
Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph, concentrating on the simplest case of abelian statistics for two particles. In spite of the fact that graphs are locally one-dimensional, anyon statistics emerge in a generalized form. A given graph may support a family of independent anyon phases associated with topologically inequivalent exchange processes. In addition, for sufficiently complex graphs, there appear new discrete-valued phases. Our analysis is simplified by considering combinatorial rather than metric graphs -- equivalently, a many-particle tight-binding model. The results demonstrate that graphs provide an arena in which to study new manifestations of quantum statistics. Possible applications include topological quantum computing, topological insulators, the fractional quantum Hall effect, superconductivity and molec...
Quantum statistics of Raman scattering model with Stokes mode generation
Tanatar, Bilal; Shumovsky, Alexander S.
1994-01-01
The model describing three coupled quantum oscillators with decay of Rayleigh mode into the Stokes and vibration (phonon) modes is examined. Due to the Manley-Rowe relations the problem of exact eigenvalues and eigenstates is reduced to the calculation of new orthogonal polynomials defined both by the difference and differential equations. The quantum statistical properties are examined in the case when initially: the Stokes mode is in the vacuum state; the Rayleigh mode is in the number state; and the vibration mode is in the number of or squeezed states. The collapses and revivals are obtained for different initial conditions as well as the change in time the sub-Poisson distribution by the super-Poisson distribution and vice versa.
Random matrices as models for the statistics of quantum mechanics
Casati, Giulio; Guarneri, Italo; Mantica, Giorgio
1986-05-01
Random matrices from the Gaussian unitary ensemble generate in a natural way unitary groups of evolution in finite-dimensional spaces. The statistical properties of this time evolution can be investigated by studying the time autocorrelation functions of dynamical variables. We prove general results on the decay properties of such autocorrelation functions in the limit of infinite-dimensional matrices. We discuss the relevance of random matrices as models for the dynamics of quantum systems that are chaotic in the classical limit. Permanent address: Dipartimento di Fisica, Via Celoria 16, 20133 Milano, Italy.
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.
Monte Carlo simulation of quantum statistical lattice models
Raedt, Hans De; Lagendijk, Ad
1985-01-01
In this article we review recent developments in computational methods for quantum statistical lattice problems. We begin by giving the necessary mathematical basis, the generalized Trotter formula, and discuss the computational tools, exact summations and Monte Carlo simulation, that will be used t
Fractional statistics and quantum theory
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
Insights into the softening of chaotic statistical models by quantum considerations
Cafaro, C.; Giffin, A.; Lupo, C.; Mancini, S.
2012-05-01
We analyze the information geometry and the entropic dynamics of a 3D Gaussian statistical model and compare our analysis to that of a 2D Gaussian statistical model obtained from the higher-dimensional model via introduction of an additional information constraint that resembles the quantum mechanical canonical minimum uncertainty relation. We uncover that the chaoticity of the 2D Gaussian statistical model, quantified by means of the Information Geometric Entropy (IGE), is softened with respect to the chaoticity of the 3D Gaussian statistical model.
On quantum statistical inference
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.
Quantum Chaos and Statistical Mechanics
Srednicki, Mark
1994-01-01
We briefly review the well known connection between classical chaos and classical statistical mechanics, and the recently discovered connection between quantum chaos and quantum statistical mechanics.
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...
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...
A new model of quantum chaotic billiards Spectral Statistics and Wavefunctions in 2D
Cuevas, E; Vergés, J A
1996-01-01
Quantum chaotic dynamics is obtained for a tight-binding model in which the energies of the atomic levels at the boundary sites are chosen at random. Results for the square lattice indicate that the energy spectrum shows a complex behavior with regions that obey the Wigner-Dyson statistics and localized and quasi-ideal states distributed according to Poisson statistics. Although the averaged spatial extension of the eigenstates in the present model scales with the size of the system as in the Gaussian Orthogonal Ensemble, the fluctuations are much larger.
Lecture notes on quantum statistics
Gill, R.D.
2001-01-01
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
A Quantitative Model for the Thermocouple Effect Using Statistical and Quantum Mechanics
Bramley, Paul; Clark, Stewart
2003-09-01
This paper employs statistical and quantum mechanics to develop a model for the mechanism underlying the Seebeck effect. The conventional view of the equilibrium criterion for valence electrons in a material is that the Fermi Energy should be constant throughout the system. However, this criterion is an approximation and it is shown to be inadequate for thermocouple systems. An improved equilibrium criterion is developed by applying statistical and quantum mechanics to determine the total flow of electrons across an arbitrary boundary within a system. Dynamic equilibrium is then considered to be the situation where the Fermi Energy either side of the boundary is such that the flow of electrons in each direction is the same. This equilibrium criterion is then applied to the conditions along the thermocouple wires and at the junctions in order to generate a model for the Seebeck effect. The equations involved for calculating the electronic structure of a material cannot be solved analytically, so a solution is achieved using numeric models employing CASTEP code running on a Sun Beowulf cluster and iterative algorithms written in the Excel™ VBA language on a PC. The model is used to calculate the EMF versus temperature function for the gold versus platinum thermocouple, which is then compared with established experimental data.
Quantum statistical zero-knowledge
2002-01-01
In this paper we propose a definition for (honest verifier) quantum statistical zero-knowledge interactive proof systems and study the resulting complexity class, which we denote QSZK. We prove several facts regarding this class that establish close connections between classical statistical zero-knowledge and our definition for quantum statistical zero-knowledge, and give some insight regarding the effect of this zero-knowledge restriction on quantum interactive proof systems.
Quantum field theory from classical statistics
Wetterich, C
2011-01-01
An Ising-type classical statistical model is shown to describe quantum fermions. For a suitable time-evolution law for the probability distribution of the Ising-spins our model describes a quantum field theory for Dirac spinors in external electromagnetic fields, corresponding to a mean field approximation to quantum electrodynamics. All quantum features for the motion of an arbitrary number of electrons and positrons, including the characteristic interference effects for two-fermion states, are described by the classical statistical model. For one-particle states in the non-relativistic approximation we derive the Schr\\"odinger equation for a particle in a potential from the time evolution law for the probability distribution of the Ising-spins. Thus all characteristic quantum features, as interference in a double slit experiment, tunneling or discrete energy levels for stationary states, are derived from a classical statistical ensemble. Concerning the particle-wave-duality of quantum mechanics, the discret...
Unifying quantum heat transfer in a nonequilibrium spin-boson model with full counting statistics
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.
On Quantum Statistical Inference, II
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...
A transition in the spectral statistics of quantum optical model by different electromagnetic fields
Sabri, Hadi; Ezzati, Ahad ollah
2017-02-01
In this paper, we have considered the effects of different quantized electromagnetic fields on the spectral statistics of two-level atoms. The Berry-Robnik distribution and the maximum likelihood estimation technique are used to analyze the effect of the mean photon numbers, the two level atoms numbers and also the quantum number of considered states on the fluctuation properties of different systems which are described by different sets of the Dicke Hamiltonian's parameters. Our results describe the obvious effect of mean photon number on the spectral statistics and show more regular dynamics when this quantity reaches 700. Also, we observed universality in the spectral statistics of considered systems when the number of two level atoms approaches an unrealistic limit ( N A 200) and there are some suggestions about the effect of the quantum number of selected levels and the atom-field coupling constant on level statistics.
Quantum information theory and quantum statistics
Energy Technology Data Exchange (ETDEWEB)
Petz, D. [Alfred Renyi Institute of Mathematics, Budapest (Hungary)
2008-07-01
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.)
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.
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.
Quantum statistical testing of a quantum random number generator
Humble, Travis S.
2014-10-01
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 operation 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.
Kadatskiy, M. A.; Khishchenko, K. V.
2016-11-01
Quantum-statistical calculations of shock compressibility of iron are performed. Electronic part of thermodynamic functions is calculated in the framework of three quantum-statistical approaches: the Thomas-Fermi, the Thomas-Fermi with quantum and exchange corrections and the Hartree-Fock-Slater models. The influence of ionic part of thermodynamic functions is taken into account separately with using three models: the ideal gas, the one-component plasma and the charged hard spheres models. The results of calculations are presented in the pressure range from 1 to 107 GPa for samples with initially densities 7.85, 4.31 and 2.27 g/cm3. Calculated Hugoniots are compared with available experimental data.
Quantum-Shell Corrections to the Finite-Temperature Thomas-Fermi-Dirac Statistical Model of the Atom
Energy Technology Data Exchange (ETDEWEB)
Ritchie, A B
2003-07-22
Quantum-shell corrections are made directly to the finite-temperature Thomas-Fermi-Dirac statistical model of the atom by a partition of the electronic density into bound and free components. The bound component is calculated using analytic basis functions whose parameters are chosen to minimize the energy. Poisson's equation is solved for the modified density, thereby avoiding the need to solve Schroedinger's equation for a self-consistent field. The shock Hugoniot is calculated for aluminum: shell effects characteristic of quantum self-consistent field models are fully captures by the present model.
Statistical features of quantum evolution
Indian Academy of Sciences (India)
Sudhir R Jain
2009-08-01
It is shown that the integral of the uncertainty of energy with respect to time is independent of the particular Hamiltonian of the quantum system for an arbitrary pseudo-unitary (and hence $\\mathcal{PT}$ -) quantum evolution. The result generalizes the time– energy uncertainty principle for pseudo-unitary quantum evolutions. Further, employing random matrix theory developed for pseudo-Hermitian systems, time correlation functions are studied in the framework of linear response theory. The results given here provide a quantum brachistochrone problem where the system will evolve in a thermodynamic environment with spectral complexity that can be modelled by random matrix theory.
Comparison of Hugoniots calculated for aluminum in the framework of three quantum-statistical models
Kadatskiy, Maxim A
2015-01-01
The results of calculations of thermodynamic properties of aluminum under shock compression in the framework of the Thomas--Fermi model, the Thomas--Fermi model with quantum and exchange corrections and the Hartree--Fock--Slater model are presented. The influences of the thermal motion and the interaction of ions are taken into account in the framework of three models: the ideal gas, the one-component plasma and the charged hard spheres. Calculations are performed in the pressure range from 1 to $10^7$ GPa. Calculated Hugoniots are compared with available experimental data.
Comparison of Hugoniots calculated for aluminum in the framework of three quantum-statistical models
Kadatskiy, M. A.; Khishchenko, K. V.
2015-11-01
The results of calculations of thermodynamic properties of aluminum under shock compression in the framework of the Thomas-Fermi model, the Thomas-Fermi model with quantum and exchange corrections and the Hartree-Fock-Slater model are presented. The influences of the thermal motion and the interaction of ions are taken into account in the framework of three models: the ideal gas, the one-component plasma and the charged hard spheres. Calculations are performed in the pressure range from 1 to 107 GPa. Calculated Hugoniots are compared with available experimental data.
Generalized classical, quantum and intermediate statistics and the Polya urn model
Energy Technology Data Exchange (ETDEWEB)
Niven, Robert K. [School of Aerospace, Civil and Mechanical Engineering, University of New South Wales at ADFA, Northcott Drive, Canberra, ACT, 2600 (Australia); Niels Bohr Institute, University of Copenhagen, Copenhagen O (Denmark)], E-mail: r.niven@adfa.edu.au; Grendar, Marian [Department of Mathematics, Faculty of Natural Sciences, Bel University, Tajovskeho 40, 974 01 Banska Bystrica (Slovakia)], E-mail: marian.grendar@savba.sk
2009-02-02
Generalized probability distributions for Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics, with unequal source ('prior') probabilities q{sub i} for each level i, are obtained by combinatorial reasoning. For equiprobable degenerate sublevels, these reduce to those given by Brillouin in 1930, more commonly given as a statistical weight for each statistic. These distributions and corresponding cross-entropy (divergence) functions are shown to be special cases of the Polya urn model, involving neither independent nor identically distributed ('ninid') sampling. The most probable Polya distribution is shown to contain the Acharya-Swamy intermediate statistic.
Hidden Statistics Approach to Quantum Simulations
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
On quantum statistics in data analysis
Pavlovic, Dusko
2008-01-01
Originally, quantum probability theory was developed to analyze statistical phenomena in quantum systems, where classical probability theory does not apply, because the lattice of measurable sets is not necessarily distributive. On the other hand, it is well known that the lattices of concepts, that arise in data analysis, are in general also non-distributive, albeit for completely different reasons. In his recent book, van Rijsbergen argues that many of the logical tools developed for quantum systems are also suitable for applications in information retrieval. I explore the mathematical support for this idea on an abstract vector space model, covering several forms of data analysis (information retrieval, data mining, collaborative filtering, formal concept analysis...), and roughly based on an idea from categorical quantum mechanics. It turns out that quantum (i.e., noncommutative) probability distributions arise already in this rudimentary mathematical framework. Moreover, a Bell-type inequality is formula...
Quantum-like microeconomics: Statistical model of distribution of investments and production
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.
Parvan, A S; Ploszajczak, M
2000-01-01
A quantum statistical model of nuclear multifragmentation is proposed. The recurrence equation method used within 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.
Trejos, Víctor M; Gil-Villegas, Alejandro
2012-05-14
Thermodynamic properties of quantum fluids are described using an extended version of the statistical associating fluid theory for potentials of variable range (SAFT-VR) that takes into account quantum corrections to the Helmholtz free energy A, based on the Wentzel-Kramers-Brillouin approximation. We present the theoretical background of this approach (SAFT-VRQ), considering two different cases depending on the continuous or discontinuous nature of the particles pair interaction. For the case of continuous potentials, we demonstrate that the standard Wigner-Kirkwood theory for quantum fluids can be derived from the de Broglie-Bohm formalism for quantum mechanics that can be incorporated within the Barker and Henderson perturbation theory for liquids in a straightforward way. When the particles interact via a discontinuous pair potential, the SAFT-VR method can be combined with the perturbation theory developed by Singh and Sinha [J. Chem. Phys. 67, 3645 (1977); and ibid. 68, 562 (1978)]. We present an analytical expression for the first-order quantum perturbation term for a square-well potential, and the theory is applied to model thermodynamic properties of hydrogen, deuterium, neon, and helium-4. Vapor-liquid equilibrium, liquid and vapor densities, isochoric and isobaric heat capacities, Joule-Thomson coefficients and inversion curves are predicted accurately with respect to experimental data. We find that quantum corrections are important for the global behavior of properties of these fluids and not only for the low-temperature regime. Predictions obtained for hydrogen compare very favorably with respect to cubic equations of state.
Trejos, Víctor M.; Gil-Villegas, Alejandro
2012-05-01
Thermodynamic properties of quantum fluids are described using an extended version of the statistical associating fluid theory for potentials of variable range (SAFT-VR) that takes into account quantum corrections to the Helmholtz free energy A, based on the Wentzel-Kramers-Brillouin approximation. We present the theoretical background of this approach (SAFT-VRQ), considering two different cases depending on the continuous or discontinuous nature of the particles pair interaction. For the case of continuous potentials, we demonstrate that the standard Wigner-Kirkwood theory for quantum fluids can be derived from the de Broglie-Bohm formalism for quantum mechanics that can be incorporated within the Barker and Henderson perturbation theory for liquids in a straightforward way. When the particles interact via a discontinuous pair potential, the SAFT-VR method can be combined with the perturbation theory developed by Singh and Sinha [J. Chem. Phys. 67, 3645 (1977); Singh and Sinha J. Chem. Phys. 68, 562 (1978)]. We present an analytical expression for the first-order quantum perturbation term for a square-well potential, and the theory is applied to model thermodynamic properties of hydrogen, deuterium, neon, and helium-4. Vapor-liquid equilibrium, liquid and vapor densities, isochoric and isobaric heat capacities, Joule-Thomson coefficients and inversion curves are predicted accurately with respect to experimental data. We find that quantum corrections are important for the global behavior of properties of these fluids and not only for the low-temperature regime. Predictions obtained for hydrogen compare very favorably with respect to cubic equations of state.
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)
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
Quantum Coins, Dice and Children: Probability and Quantum Statistics
Chow, Chi-Keung; Cohen, Thomas D.
1999-01-01
We discuss counterintuitive aspects of probabilities for systems of identical particles obeying quantum statistics. Quantum coins and children (two level systems) and quantum dice (many level systems) are used as examples. It is emphasized that, even in the absence of interactions, (anti)symmetrizations of multi-particle wavefunctions destroy statistical independences and often lead to dramatic departures from our intuitive expectations.
Energy Technology Data Exchange (ETDEWEB)
Mohammadi, M [Department of Physics, Science and Research Campus Azad University of Tehran, Tehran (Iran, Islamic Republic of); Naderi, M H [Quantum Optics Group, Department of Physics, University of Isfahan, Isfahan (Iran, Islamic Republic of); Soltanolkotabi, M [Quantum Optics Group, Department of Physics, University of Isfahan, Isfahan (Iran, Islamic Republic of)
2007-02-09
The temporal evolution of quantum statistical properties of an interacting atom-radiation field system in the presence of a classical homogeneous gravitational field is investigated within the framework of the Jaynes-Cummings model. To analyse the dynamical evolution of the atom-radiation system a quantum treatment of the internal and external dynamics of the atom is presented based on an alternative su(2) dynamical algebraic structure. By solving the Schroedinger equation in the interaction picture, the evolving state of the system is found by which the influence of the gravitational field on the dynamical behaviour of the atom-radiation system is explored. Assuming that initially the radiation field is prepared in a coherent state and the two-level atom is in a coherent superposition of the excited and ground states, the influence of gravity on the collapses and revivals of the atomic population inversion, atomic dipole squeezing, atomic momentum diffusion, photon counting statistics and quadrature squeezing of the radiation field is studied.
Statistical thermodynamics of polymer quantum systems
Chacón-Acosta, Guillermo; Dagdug, Leonardo; Morales-Técotl, Hugo A
2011-01-01
Polymer quantum systems are mechanical models quantized similarly as loop quantum gravity. It is actually in quantizing gravity that the polymer term holds proper as the quantum geometry excitations yield a reminiscent of a polymer material. In such an approach both non-singular cosmological models and a microscopic basis for the entropy of some black holes have arisen. Also important physical questions for these systems involve thermodynamics. With this motivation, in this work, we study the statistical thermodynamics of two one dimensional {\\em polymer} quantum systems: an ensemble of oscillators that describe a solid and a bunch of non-interacting particles in a box, which thus form an ideal gas. We first study the spectra of these polymer systems. It turns out useful for the analysis to consider the length scale required by the quantization and which we shall refer to as polymer length. The dynamics of the polymer oscillator can be given the form of that for the standard quantum pendulum. Depending on the...
Somers, Kieran P; Simmie, John M; Metcalfe, Wayne K; Curran, Henry J
2014-03-21
Due to the rapidly growing interest in the use of biomass derived furanic compounds as potential platform chemicals and fossil fuel replacements, there is a simultaneous need to understand the pyrolysis and combustion properties of such molecules. To this end, the potential energy surfaces for the pyrolysis relevant reactions of the biofuel candidate 2-methylfuran have been characterized using quantum chemical methods (CBS-QB3, CBS-APNO and G3). Canonical transition state theory is employed to determine the high-pressure limiting kinetics, k(T), of elementary reactions. Rice-Ramsperger-Kassel-Marcus theory with an energy grained master equation is used to compute pressure-dependent rate constants, k(T,p), and product branching fractions for the multiple-well, multiple-channel reaction pathways which typify the pyrolysis reactions of the title species. The unimolecular decomposition of 2-methylfuran is shown to proceed via hydrogen atom transfer reactions through singlet carbene intermediates which readily undergo ring opening to form collisionally stabilised acyclic C5H6O isomers before further decomposition to C1-C4 species. Rate constants for abstraction by the hydrogen atom and methyl radical are reported, with abstraction from the alkyl side chain calculated to dominate. The fate of the primary abstraction product, 2-furanylmethyl radical, is shown to be thermal decomposition to the n-butadienyl radical and carbon monoxide through a series of ring opening and hydrogen atom transfer reactions. The dominant bimolecular products of hydrogen atom addition reactions are found to be furan and methyl radical, 1-butene-1-yl radical and carbon monoxide and vinyl ketene and methyl radical. A kinetic mechanism is assembled with computer simulations in good agreement with shock tube speciation profiles taken from the literature. The kinetic mechanism developed herein can be used in future chemical kinetic modelling studies on the pyrolysis and oxidation of 2-methylfuran
Quantum entanglement and teleportation using statistical correlations
Indian Academy of Sciences (India)
Atul Kumar; Mangala Sunder Krishnan
2009-09-01
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 2-particle system. A relation between the probability and statistical parameters is established using the correlated density matrices for the particles.
Quantum Statistical Calculation of Exchange Bias
Institute of Scientific and Technical Information of China (English)
WANG Huai-Yu; DAI Zhen-Hong
2004-01-01
The phenomenon of exchange bias of ferromagnetic (FM) films, which are coupled with an antiferromagnetic (AFM) film, is studied by Heisenberg model by use of the many-body Green's function method of quantum statistical theory for the uncompensated case. Exchange bias HE and coercivity Hc are calculated as functions of the FM film thickness L, temperature, the strength of the exchange interaction across the interface between FM and AFM and the anisotropy of the FM. Hc decreases with increasing L when the FM film is beyond some thickness. The dependence of the exchange bias HE on the FM film thickness and on temperature is also qualitatively in agreement with experiments.
Aoiz, F J; González-Lezana, T; Sáez Rábanos, V
2008-09-01
A detailed comparison of statistical models based on the quasiclassical trajectory (SQCT) and quantum mechanical (SQM) methods is presented in this work for the C((1)D)+H(2), S((1)D)+H(2), O((1)D)+H(2) and N((2)D)+H(2) insertion reactions. Reaction probabilities, integral (ICS) and differential (DCS) cross sections at different levels of product's state resolution are shown and discussed for these reactions. The agreement is in most cases excellent and indicates that the effect of tunneling through the centrifugal barrier is negligible. However, if there exists a dynamical barrier, as in the case of the N((2)D)+H(2) reaction, some of the SQM results can be slightly different than those calculated with the SQCT model. The rationale of the observed similarities and discrepancies can be traced back to the specific topologies of the potential energy surfaces for each of the reactions examined. The SQCT model is sensitive enough to show the relatively small inaccuracies resulting from the decoupling inherent to the centrifugal sudden approximation when used in the SQM calculations. In addition, the effect of ignoring the parity conservation is also examined. This effect is in general minor except in particular cases such as the DCS from initial rotational state j=0, which requires, in order to reproduce the sharp forward and backward peaks, the explicit conservation of parity.
Spin Glass a Bridge Between Quantum Computation and Statistical Mechanics
Ohzeki, Masayuki
2013-09-01
In this chapter, we show two fascinating topics lying between quantum information processing and statistical mechanics. First, we introduce an elaborated technique, the surface code, to prepare the particular quantum state with robustness against decoherence. Interestingly, the theoretical limitation of the surface code, accuracy threshold, to restore the quantum state has a close connection with the problem on the phase transition in a special model known as spin glasses, which is one of the most active researches in statistical mechanics. The phase transition in spin glasses is an intractable problem, since we must strive many-body system with complicated interactions with change of their signs depending on the distance between spins. Fortunately, recent progress in spin-glass theory enables us to predict the precise location of the critical point, at which the phase transition occurs. It means that statistical mechanics is available for revealing one of the most interesting parts in quantum information processing. We show how to import the special tool in statistical mechanics into the problem on the accuracy threshold in quantum computation. Second, we show another interesting technique to employ quantum nature, quantum annealing. The purpose of quantum annealing is to search for the most favored solution of a multivariable function, namely optimization problem. The most typical instance is the traveling salesman problem to find the minimum tour while visiting all the cities. In quantum annealing, we introduce quantum fluctuation to drive a particular system with the artificial Hamiltonian, in which the ground state represents the optimal solution of the specific problem we desire to solve. Induction of the quantum fluctuation gives rise to the quantum tunneling effect, which allows nontrivial hopping from state to state. We then sketch a strategy to control the quantum fluctuation efficiently reaching the ground state. Such a generic framework is called
DEFF Research Database (Denmark)
Van Driel, A.F.; Nikolaev, I.S.; Vergeer, P.
2007-01-01
analysis to recent examples of colloidal quantum dot emission in suspensions and in photonic crystals, and we find that this important class of emitters is well described by a log-normal distribution of decay rates with a narrow and a broad distribution, respectively. Finally, we briefly discuss......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...
Statistical Properties of Quantum Spectra in Nuclei
Institute of Scientific and Technical Information of China (English)
2001-01-01
Some aspects of quantum chaos in a finite system have been studied based on the analysis of statistical behaviors of quantum spectrum in nuclei. The experiment data show the transition from order to chaos with increasing excitation energy in spherical nuclei. The dependence of the order to chaos transition on nuclear deformation and nuclear rotating is described. The influence of pairing effect on the order to chaos transition is also discussed. Some important experiment phenomena in nuclear
On quantum statistical mechanics; A study guide
Majewski, W. A.
2016-01-01
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical mechanics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in the analysis of large quantum systems, and their consequences. These include the emergence of algebraic approach and the necessity of employment of infinite dimensional structures. As an illustration, a quantization of stochastic processes, new formalism...
Nonrenewal statistics in transport through quantum dots
Ptaszyński, Krzysztof
2017-01-01
The distribution of waiting times between successive tunneling events is an already established method to characterize current fluctuations in mesoscopic systems. Here, I investigate mechanisms generating correlations between subsequent waiting times in two model systems, a pair of capacitively coupled quantum dots and a single-level dot attached to spin-polarized leads. Waiting time correlations are shown to give insight into the internal dynamics of the system; for example they allow distinction between different mechanisms of the noise enhancement. Moreover, the presence of correlations breaks the validity of the renewal theory. This increases the number of independent cumulants of current fluctuation statistics, thus providing additional sources of information about the transport mechanism. I also propose a method for inferring the presence of waiting time correlations based on low-order current correlation functions. This method gives a way to extend the analysis of nonrenewal current fluctuations to the systems for which single-electron counting is not experimentally feasible. The experimental relevance of the findings is also discussed; for example reanalysis of previous results concerning transport in quantum dots is suggested.
Energy level statistics of quantum dots.
Tsau, Chien-Yu; Nghiem, Diu; Joynt, Robert; Woods Halley, J
2007-05-08
We investigate the charging energy level statistics of disordered interacting electrons in quantum dots by numerical calculations using the Hartree approximation. The aim is to obtain a global picture of the statistics as a function of disorder and interaction strengths. We find Poisson statistics at very strong disorder, Wigner-Dyson statistics for weak disorder and interactions, and a Gaussian intermediate regime. These regimes are as expected from previous studies and fundamental considerations, but we also find interesting and rather broad crossover regimes. In particular, intermediate between the Gaussian and Poisson regimes we find a two-sided exponential distribution for the energy level spacings. In comparing with experiment, we find that this distribution may be realized in some quantum dots.
Energy level statistics of quantum dots
Energy Technology Data Exchange (ETDEWEB)
Tsau, C-Y [University of Wisconsin-Madison, Madison, WI 53706 (United States); Nghiem, Diu [University of Wisconsin-Madison, Madison, WI 53706 (United States); Joynt, Robert [University of Wisconsin-Madison, Madison, WI 53706 (United States); Halley, J Woods [School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455 (United States)
2007-05-08
We investigate the charging energy level statistics of disordered interacting electrons in quantum dots by numerical calculations using the Hartree approximation. The aim is to obtain a global picture of the statistics as a function of disorder and interaction strengths. We find Poisson statistics at very strong disorder, Wigner-Dyson statistics for weak disorder and interactions, and a Gaussian intermediate regime. These regimes are as expected from previous studies and fundamental considerations, but we also find interesting and rather broad crossover regimes. In particular, intermediate between the Gaussian and Poisson regimes we find a two-sided exponential distribution for the energy level spacings. In comparing with experiment, we find that this distribution may be realized in some quantum dots.
Energy level statistics of quantum dots
Tsau, Chien-Yu; Nghiem, Diu; Joynt, Robert; Halley, J. Woods
2007-05-01
We investigate the charging energy level statistics of disordered interacting electrons in quantum dots by numerical calculations using the Hartree approximation. The aim is to obtain a global picture of the statistics as a function of disorder and interaction strengths. We find Poisson statistics at very strong disorder, Wigner-Dyson statistics for weak disorder and interactions, and a Gaussian intermediate regime. These regimes are as expected from previous studies and fundamental considerations, but we also find interesting and rather broad crossover regimes. In particular, intermediate between the Gaussian and Poisson regimes we find a two-sided exponential distribution for the energy level spacings. In comparing with experiment, we find that this distribution may be realized in some quantum dots.
QInfer: Statistical inference software for quantum applications
Granade, Christopher; Hincks, Ian; Casagrande, Steven; Alexander, Thomas; Gross, Jonathan; Kononenko, Michal; Sanders, Yuval
2016-01-01
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.
Spin & Statistics in Nonrelativistic Quantum Mechanics, II
Kuckert, B; Kuckert, Bernd; Mund, Jens
2004-01-01
Recently a sufficient and necessary condition for Pauli's spin- statistics connection in nonrelativistic quantum mechanics has been established [quant-ph/0208151]. The two-dimensional part of this result is extended to n-particle systems and reformulated and further simplified in a more geometric language.
Quantum approach to classical statistical mechanics.
Somma, R D; Batista, C D; Ortiz, G
2007-07-20
We present a new approach to study the thermodynamic properties of d-dimensional classical systems by reducing the problem to the computation of ground state properties of a d-dimensional quantum model. This classical-to-quantum mapping allows us to extend the scope of standard optimization methods by unifying them under a general framework. The quantum annealing method is naturally extended to simulate classical systems at finite temperatures. We derive the rates to assure convergence to the optimal thermodynamic state using the adiabatic theorem of quantum mechanics. For simulated and quantum annealing, we obtain the asymptotic rates of T(t) approximately (pN)/(k(B)logt) and gamma(t) approximately (Nt)(-c/N), for the temperature and magnetic field, respectively. Other annealing strategies are also discussed.
Statistical properties of quantum spectra in nuclei
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Some aspects of quantum chaos in a finite system have been studied based on the analysis of statistical behavior of quantum spectra in nuclei.The experiment data show the transition from order to chaos with increasing excitation energy in spherical nuclei.The dependence of the order to chaos transition on nuclear deformation and nuclear rotating is described.The influence of pairing effect on the order to chaos transition is also discussed.Some important experiment phenomena in nuclear physics have been understood from the point of view of the interplay between order and chaos.
Applications of quantum entropy to statistics
Energy Technology Data Exchange (ETDEWEB)
Silver, R.N.; Martz, H.F.
1994-07-01
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.
Tailored quantum statistics from broadband states of light
Hartmann, S; Molitor, A; Reichert, M; Elsäßer, W; Walser, R
2014-01-01
We analyze the statistics of photons originating from amplified spontaneous emission generated by a quantum dot superluminescent diode. Experimentally detectable emission properties are taken into account by parametrizing the corresponding quantum state as a multi-mode phase-randomized Gaussian density operator. The validity of this model is proven in two subsequent experiments using fast two-photon-absorption detection observing second order equal-time- as well as second order fully time-resolved intensity correlations on femtosecond timescales. In the first experiment, we study the photon statistics when the number of contributing longitudinal modes is systematically reduced by applying well-controlled optical feedback. In a second experiment, we add coherent light from a single-mode laserdiode to quantum dot superluminescent diode broadband radiation. Tuning the power ratio, we realize tailored second order correlations ranging from Gaussian to Poissonian statistics. Both experiments are very well matched ...
Statistical dynamics of a non-Abelian anyonic quantum walk
Lehman, Lauri; Brennen, Gavin K; Pachos, Jiannis K; Wang, Zhenghan
2010-01-01
We study the single particle dynamics of a mobile non-Abelian anyon hopping around many pinned anyons on a surface. The dynamics is modelled by a discrete time quantum walk and the spatial degree of freedom of the mobile anyon becomes entangled with the fusion degrees of freedom of the collective system. Each quantum trajectory makes a closed braid on the world lines of the particles establishing a direct connection between statistical dynamics and quantum link invariants. We find that asymptotically a mobile Ising anyon becomes so entangled with its environment that its statistical dynamics reduces to a classical random walk with linear dispersion in contrast to particles with Abelian statistics which have quadratic dispersion.
Emergence of Quantum Mechanics from a Sub-Quantum Statistical Mechanics
Grössing, Gerhard
2015-10-01
A research program within the scope of theories on "Emergent Quantum Mechanics" is presented, which has gained some momentum in recent years. Via the modeling of a quantum system as a non-equilibrium steady-state maintained by a permanent throughput of energy from the zero-point vacuum, the quantum is considered as an emergent system. We implement a specific "bouncer-walker" model in the context of an assumed sub-quantum statistical physics, in analogy to the results of experiments by Couder and Fort on a classical wave-particle duality. We can thus give an explanation of various quantum mechanical features and results on the basis of a "21st century classical physics", such as the appearance of Planck's constant, the Schrödinger equation, etc. An essential result is given by the proof that averaged particle trajectories' behaviors correspond to a specific type of anomalous diffusion termed "ballistic" diffusion on a sub-quantum level...
Manos, T
2015-01-01
We study the quantum kicked rotator in the classically fully chaotic regime $K=10$ and for various values of the quantum parameter $k$ using Izrailev's $N$-dimensional model for various $N \\le 3000$, which in the limit $N \\rightarrow \\infty$ tends to the exact quantized kicked rotator. By numerically calculating the eigenfunctions in the basis of the angular momentum we find that the localization length ${\\cal L}$ for fixed parameter values has a certain distribution, in fact its inverse is Gaussian distributed, in analogy and in connection with the distribution of finite time Lyapunov exponents of Hamilton systems. However, unlike the case of the finite time Lyapunov exponents, this distribution is found to be independent of $N$, and thus survives the limit $N=\\infty$. This is different from the tight-binding model of Anderson localization. The reason is that the finite bandwidth approximation of the underlying Hamilton dynamical system in the Shepelyansky picture (D.L. Shepelyansky, {\\em Phys. Rev. Lett.} {...
Electron Energy Level Statistics in Graphene Quantum Dots
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 experi
PT Symmetry in Classical and Quantum Statistical Mechanics
Meisinger, Peter N
2012-01-01
PT-symmetric Hamiltonians and transfer matrices arise naturally in statistical mechanics. These classical and quantum models often require the use of complex or negative weights and thus fall outside of the conventional equilibrium statistical mechanics of Hermitian systems. PT-symmetric models form a natural class where the partition function is necessarily real, but not necessarily positive. The correlation functions of these models display a much richer set of behaviors than Hermitian systems, displaying sinusoidally-modulated exponential decay, as in a dense fluid, or even sinusoidal modulation without decay. Classical spin models with PT symmetry include Z(N) models with a complex magnetic field, the chiral Potts model and the anisotropic next-nearest-neighbor Ising (ANNNI) model. Quantum many-body problems with a non-zero chemical potential have a natural PT-symmetric representation related to the sign problem. Two-dimensional QCD with heavy quarks at non-zero chemical potential can be solved by diagona...
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.
Statistical properties of quantum spectra in nuclei
Institute of Scientific and Technical Information of China (English)
WU; Xizhen
2001-01-01
［1］Wu Xizhen,Sakata,F.,Zhuo Yizhong et al.,Dynamic realization of statistical state in finite systems,Phys.ReV.C,1996,53:1233-1244.［2］Weidenmüller,H.A.,Statistical theory of nuclear reactions and the Gaussian Othogonal Ensemble,Annals of Physics,1984,158:120-141.［3］Hag,R.U.,Pandey,A.,Bohigas,O.,Fluctuation properties of nuclear energy levels:Do theory and experiment agree? Phys.Rev.Lett.,1982,48:1086-1089.［4］Wu Xizhen,Gu Jianzhong,Iwamoto,A.,Statistical properties of quasiparticle spectra in deformed nuclei,Phys.Rev.C,1999,59:215-220.［5］Garrett,J.D.,Robinson,J.Q.,Foglia,A.J.et al.,Nuclear level repulsion and order vs chaos,Phys.Lett.B,1997,392:24-29.［6］Bohigas,O.,Hag,R.U.,Pandy,A.,Fluctuation properties of nuclear energy levels and widths comparison of theory with experiment,in Nuclear Data for Science and Technology (ed.Bockhoff,K.H.),Dordrecht:Reidel,1983,809-813.［7］Heiss,W.D.,Nazmitdinov,R.G.,Radu,S.,Chaos in axially symmetric potentials with Octupole deformation,Phys.Rev.Lett.,1994,72:2351-2354.［8］Wu Xizhen,Gu Jianzhong,Zhuo Yizhong et al.,Possible understanding of hyperdeformed 144-146Ba nuclei appearing in the spontaneous fission of 252Cf,Phys.Rev.Lett.,1997,79:4542-4545.［9］Ter-Akopian,G.M.,Hamilton,J.H.,Oganessian,Y.T.et al.,New spontaneous fission mode for 252Cf:Indication of hyperdeformed 144,145,146Ba at scission,Phys.Rev.Lett.,1996,77:32-35.［10］Adamian,G.G.,Antonenko,N.V.,Ivanova,S.P.et al.,Problems in description of fusion of heavy nuclei in the two-center shell model approach,Nucl.Phys.A,1999,646:29-52.［11］Hofmann,H.,A quantal transport theory for nuclear collective motion:the metrits of a locally harmonic approximation method,Phys.Rep.,1997,284:139-380.［12］Gu Jianzhong,Wu Xizhen,Zhuo Yizhong,Quantum chaotic motion of a single particle in heavy nuclei,Nucl.Phys.A,1997,625:621-632.［13］Gu Jianzhong,Wu Xizhen,Zhuo Yizhong,The single-particle spectrum and its spacing and curvature distributions in
Statistics of Quantum Turbulence in Superfluid He
L'vov, V. S.; Pomyalov, A.
2016-11-01
Based on our current understanding of statistics of quantum turbulence as well as on results of intensive ongoing analytical, numerical and experimental studies, we overview here the following problems in the large-scale, space-homogeneous, steady-state turbulence of superfluid ^4 He and ^3 He: (1) energy spectra of normal and superfluid velocity components; (2) cross-correlation function of normal and superfluid velocities; (3) energy dissipation by mutual friction and viscosity; (4) energy exchange between normal and superfluid components; (5) high-order statistics and intermittency effects. The statistical properties are discussed for turbulence in different types of flows: coflow of ^4 He; turbulent ^3 He with the laminar normal fluid; pure superflow and counterflow in ^4 He.
Exploring gravitational statistics not based on quantum dynamical assumptions
Mandrin, P A
2016-01-01
Despite considerable progress in several approaches to quantum gravity, there remain uncertainties on the conceptual level. One issue concerns the different roles played by space and time in the canonical quantum formalism. This issue occurs because the Hamilton-Jacobi dynamics is being quantised. The question then arises whether additional physically relevant states could exist which cannot be represented in the canonical form or as a partition function. For this reason, the author has explored a statistical approach (NDA) which is not based on quantum dynamical assumptions and does not require space-time splitting boundary conditions either. For dimension 3+1 and under thermal equilibrium, NDA simplifies to a path integral model. However, the general case of NDA cannot be written as a partition function. As a test of NDA, one recovers general relativity at low curvature and quantum field theory in the flat space-time approximation. Related paper: arxiv:1505.03719.
Tailored quantum statistics from broadband states of light
Hartmann, S.; Friedrich, F.; Molitor, A.; Reichert, M.; Elsäßer, W.; Walser, R.
2015-04-01
We analyze the statistics of photons originating from amplified spontaneous emission generated by a quantum dot superluminescent diode. Experimentally detectable emission properties are taken into account by parametrizing the corresponding quantum state as a multimode phase-randomized Gaussian density operator. The validity of this model is proven in two subsequent experiments using fast two-photon-absorption detection observing second-order equal-time and second-order fully time-resolved intensity correlations on femtosecond timescales. In the first experiment, we study the photon statistics when the number of contributing longitudinal modes is systematically reduced by applying well-controlled optical feedback. In a second experiment, we add coherent light from a single-mode laser diode to quantum dot superluminescent diode broadband radiation. Tuning the power ratio, we realize tailored second-order correlations ranging from Gaussian to Poissonian statistics. Both experiments are very well matched by theory, thus giving first insights into the quantum properties of radiation from quantum dot superluminescent diodes.
Quantum Statistical Theory of Polarization Mode Dispersion
Institute of Scientific and Technical Information of China (English)
ZHANG Yong-Sheng; GUO Guang-Can
2006-01-01
@@ Polarization mode dispersion is modelled as decoherence of polarization under the disturbance of environment and the coupling with frequency. This model is described by the quantum master equation and the Langevin equation. It can be predicted that the optical beam is depolarized exponentially in a fibre and the differential group delay (DGD) is proportional to the square root of the propagation distance. The distribution of the DGD can also be calculated.
Statistical Quadrature Evolution for Continuous-Variable Quantum Key Distribution
Gyongyosi, Laszlo; Imre, Sandor
2016-05-01
We propose a statistical quadrature evolution (SQE) method for multicarrier continuous-variable quantum key distribution (CVQKD). A multicarrier CVQKD protocol utilizes Gaussian subcarrier quantum continuous variables (CV) for information transmission. The SQE framework provides a minimal error estimate of the quadratures of the CV quantum states from the discrete, measured noisy subcarrier variables. We define a method for the statistical modeling and processing of noisy Gaussian subcarrier quadratures. We introduce the terms statistical secret key rate and statistical private classical information, which quantities are derived purely by the statistical functions of our method. We prove the secret key rate formulas for a multiple access multicarrier CVQKD. The framework can be established in an arbitrary CVQKD protocol and measurement setting, and are implementable by standard low-complexity statistical functions, which is particularly convenient for an experimental CVQKD scenario. This work was partially supported by the GOP-1.1.1-11-2012-0092 project sponsored by the EU and European Structural Fund, by the Hungarian Scientific Research Fund - OTKA K-112125, and by the COST Action MP1006.
Quantum Informatics View of Statistical Data Processing
Bogdanov, Yu. I.; Bogdanova, N. A.
2011-01-01
Application of root density estimator to problems of statistical data analysis is demonstrated. Four sets of basis functions based on Chebyshev-Hermite, Laguerre, Kravchuk and Charlier polynomials are considered. The sets may be used for numerical analysis in problems of reconstructing statistical distributions by experimental data. Examples of numerical modeling are given.
Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics
Jaksic, V; Pillet, C -A; Seiringer, R
2011-01-01
We extend the mathematical theory of quantum hypothesis testing to the general $W^*$-algebraic setting and explore its relation with recent developments in non-equilibrium quantum statistical mechanics. In particular, we relate the large deviation principle for the full counting statistics of entropy flow to quantum hypothesis testing of the arrow of time.
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. Th...... 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....
Statistical entropy of open quantum systems
Durão, L. M. M.; Caldeira, A. O.
2016-12-01
Dissipative quantum systems are frequently described within the framework of the so-called "system-plus-reservoir" approach. In this work we assign their description to the Maximum Entropy Formalism and compare the resulting thermodynamic properties with those of the well-established approaches. Due to the non-negligible coupling to the heat reservoir, these systems are nonextensive by nature, and the former task may require the use of nonextensive parameter dependent informational entropies. In doing so, we address the problem of choosing appropriate forms of those entropies in order to describe a consistent thermodynamics for dissipative quantum systems. Nevertheless, even having chosen the most successful and popular forms of those entropies, we have proven our model to be a counterexample where this sort of approach leads us to wrong results.
PT symmetry in classical and quantum statistical mechanics.
Meisinger, Peter N; Ogilvie, Michael C
2013-04-28
PT-symmetric Hamiltonians and transfer matrices arise naturally in statistical mechanics. These classical and quantum models often require the use of complex or negative weights and thus fall outside the conventional equilibrium statistical mechanics of Hermitian systems. PT-symmetric models form a natural class where the partition function is necessarily real, but not necessarily positive. The correlation functions of these models display a much richer set of behaviours than Hermitian systems, displaying sinusoidally modulated exponential decay, as in a dense fluid, or even sinusoidal modulation without decay. Classical spin models with PT-symmetry include Z(N) models with a complex magnetic field, the chiral Potts model and the anisotropic next-nearest-neighbour Ising model. Quantum many-body problems with a non-zero chemical potential have a natural PT-symmetric representation related to the sign problem. Two-dimensional quantum chromodynamics with heavy quarks at non-zero chemical potential can be solved by diagonalizing an appropriate PT-symmetric Hamiltonian.
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...
Quench echo and work statistics in integrable quantum field theories.
Pálmai, T; Sotiriadis, S
2014-11-01
We propose a boundary thermodynamic Bethe ansatz calculation technique to obtain the Loschmidt echo and the statistics of the work done when a global quantum quench is performed on an integrable quantum field theory. We derive an analytic expression for the lowest edge of the probability density function and find that it exhibits universal features, in the sense that its scaling form depends only on the statistics of excitations. We perform numerical calculations on the sinh-Gordon model, a deformation of the free boson theory, and we obtain that by turning on the interaction the density function develops fermionic properties. The calculations are facilitated by a previously unnoticed property of the thermodynamic Bethe ansatz construction.
Numerical computation for teaching quantum statistics
Price, Tyson; Swendsen, Robert H.
2013-11-01
The study of ideal quantum gases reveals surprising quantum effects that can be observed in macroscopic systems. The properties of bosons are particularly unusual because a macroscopic number of particles can occupy a single quantum state. We describe a computational approach that supplements the usual analytic derivations applicable in the thermodynamic limit. The approach involves directly summing over the quantum states for finite systems and avoids the need for doing difficult integrals. The results display the unusual behavior of quantum gases even for relatively small systems.
Quantum statistical derivation of the macroscopic Maxwell equations
Schram, K.
1960-01-01
The macroscopic Maxwell equations in matter are derived on a quantum statistical basis from the microscopic equations for the field operators. Both the density operator formalism and the Wigner distribution function method are discussed. By both methods it can be proved that the quantum statistical
Quantum cosmological metroland model
Anderson, E.; Franzen, A.T.
2010-01-01
Relational particle mechanics is useful for modelling whole-universe issues such as quantum cosmology or the problem of time in quantum gravity, including some aspects outside the reach of comparably complex mini-superspace models. In this paper, we consider the mechanics of pure shape and not scale
Modeling cosmic void statistics
Hamaus, Nico; Sutter, P. M.; Wandelt, Benjamin D.
2016-10-01
Understanding the internal structure and spatial distribution of cosmic voids is crucial when considering them as probes of cosmology. We present recent advances in modeling void density- and velocity-profiles in real space, as well as void two-point statistics in redshift space, by examining voids identified via the watershed transform in state-of-the-art ΛCDM n-body simulations and mock galaxy catalogs. The simple and universal characteristics that emerge from these statistics indicate the self-similarity of large-scale structure and suggest cosmic voids to be among the most pristine objects to consider for future studies on the nature of dark energy, dark matter and modified gravity.
Algebraic-statistical approach to quantum mechanics
Slavnov, D A
2001-01-01
It is proposed the scheme of quantum mechanics, in which a Hilbert space and the linear operators are not primary elements of the theory. Instead of it certain variant of the algebraic approach is considered. The elements of noncommutative algebra (observables) and the nonlinear functionals on this algebra (physical states) are used as the primary constituents. The functionals associate with results of a particular measurement. It is suggested to consider certain ensembles of the physical states as quantum states of the standart quantum mechanics. It is shown that in such scheme the mathematical formalism of the standart quantum mechanics can be reproduced completely.
Statistical mechanics of quantum-classical systems with holonomic constraints.
Sergi, Alessandro
2006-01-14
The statistical mechanics of quantum-classical systems with holonomic constraints is formulated rigorously by unifying the classical Dirac bracket and the quantum-classical bracket in matrix form. The resulting Dirac quantum-classical theory, which conserves the holonomic constraints exactly, is then used to formulate time evolution and statistical mechanics. The correct momentum-jump approximation for constrained systems arises naturally from this formalism. Finally, in analogy with what was found in the classical case, it is shown that the rigorous linear-response function of constrained quantum-classical systems contains nontrivial additional terms which are absent in the response of unconstrained systems.
Quantum-statistical equation-of-state models of dense plasmas: high-pressure Hugoniot shock adiabats
Pain, Jean-Christophe
2007-01-01
We present a detailed comparison of two self-consistent equation-of-state models which differ from their electronic contribution: the atom in a spherical cell and the atom in a jellium of charges. It is shown that both models are well suited for the calculation of Hugoniot shock adiabats in the high pressure range (1 Mbar-10 Gbar), and that the atom-in-a-jellium model provides a better treatment of pressure ionization. Comparisons with experimental data are also presented. Shell effects on shock adiabats are reviewed in the light of these models. They lead to additional features not only in the variations of pressure versus density, but also in the variations of shock velocity versus particle velocity. Moreover, such effects are found to be responsible for enhancement of the electronic specific heat.
Quantum Statistical Entropy of Spherical Black Holes in Higher Dimensions
Institute of Scientific and Technical Information of China (English)
XU Dian-Yan
2000-01-01
The free energy and entropy of a general spherically symmetry black hole are calculated by quantum statistic method with brick wall model Two different kinds of approximation are used to calculate the number of states in transverse spatial space. The final results are approximately equal except a rational numerical constant. The formulas of free energy and entropy, evaluated by each one of the two different kinds of approximation, are the same except some numerical constants. The free energy and entropy are dependent on the spacetime dimensionsD. When D = 4, they reduce to the usual well known results.
Dielectronic recombination rate in statistical model
Demura A.V.; Leontyev D.S.; Lisitsa V.S.; Shurigyn V.A.
2017-01-01
The dielectronic recombination rate of multielectron ions was calculated by means of the statistical approach. It is based on an idea of collective excitations of atomic electrons with the local plasma frequencies. These frequencies are expressed via the Thomas-Fermi model electron density distribution. The statistical approach provides fast computation of DR rates that are compared with the modern quantum mechanical calculations. The results are important for current studies of thermonuclear...
Dielectronic recombination rate in statistical model
Directory of Open Access Journals (Sweden)
Demura A.V.
2017-01-01
Full Text Available The dielectronic recombination rate of multielectron ions was calculated by means of the statistical approach. It is based on an idea of collective excitations of atomic electrons with the local plasma frequencies. These frequencies are expressed via the Thomas-Fermi model electron density distribution. The statistical approach provides fast computation of DR rates that are compared with the modern quantum mechanical calculations. The results are important for current studies of thermonuclear plasmas with the tungsten impurities.
Dielectronic recombination rate in statistical model
Demura, A. V.; Leontyev, D. S.; Lisitsa, V. S.; Shurigyn, V. A.
2016-12-01
The dielectronic recombination rate of multielectron ions was calculated by means of the statistical approach. It is based on an idea of collective excitations of atomic electrons with the local plasma frequencies. These frequencies are expressed via the Thomas-Fermi model electron density distribution. The statistical approach provides fast computation of DR rates that are compared with the modern quantum mechanical calculations. The results are important for current studies of thermonuclear plasmas with the tungsten impurities.
The quantum Rabi model: solution and dynamics
Xie, Qiongtao; Zhong, Honghua; Batchelor, Murray T.; Lee, Chaohong
2017-03-01
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.
The quantum Rabi model: solution and dynamics
Xie, Qiongtao; Batchelor, Murray T; Lee, Chaohong
2016-01-01
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.
Nguyen, Trong-Nghia; Lee, Yun-Min; Wu, Jong-Shinn; Lin, Ming-Chang
2017-02-01
H, H2, and SiH x + (x ≤ 4) ions coexist under plasma-enhanced chemical vapor deposition (PECVD) conditions. We have studied the kinetics of their interactions by high-level quantum chemical and statistical theory calculations, and compared the results with classical Langevin values (˜2 × 10-9 cm3 molecule-1 s-1 independent of temperature). The results indicate that, for H capturing by SiH x + (x ≤ 4), both theories agree within a factor of 2-4, whereas for H2 capturing by SiH x + (x ≤ 3), the modern theory gives higher and weakly temperature-dependent values by up to more than one order of magnitude, attributable to reaction path degeneracies and increased entropies of activation. The heats of formation and structural parameters of SiH x + ions (x ≤ 5) in this work agree well with available experimental data. For practical applications, we have provided tables of rate constants for modeling various processes of relevance to the PECVD of a-Si:H films.
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.
Statistical models for nuclear decay from evaporation to vaporization
Cole, A J
2000-01-01
Elements of equilibrium statistical mechanics: Introduction. Microstates and macrostates. Sub-systems and convolution. The Boltzmann distribution. Statistical mechanics and thermodynamics. The grand canonical ensemble. Equations of state for ideal and real gases. Pseudo-equilibrium. Statistical models of nuclear decay. Nuclear physics background: Introduction. Elements of the theory of nuclear reactions. Quantum mechanical description of scattering from a potential. Decay rates and widths. Level and state densities in atomic nuclei. Angular momentum in quantum mechanics. History of statistical
Relativistic quantum level-spacing statistics in chaotic graphene billiards.
Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso
2010-05-01
An outstanding problem in quantum nonlinear dynamics concerns about the energy-level statistics in experimentally accessible relativistic quantum systems. We demonstrate, using chaotic graphene confinements where electronic motions are governed by the Dirac equation in the low-energy regime, that the level-spacing statistics are those given by Gaussian orthogonal ensemble (GOE) random matrices. Weak magnetic field can change the level-spacing statistics to those of Gaussian unitary ensemble for electrons in graphene. For sufficiently strong magnetic field, the GOE statistics are restored due to the appearance of Landau levels.
Institute of Scientific and Technical Information of China (English)
吴宁; 阮图南
1996-01-01
A quantum mechanical model with one bosonic degree of freedom is discussed in detail. Conventionally, when a quantum mechanical model is constructed, one must know the corresponding classical model. And by applying the correspondence between the classical Poisson brackets and the canonical commutator, the canonical quantization condition can be obtained. In the quantum model, study of the corresponding classical model is needed first. In this model, the Lagrangian is an operator gauge invariant. After localization, in order to keep gauge invariance, the operator gauge potential must be introduced. The Eular-Lagrange equation of motion of the dynamical argument gives the usual operator equation of motion. And the operator gauge potential just gjves a constraint. This constraint is just the usual canonical quantization condition.
Fast Quantum Algorithm for Predicting Descriptive Statistics of Stochastic Processes
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.
Statistical constraints on state preparation for a quantum computer
Indian Academy of Sciences (India)
Subhash Kak
2001-10-01
Quantum computing algorithms require that the quantum register be initially present in a superposition state. To achieve this, we consider the practical problem of creating a coherent superposition state of several qubits. We show that the constraints of quantum statistics require that the entropy of the system be brought down when several independent qubits are assembled together. In particular, we have: (i) not all initial states are realizable as pure states; (ii) the temperature of the system must be reduced. These factors, in addition to decoherence and sensitivity to errors, must be considered in the implementation of quantum computers.
Statistical approach to quantum field theory an introduction
Wipf, Andreas
2013-01-01
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 w...
Anyonic statistics and large horizon diffeomorphisms for Loop Quantum Gravity Black Holes
Pithis, Andreas G A
2014-01-01
In this article we investigate the role played by large diffeomorphisms of quantum Isolated Horizons for the statistics of LQG Black Holes by means of their relation to the braid group. To this aim the symmetries of Chern-Simons theory are recapitulated with particular regard to the aforementioned type of diffeomorphisms. For the punctured spherical horizon, these are elements of the mapping class group of $S^2$, which is almost isomorphic to a corresponding braid group on this particular manifold. The mutual exchange of quantum entities in $2$-dimensions is communicated by the braid group, rendering the statistics anyonic. With this we argue that the quantum Isolated Horizon model of LQG based on $SU(2)_k$-Chern-Simons theory exhibits non-abelian anyonic statistics. In this way a connection to theory behind the fractional quantum Hall effect and that of topological quantum computation is established, where non-abelian anyons play a significant role.
Algebraic Statistics for Network Models
2014-02-19
AFRL-OSR-VA-TR-2014-0070 (DARPA) Algebraic Statistics for Network Models SONJA PETROVIC PENNSYLVANIA STATE UNIVERSITY 02/19/2014 Final Report...DARPA GRAPHS Phase I Algebraic Statistics for Network Models FA9550-12-1-0392 Sonja Petrović petrovic@psu.edu1 Department of Statistics Pennsylvania...Department of Statistics, Heinz College , Machine Learning Department, Cylab Carnegie Mellon University 1. Abstract This project focused on the family of
Quantum Correlations from the Conditional Statistics of Incomplete Data
Sperling, J.; Bartley, T. J.; Donati, G.; Barbieri, M.; Jin, X.-M.; Datta, A.; Vogel, W.; Walmsley, I. A.
2016-08-01
We study, in theory and experiment, the quantum properties of correlated light fields measured with click-counting detectors providing incomplete information on the photon statistics. We establish a correlation parameter for the conditional statistics, and we derive the corresponding nonclassicality criteria for detecting conditional quantum correlations. Classical bounds for Pearson's correlation parameter are formulated that allow us, once they are violated, to determine nonclassical correlations via the joint statistics. On the one hand, we demonstrate nonclassical correlations in terms of the joint click statistics of light produced by a parametric down-conversion source. On the other hand, we verify quantum correlations of a heralded, split single-photon state via the conditional click statistics together with a generalization to higher-order moments. We discuss the performance of the presented nonclassicality criteria to successfully discern joint and conditional quantum correlations. Remarkably, our results are obtained without making any assumptions on the response function, quantum efficiency, and dark-count rate of photodetectors.
Quantum Correlations from the Conditional Statistics of Incomplete Data.
Sperling, J; Bartley, T J; Donati, G; Barbieri, M; Jin, X-M; Datta, A; Vogel, W; Walmsley, I A
2016-08-19
We study, in theory and experiment, the quantum properties of correlated light fields measured with click-counting detectors providing incomplete information on the photon statistics. We establish a correlation parameter for the conditional statistics, and we derive the corresponding nonclassicality criteria for detecting conditional quantum correlations. Classical bounds for Pearson's correlation parameter are formulated that allow us, once they are violated, to determine nonclassical correlations via the joint statistics. On the one hand, we demonstrate nonclassical correlations in terms of the joint click statistics of light produced by a parametric down-conversion source. On the other hand, we verify quantum correlations of a heralded, split single-photon state via the conditional click statistics together with a generalization to higher-order moments. We discuss the performance of the presented nonclassicality criteria to successfully discern joint and conditional quantum correlations. Remarkably, our results are obtained without making any assumptions on the response function, quantum efficiency, and dark-count rate of photodetectors.
Quantum cosmological metroland model
Energy Technology Data Exchange (ETDEWEB)
Anderson, Edward [DAMTP, Cambridge (United Kingdom); Franzen, Anne, E-mail: ea212@cam.ac.u, E-mail: a.t.franzen@uu.n [Spinoza Institute, Utrecht (Netherlands)
2010-02-21
Relational particle mechanics is useful for modelling whole-universe issues such as quantum cosmology or the problem of time in quantum gravity, including some aspects outside the reach of comparably complex mini-superspace models. In this paper, we consider the mechanics of pure shape and not scale of four particles on a line, so that the only physically significant quantities are ratios of relative separations between the constituents' physical objects. Many of our ideas and workings extend to the N-particle case. As such models' configurations resemble depictions of metro lines in public transport maps, we term them 'N-stop metrolands'. This 4-stop model's configuration space is a 2-sphere, from which our metroland mechanics interpretation is via the 'cubic' tessellation. This model yields conserved quantities which are mathematically SO(3) objects like angular momenta but are physically relative dilational momenta (i.e. coordinates dotted with momenta). We provide and interpret various exact and approximate classical and quantum solutions for 4-stop metroland; from these results one can construct expectations and spreads of shape operators that admit interpretations as relative sizes and the 'homogeneity of the model universe's contents', and also objects of significance for the problem of time in quantum gravity (e.g. in the naive Schroedinger and records theory timeless approaches).
Microscopic quantum structure of black hole and vacuum versus quantum statistical origin of gravity
Wang, Shun-Jin
2012-01-01
The Planckon densely piled model of vacuum is proposed. Based on it, the microscopic quantum structure of Schwarzschild black hole and quantum statistical origin of its gravity are studied. It is shown that thermodynamic temperature equilibrium and mechanical acceleration balance make the space-time of the black hole horizon singular and Casimir effect works inside the horizon. This effect makes the inside vacuum have less zero fluctuation energy than the outside vacuum, and a temperature difference as well as gravity as thermal pressure are created. A dual relation between inside and outside regions of the black hole is found. By dual relation, an attractor behaviour of the horizon surface is unveiled. Outside horizon, there exist thermodynamic non-equilibrium and mechanical non-balance which lead to outward centrifugal energy flow and inward gravitation energy flow, their compensation establishes local equilibrium. The lost vacuum energy in negative gravitation potential regions has been removed to the blac...
A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals
Energy Technology Data Exchange (ETDEWEB)
Sinitskiy, Anton V.; Voth, Gregory A., E-mail: gavoth@uchicago.edu [Department of Chemistry, James Franck Institute, Institute for Biophysical Dynamics, and Computation Institute, The University of Chicago, 5735 S. Ellis Ave., Chicago, Illinois 60637 (United States)
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.
A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals.
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.
Statistical Model for Content Extraction
DEFF Research Database (Denmark)
2011-01-01
We present a statistical model for content extraction from HTML documents. The model operates on Document Object Model (DOM) tree of the corresponding HTML document. It evaluates each tree node and associated statistical features to predict significance of the node towards overall content...
Anderson Localization with Second Quantized Fields: Quantum Statistical Aspects
Thompson, Clinton; Agarwal, G S
2010-01-01
We report a theoretical study of Anderson localization of nonclassical light with emphasis on the quantum statistical aspects of localized light. We demonstrate, from the variance in mean intensity of localized light, as well as site-to-site correlations, that the localized light carries signatures of quantum statistics of input light. For comparison, we also present results for input light with coherent field statistics and thermal field statistics. Our results show that there is an enhancement in fluctuations of localized light due to the medium's disorder. We also find superbunching of the localized light, which may be useful for enhancing the interaction between radiation and matter. Another important consequence of sub-Poissonian statistics of the incoming light is to quench the total fluctuations at the output. Finally, we compare the effects of Gaussian and Rectangular distributions for the disorder, and show that Gaussian disorder accelerates the localization of light.
Methods of statistical model estimation
Hilbe, Joseph
2013-01-01
Methods of Statistical Model Estimation examines the most important and popular methods used to estimate parameters for statistical models and provide informative model summary statistics. Designed for R users, the book is also ideal for anyone wanting to better understand the algorithms used for statistical model fitting. The text presents algorithms for the estimation of a variety of regression procedures using maximum likelihood estimation, iteratively reweighted least squares regression, the EM algorithm, and MCMC sampling. Fully developed, working R code is constructed for each method. Th
Statistical mechanics of confined quantum particles
Bannur, V M; Bannur, Vishnu M.
2006-01-01
We develop statistical mechanics and thermodynamics of Bose and Fermi systems in relativistic harmonic oscillator (RHO) confining potential, which may be applicable in quark gluon plasma (QGP), astrophysics, Bose-Einstein condensation (BEC), condensed matter physics etc. Detailed study of QGP system is carried out and compared with lattice results. Further, as an application, our equation of state (EoS) of QGP is used to study compact stars like quark star.
Statistical Mechanics of Confined Quantum Particles
Bannur, Vishnu M.; Udayanandan, K. M.
We develop statistical mechanics and thermodynamics of Bose and Fermi systems in relativistic harmonic oscillator (RHO) confining potential, which is applicable in quark gluon plasma (QGP), astrophysics, Bose-Einstein condensation (BEC) etc. Detailed study of QGP system is carried out and compared with lattice results. Furthermore, as an application, our equation of state (EoS) of QGP is used to study compact stars like quark star.
LP Approach to Statistical Modeling
Mukhopadhyay, Subhadeep; Parzen, Emanuel
2014-01-01
We present an approach to statistical data modeling and exploratory data analysis called `LP Statistical Data Science.' It aims to generalize and unify traditional and novel statistical measures, methods, and exploratory tools. This article outlines fundamental concepts along with real-data examples to illustrate how the `LP Statistical Algorithm' can systematically tackle different varieties of data types, data patterns, and data structures under a coherent theoretical framework. A fundament...
Thermodynamics of Van der Waals Fluids with quantum statistics
Redlich, Krzysztof
2016-01-01
We consider thermodynamics of the van der Waals fluid of quantum systems. We derive general relations of thermodynamic functions and parameters of any ideal gas and the corresponding van der Waals fluid. This provides unambiguous generalization of the classical van der Waals theory to quantum statistical systems. As an example, we apply the van der Waals fluid with fermi statistics to characterize the liquid-gas critical point in nuclear matter. We also introduce the Bose-Einstein condensation in the relativistic van der Waals boson gas, and argue, that it exhibits two-phase structure separated in space.
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)
Gawron, Piotr; Kurzyk, Dariusz; Puchała, Zbigniew
2013-05-01
We consider an extension of discrete time Markov chain queueing model to the quantum domain by use of discrete time quantum Markov chain. We introduce methods for numerical analysis of such models. Using these tools we show that quantum model behaves fundamentally different from the classical one.
Mesoscopic full counting statistics and exclusion models
Roche, P.-E.; Derrida, B.; Douçot, B.
2005-02-01
We calculate the distribution of current fluctuations in two simple exclusion models. Although these models are classical, we recover even for small systems such as a simple or a double barrier, the same distibution of current as given by traditional formalisms for quantum mesoscopic conductors. Due to their simplicity, the full counting statistics in exclusion models can be reduced to the calculation of the largest eigenvalue of a matrix, the size of which is the number of internal configurations of the system. As examples, we derive the shot noise power and higher order statistics of current fluctuations (skewness, full counting statistics, ....) of various conductors, including multiple barriers, diffusive islands between tunnel barriers and diffusive media. A special attention is dedicated to the third cumulant, which experimental measurability has been demonstrated lately.
Statistical Mechanics of Classical and Quantum Computational Complexity
Laumann, C. R.; Moessner, R.; Scardicchio, A.; Sondhi, S. L.
The quest for quantum computers is motivated by their potential for solving problems that defy existing, classical, computers. The theory of computational complexity, one of the crown jewels of computer science, provides a rigorous framework for classifying the hardness of problems according to the computational resources, most notably time, needed to solve them. Its extension to quantum computers allows the relative power of quantum computers to be analyzed. This framework identifies families of problems which are likely hard for classical computers ("NP-complete") and those which are likely hard for quantum computers ("QMA-complete") by indirect methods. That is, they identify problems of comparable worst-case difficulty without directly determining the individual hardness of any given instance. Statistical mechanical methods can be used to complement this classification by directly extracting information about particular families of instances—typically those that involve optimization—by studying random ensembles of them. These pose unusual and interesting (quantum) statistical mechanical questions and the results shed light on the difficulty of problems for large classes of algorithms as well as providing a window on the contrast between typical and worst case complexity. In these lecture notes we present an introduction to this set of ideas with older work on classical satisfiability and recent work on quantum satisfiability as primary examples. We also touch on the connection of computational hardness with the physical notion of glassiness.
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....
Statistical Structures Underlying Quantum Mechanics and Social Science
Wright, R
2003-01-01
Common observations of the unpredictability of human behavior and the influence of one question on the answer to another suggest social science experiments are probabilistic and may be mutually incompatible with one another, characteristics attributed to quantum mechanics (as distinguished from classical mechanics). This paper examines this superficial similarity in depth using the Foulis-Randall Operational Statistics language. In contradistinction to physics, social science deals with complex, open systems for which the set of possible experiments is unknowable and outcome interference is a graded phenomenon resulting from the ways the human brain processes information. It is concluded that social science is, in some ways, "less classical" than quantum mechanics, but that generalized "quantum" structures may provide appropriate descriptions of social science experiments. Specific challenges to extending "quantum" structures to social science are identified.
Statistical modeling for degradation data
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.
Twisted Conformal Algebra and Quantum Statistics of Harmonic Oscillators
Directory of Open Access Journals (Sweden)
J. Naji
2014-01-01
Full Text Available We consider noncommutative two-dimensional quantum harmonic oscillators and extend them to the case of twisted algebra. We obtained modified raising and lowering operators. Also we study statistical mechanics and thermodynamics and calculated partition function which yields the free energy of the system.
New results in the quantum statistical approach to parton distributions
Soffer, Jacques; Bourrely, Claude
2014-01-01
We will describe the quantum statistical approach to parton distributions allowing to obtain simultaneously the unpolarized distributions and the helicity distributions. We will present some recent results, in particular related to the nucleon spin structure in QCD. Future measurements are challenging to check the validity of this novel physical framework.
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.
Linear response theory in quantum statistical mechanics
Jaksic, V; Pillet, C A
2005-01-01
This note is a continuation of a recent paper [1:mp_arc 05-215] where we have proven the Green-Kubo formula and the Onsager reciprocity relations for heat fluxes. In this note we extend the derivation of the Green-Kubo formula to heat and charge fluxes and discuss some other generalizations of the model and results of [1].
Foundational Issues in Statistical Modeling: Statistical Model Specification and Validation
Directory of Open Access Journals (Sweden)
Aris Spanos
2011-01-01
Full Text Available Statistical model specification and validation raise crucial foundational problems whose pertinent resolution holds the key to learning from data by securing the reliability of frequentist inference. The paper questions the judiciousness of several current practices, including the theory-driven approach, and the Akaike-type model selection procedures, arguing that they often lead to unreliable inferences. This is primarily due to the fact that goodness-of-fit/prediction measures and other substantive and pragmatic criteria are of questionable value when the estimated model is statistically misspecified. Foisting one's favorite model on the data often yields estimated models which are both statistically and substantively misspecified, but one has no way to delineate between the two sources of error and apportion blame. The paper argues that the error statistical approach can address this Duhemian ambiguity by distinguishing between statistical and substantive premises and viewing empirical modeling in a piecemeal way with a view to delineate the various issues more effectively. It is also argued that Hendry's general to specific procedures does a much better job in model selection than the theory-driven and the Akaike-type procedures primary because of its error statistical underpinnings.
Statistical modelling with quantile functions
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...
Quantum Common Causes and Quantum Causal Models
Allen, John-Mark A.; Barrett, Jonathan; Horsman, Dominic C.; Lee, Ciarán M.; Spekkens, Robert W.
2017-07-01
Reichenbach's principle asserts that if two observed variables are found to be correlated, then there should be a causal explanation of these correlations. Furthermore, if the explanation is in terms of a common cause, then the conditional probability distribution over the variables given the complete common cause should factorize. The principle is generalized by the formalism of causal models, in which the causal relationships among variables constrain the form of their joint probability distribution. In the quantum case, however, the observed correlations in Bell experiments cannot be explained in the manner Reichenbach's principle would seem to demand. Motivated by this, we introduce a quantum counterpart to the principle. We demonstrate that under the assumption that quantum dynamics is fundamentally unitary, if a quantum channel with input A and outputs B and C is compatible with A being a complete common cause of B and C , then it must factorize in a particular way. Finally, we show how to generalize our quantum version of Reichenbach's principle to a formalism for quantum causal models and provide examples of how the formalism works.
Quantum probability, choice in large worlds, and the statistical structure of reality.
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.
Sensometrics: Thurstonian and Statistical Models
DEFF Research Database (Denmark)
Christensen, Rune Haubo Bojesen
of human senses. Thurstonian models provide a stochastic model for the data-generating mechanism through a psychophysical model for the cognitive processes and in addition provides an independent measure for quantification of sensory differences. In the interest of cost-reduction and health...... of generalized linear mixed models, cumulative link models and cumulative link mixed models. The relation between the Wald, likelihood and score statistics is expanded upon using the shape of the (profile) likelihood function as common reference....
Statistical estimation of the efficiency of quantum state tomography protocols.
Bogdanov, Yu I; Brida, G; Genovese, M; Kulik, S P; Moreva, E V; Shurupov, A P
2010-07-02
A novel operational method for estimating the efficiency of quantum state tomography protocols is suggested. It is based on a priori estimation of the quality of an arbitrary protocol by means of universal asymptotic fidelity distribution and condition number, which takes minimal value for better protocol. We prove the adequacy of the method both with numerical modeling and through the experimental realization of several practically important protocols of quantum state tomography.
Quantum random oracle model for quantum digital signature
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.
Quantum statistics as geometry: Conflict, Mechanism, Interpretation, and Implication
Galehouse, Daniel C
2015-01-01
The conflict between the determinism of geometry in general relativity and the essential statistics of quantum mechanics blocks the development of a unified theory. Electromagnetic radiation is essential to both fields and supplies a common meeting ground. It is proposed that a suitable mechanism to resolve these differences can be based on the use of a time-symmetric treatment for the radiation. Advanced fields of the absorber can be interpreted to supply the random character of spontaneous emission. This allows the statistics of the Born rule to come from the spontaneous emission that occurs during a physical measurement. When the absorber is included, quantum mechanics is completely deterministic. It is suggested that the peculiar properties of kaons may be induced by the advanced effects of the neutrino field. Schr\\"odinger's cat loses its enigmatic personality and the identification of mental processes as an essential component of a measurement is no longer needed.
A Statistical Programme Assignment Model
DEFF Research Database (Denmark)
Rosholm, Michael; Staghøj, Jonas; Svarer, Michael
assignment mechanism, which is based on the discretionary choice of case workers. This is done in a duration model context, using the timing-of-events framework to identify causal effects. We compare different assignment mechanisms, and the results suggest that a significant reduction in the average...... 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....
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...
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...... assignment mechanism, which is based on the discretionary choice of case workers. This is done in a duration model context, using the timing-of-events framework to identify causal effects. We compare different assignment mechanisms, and the results suggest that a significant reduction in the average...... 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....
Lifetime statistics of quantum chaos studied by a multiscale analysis
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.
Image quantization: statistics and modeling
Whiting, Bruce R.; Muka, Edward
1998-07-01
A method for analyzing the effects of quantization, developed for temporal one-dimensional signals, is extended to two- dimensional radiographic images. By calculating the probability density function for the second order statistics (the differences between nearest neighbor pixels) and utilizing its Fourier transform (the characteristic function), the effect of quantization on image statistics can be studied by the use of standard communication theory. The approach is demonstrated by characterizing the noise properties of a storage phosphor computed radiography system and the image statistics of a simple radiographic object (cylinder) and by comparing the model to experimental measurements. The role of quantization noise and the onset of contouring in image degradation are explained.
Lecture notes on "Quantum chromodynamics and statistical physics"
Munier, Stephane
2014-01-01
The concepts and methods used for the study of disordered systems have proven useful in the analysis of the evolution equations of quantum chromodynamics in the high-energy regime: Indeed, parton branching in the semi-classical approximation relevant at high energies is a peculiar branching-diffusion process, and parton branching supplemented by saturation effects (such as gluon recombination) is a reaction-diffusion process. In these lectures, we first introduce the basic concepts in the context of simple toy models, we study the properties of the latter, and show how the results obtained for the simple models may be taken over to quantum chromodynamics.
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...
Statistical modeling of program performance
Directory of Open Access Journals (Sweden)
A. P. Karpenko
2014-01-01
Full Text Available A task of evaluation of program performance often occurs in the process of design of computer systems or during iterative compilation. A traditional way to solve this problem is emulation of program execution on the target system. A modern alternative approach to evaluation of program performance is based on statistical modeling of program performance on a computer under investigation. This statistical method of modeling program performance called Velocitas was introduced in this work. The method and its implementation in the Adaptor framework were presented. Investigation of the method's effectiveness showed high adequacy of program performance prediction.
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 relation to the so-called uniform infinite tree and results on the Hausdorff and spectral dimension of two-dimensional space-time obtained in B. Durhuus, T. Jonsson, J.F. Wheater, J. Stat. Phys. 139, 859 (2010) are briefly outlined. For the latter we discuss results on the absence of spontaneous...... magnetization and argue that, in the generic case, the values of the Hausdorff and spectral dimension of the underlying infinite trees are not influenced by the coupling to an Ising model in a constant magnetic field (B. Durhuus, G.M. Napolitano, in preparation)...
Errors in quantum tomography: diagnosing systematic versus statistical errors
Langford, Nathan K.
2013-03-01
A prime goal of quantum tomography is to provide quantitatively rigorous characterization of quantum systems, be they states, processes or measurements, particularly for the purposes of trouble-shooting and benchmarking experiments in quantum information science. A range of techniques exist to enable the calculation of errors, such as Monte-Carlo simulations, but their quantitative value is arguably fundamentally flawed without an equally rigorous way of authenticating the quality of a reconstruction to ensure it provides a reasonable representation of the data, given the known noise sources. A key motivation for developing such a tool is to enable experimentalists to rigorously diagnose the presence of technical noise in their tomographic data. In this work, I explore the performance of the chi-squared goodness-of-fit test statistic as a measure of reconstruction quality. I show that its behaviour deviates noticeably from expectations for states lying near the boundaries of physical state space, severely undermining its usefulness as a quantitative tool precisely in the region which is of most interest in quantum information processing tasks. I suggest a simple, heuristic approach to compensate for these effects and present numerical simulations showing that this approach provides substantially improved performance.
Textual information access statistical models
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
Quantum theory and statistical thermodynamics principles and worked examples
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...
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
Quantum Computation Beyond the Circuit Model
Jordan, Stephen P.
2008-01-01
The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers. However, several other models of quantum computation exist which provide useful alternative frameworks for both discovering new quantum algorithms and devising new physical implementations of quantum computers. In this thesis, I first present necessary background material for a ge...
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.
Statistical theory of designed quantum transport across disordered networks.
Walschaers, Mattia; Mulet, Roberto; Wellens, Thomas; Buchleitner, Andreas
2015-04-01
We explain how centrosymmetry, together with a dominant doublet of energy eigenstates in the local density of states, can guarantee interference-assisted, strongly enhanced, strictly coherent quantum excitation transport between two predefined sites of a random network of two-level systems. Starting from a generalization of the chaos-assisted tunnelling mechanism, we formulate a random matrix theoretical framework for the analytical prediction of the transfer time distribution, of lower bounds of the transfer efficiency, and of the scaling behavior of characteristic statistical properties with the size of the network. We show that these analytical predictions compare well to numerical simulations, using Hamiltonians sampled from the Gaussian orthogonal ensemble.
A Statistical Theory of Designed Quantum Transport Across Disordered Networks
Walschaers, Mattia; Wellens, Thomas; Buchleitner, Andreas
2014-01-01
We explain how centrosymmetry, together with a dominant doublet in the local density of states, can guarantee interference-assisted, strongly enhanced, strictly coherent quantum excitation transport between two predefined sites of a random network of two-level systems. Starting from a generalisation of the chaos assisted tunnelling mechanism, we formulate a random matrix theoretical framework for the analytical prediction of the transfer time distribution, of lower bounds of the transfer efficiency, and of the scaling behaviour of characteristic statistical properties with the size of the network.
Quantum dissipative Higgs model
Energy Technology Data Exchange (ETDEWEB)
Amooghorban, Ehsan, E-mail: Ehsan.amooghorban@sci.sku.ac.ir; Mahdifar, Ali, E-mail: mahdifar_a@sci.sku.ac.ir
2015-09-15
By using a continuum of oscillators as a reservoir, we present a classical and a quantum-mechanical treatment for the Higgs model in the presence of dissipation. In this base, a fully canonical approach is used to quantize the damped particle on a spherical surface under the action of a conservative central force, the conjugate momentum is defined and the Hamiltonian is derived. The equations of motion for the canonical variables and in turn the Langevin equation are obtained. It is shown that the dynamics of the dissipative Higgs model is not only determined by a projected susceptibility tensor that obeys the Kramers–Kronig relations and a noise operator but also the curvature of the spherical space. Due to the gnomonic projection from the spherical space to the tangent plane, the projected susceptibility displays anisotropic character in the tangent plane. To illuminate the effect of dissipation on the Higgs model, the transition rate between energy levels of the particle on the sphere is calculated. It is seen that appreciable probabilities for transition are possible only if the transition and reservoir’s oscillators frequencies to be nearly on resonance.
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.
Statistical bootstrap model and annihilations
Möhring, H J
1974-01-01
The statistical bootstrap model (SBM) describes the decay of single, high mass, hadronic states (fireballs, clusters) into stable particles. Coupling constants B, one for each isospin multiplet of stable particles, are the only free parameter of the model. They are related to the maximum temperature parameter T/sub 0/. The various versions of the SMB can be classified into two groups: full statistical bootstrap models and linear ones. The main results of the model are the following: i) All momentum spectra are isotropic; especially the exclusive ones are described by invariant phase space. The inclusive and semi-inclusive single-particle distributions are asymptotically of pure exponential shape; the slope is governed by T /sub 0/ only. ii) The model parameter B for pions has been obtained by fitting the multiplicity distribution in pp and pn at rest, and corresponds to T/sub 0/=0.167 GeV in the full SBM with exotics. The average pi /sup -/ multiplicity for the linear and the full SBM (both with exotics) is c...
Einstein's quantum theory of the monatomic ideal gas: non-statistical arguments for a new statistics
Pérez, Enric
2010-01-01
In this article, we analyze the third of three papers, in which Einstein presented his quantum theory of the ideal gas of 1924-1925. Although it failed to attract the attention of Einstein's contemporaries and although also today very few commentators refer to it, we argue for its significance in the context of Einstein's quantum researches. It contains an attempt to extend and exhaust the characterization of the monatomic ideal gas without appealing to combinatorics. Its ambiguities illustrate Einstein's confusion with his initial success in extending Bose's results and in realizing the consequences of what later became to be called Bose-Einstein statistics. We discuss Einstein's motivation for writing a non-combinatorial paper, partly in response to criticism by his friend Ehrenfest, and we paraphrase its content. Its arguments are based on Einstein's belief in the complete analogy between the thermodynamics of light quanta and of material particles and invoke considerations of adiabatic transformations as ...
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.
Quantum-like Modeling of Cognition
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).
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.
Reimann, Peter; Evstigneev, Mykhaylo
2013-11-01
Focusing on isolated macroscopic systems, described in terms of either a quantum mechanical or a classical model, our two key questions are how far does an initial ensemble (usually far from equilibrium and largely unknown in detail) evolve towards a stationary long-time behavior (equilibration) and how far is this steady state in agreement with the microcanonical ensemble as predicted by statistical mechanics (thermalization). A recently developed quantum mechanical treatment of the problem is briefly summarized, putting particular emphasis on the realistic modeling of experimental measurements and nonequilibrium initial conditions. Within this framework, equilibration can be proven under very weak assumptions about those measurements and initial conditions, while thermalization still requires quite strong additional hypotheses. An analogous approach within the framework of classical mechanics is developed and compared with the quantum case. In particular, the assumptions to guarantee classical equilibration are now rather strong, while thermalization then follows under relatively weak additional conditions.
Statistical models for trisomic phenotypes
Energy Technology Data Exchange (ETDEWEB)
Lamb, N.E.; Sherman, S.L.; Feingold, E. [Emory Univ., Atlanta, GA (United States)
1996-01-01
Certain genetic disorders are rare in the general population but more common in individuals with specific trisomies, which suggests that the genes involved in the etiology of these disorders may be located on the trisomic chromosome. As with all aneuploid syndromes, however, a considerable degree of variation exists within each phenotype so that any given trait is present only among a subset of the trisomic population. We have previously presented a simple gene-dosage model to explain this phenotypic variation and developed a strategy to map genes for such traits. The mapping strategy does not depend on the simple model but works in theory under any model that predicts that affected individuals have an increased likelihood of disomic homozygosity at the trait locus. This paper explores the robustness of our mapping method by investigating what kinds of models give an expected increase in disomic homozygosity. We describe a number of basic statistical models for trisomic phenotypes. Some of these are logical extensions of standard models for disomic phenotypes, and some are more specific to trisomy. Where possible, we discuss genetic mechanisms applicable to each model. We investigate which models and which parameter values give an expected increase in disomic homozygosity in individuals with the trait. Finally, we determine the sample sizes required to identify the increased disomic homozygosity under each model. Most of the models we explore yield detectable increases in disomic homozygosity for some reasonable range of parameter values, usually corresponding to smaller trait frequencies. It therefore appears that our mapping method should be effective for a wide variety of moderately infrequent traits, even though the exact mode of inheritance is unlikely to be known. 21 refs., 8 figs., 1 tab.
Exact integrability in quantum field theory and statistical systems
Thacker, H. B.
1981-04-01
The properties of exactly integrable two-dimensional quantum systems are reviewed and discussed. The nature of exact integrability as a physical phenomenon and various aspects of the mathematical formalism are explored by discussing several examples, including detailed treatments of the nonlinear Schrödinger (delta-function gas) model, the massive Thirring model, and the six-vertex (ice) model. The diagonalization of a Hamiltonian by Bethe's Ansatz is illustrated for the nonlinear Schrödínger model, and the integral equation method of Lieb for obtaining the spectrum of the many-body system from periodic boundary conditions is reviewed. Similar methods are applied to the massive Thirring model, where the fermion-antifermion and bound-state spectrum are obtained explicitly by the integral equation method. After a brief review of the classical inverse scattering method, the quantum inverse method for the nonlinear Schrödinger model is introduced and shown to be an algebraization of the Bethe Ansatz technique. In the quantum inverse method, an auxiliary linear problem is used to define nonlocal operators which are functionals of the original local field on a fixed-time string of arbitrary length. The particular operators for which the string is infinitely long (free boundary conditions) or forms a closed loop around a cylinder (periodic boundary conditions) correspond to the quantized scattering data and have a special significance. One of them creates the Bethe eigenstates, while the other is the generating function for an infinite number of conservation laws. The analogous operators on a lattice are constructed for the symmetric six-vertex model, where the object which corresponds to a solution of the auxiliary linear problem is a string of vertices contracted over horizontal links (arrows). The relationship between the quantum inverse method and the transfer matrix formalism is exhibited. The inverse Gel'fand-Levitan transform which expresses the local field
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.
Quantum Origin of the Primordial Fluctuation Spectrum and its Statistics
Leon, Gabriel; Sudarsky, Daniel
2013-01-01
The account of the origin of cosmic structure, as provided by the standard inflationary paradigm, is not fully satisfactory, as has been argued in Perez et al 2006. The central point of that work is to point out the need to discuss and explore the physical mechanism that is capable of generating the inhomogeneity and anisotropy of our Universe, starting from an exactly homogeneous and isotropic initial state associated with the early inflationary regime. We review this issue briefly here together with the proposal to address this shortcoming in terms of a dynamical collapse of the vacuum state of the inflaton field. We also briefly indicate how this issues might be connected to other questions being faced in the study of the quantum/gravity interface, and their relevance to the investigations concerning the statistical characterization of the primordial spectrum.
An overview of quantum computation models: quantum automata
Institute of Scientific and Technical Information of China (English)
2008-01-01
Quantum automata,as theoretical models of quantum computers,include quantum finite automata (QFA),quantum sequential machines (QSM),quantum pushdown automata (QPDA),quantum Turing machines (QTM),quantum cellular automata (QCA),and the others,for example,automata theory based on quantum logic (orthomodular lattice-valued automata).In this paper,we try to outline a basic progress in the research on these models,focusing on QFA,QSM,QPDA,QTM,and orthomodular lattice-valued automata.Also,other models closely relative to them are mentioned.In particular,based on the existing results in the literature,we finally address a number of problems to be studied in future.
Bayesian Model Selection and Statistical Modeling
Ando, Tomohiro
2010-01-01
Bayesian model selection is a fundamental part of the Bayesian statistical modeling process. The quality of these solutions usually depends on the goodness of the constructed Bayesian model. Realizing how crucial this issue is, many researchers and practitioners have been extensively investigating the Bayesian model selection problem. This book provides comprehensive explanations of the concepts and derivations of the Bayesian approach for model selection and related criteria, including the Bayes factor, the Bayesian information criterion (BIC), the generalized BIC, and the pseudo marginal lik
Huang, Y C; Zhang, N
2004-01-01
Classical statistical average values are generally generalized to average values of quantum mechanics, it is discovered that quantum mechanics is direct generalization of classical statistical mechanics, and we generally deduce both a general new continuous eigenvalue equation and a general discrete eigenvalue equation in quantum mechanics, and discover that a eigenvalue of quantum mechanics is just an extreme value of an operator in possibility distribution, the eigenvalue f is just classical observable quantity. A general classical statistical uncertain relation is further given, the general classical statistical uncertain relation is generally generalized to quantum uncertainty principle, the two lost conditions in classical uncertain relation and quantum uncertainty principle, respectively, are found. We generally expound the relations among uncertainty principle, singularity and condensed matter stability, discover that quantum uncertainty principle prevents from the appearance of singularity of the elec...
Quantum statistics of classical particles derived from the condition of free diffusion coefficient
Hoyuelos, Miguel
2016-01-01
We derive an equation for the current of particles in energy space; particles are subject to a mean field effective potential that may represent quantum effects. From the assumption that non-interacting particles imply a free diffusion coefficient in energy space we derive Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein statistics. Other new statistics are associated to a free diffusion coefficient; their thermodynamic properties are analyzed using the grand partition function. A negative relation between pressure and energy density for low temperatures can be derived, suggesting a possible connection with cosmological dark energy models.
Quantum statistics of classical particles derived from the condition of a free diffusion coefficient
Hoyuelos, M.; Sisterna, P.
2016-12-01
We derive an equation for the current of particles in energy space; particles are subject to a mean-field effective potential that may represent quantum effects. From the assumption that noninteracting particles imply a free diffusion coefficient in energy space, we derive Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein statistics. Other new statistics are associated to a free diffusion coefficient; their thermodynamic properties are analyzed using the grand partition function. A negative relation between pressure and energy density for low temperatures can be derived, suggesting a possible connection with cosmological dark energy models.
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.
Quantum-Like Bayesian Networks for Modeling Decision Making.
Moreira, Catarina; Wichert, Andreas
2016-01-01
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.
Statistical Analysis by Statistical Physics Model for the STOCK Markets
Wang, Tiansong; Wang, Jun; Fan, Bingli
A new stochastic stock price model of stock markets based on the contact process of the statistical physics systems is presented in this paper, where the contact model is a continuous time Markov process, one interpretation of this model is as a model for the spread of an infection. Through this model, the statistical properties of Shanghai Stock Exchange (SSE) and Shenzhen Stock Exchange (SZSE) are studied. In the present paper, the data of SSE Composite Index and the data of SZSE Component Index are analyzed, and the corresponding simulation is made by the computer computation. Further, we investigate the statistical properties, fat-tail phenomena, the power-law distributions, and the long memory of returns for these indices. The techniques of skewness-kurtosis test, Kolmogorov-Smirnov test, and R/S analysis are applied to study the fluctuation characters of the stock price returns.
Statistical Behaviors of Quantum Spectra in Superheavy Nuclei
Institute of Scientific and Technical Information of China (English)
WUXi-zhen; LIZhu-xia; WANGNing
2003-01-01
Recently, the statistical features of spectra for the deformed space explored by the fission have been studied and a new insight into fission and hyperdeformation has been given. The extension of this kind of investigations to superheavy nuclear systems is a very valuable. In this paper we study the nearest neighbor level-spacing distributions of superheavy systems based on mean field models.
Quantum statistical effects in the mass transport of interstitial solutes in a crystalline solid
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.
"Electronium": A Quantum Atomic Teaching Model.
Budde, Marion; Niedderer, Hans; Scott, Philip; Leach, John
2002-01-01
Outlines an alternative atomic model to the probability model, the descriptive quantum atomic model Electronium. Discusses the way in which it is intended to support students in learning quantum-mechanical concepts. (Author/MM)
Directory of Open Access Journals (Sweden)
Carlos C. Aranda
2012-04-01
Full Text Available In this article, we consider systems of nonlinear elliptic problems and their relations with minimal sufficient statistics, which is a fundamental tool in classics statistics. This allows us to introduce new experimental tools in quantum physics.
Visualizing statistical models and concepts
Farebrother, RW
2002-01-01
Examines classic algorithms, geometric diagrams, and mechanical principles for enhancing visualization of statistical estimation procedures and mathematical concepts in physics, engineering, and computer programming.
Discrete dynamical models: combinatorics, statistics and continuum approximations
Kornyak, Vladimir V
2015-01-01
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical description of such models. We demonstrate that many concepts of continuous physics --- such as continuous symmetries, the principle of least action, Lagrangians, deterministic evolution equations --- can be obtained from combinatorial structures as a result of the large number approximation. We propose a constructive description of quantum behavior that provides, in particular, a natural explanation of appearance of complex numbers in the formalism of quantum mechanics. Some approaches to construction of discrete models of quantum evolution that involve gauge connections are discussed.
Quantum statistical mechanics selected works of N N Bogolubov
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
Institute of Scientific and Technical Information of China (English)
ZHANG Qi-Ren
2007-01-01
We show that the quantum world with non-local states and original statistics is statistically separable.According to relativistic dynamics, the super-luminal signal transmission is impossible. The present quantum theory is therefore consistent with the relativity and the causality.
Theorems on Estimating Perturbative Coefficients in Quantum Field Theory and Statistical Physics
Energy Technology Data Exchange (ETDEWEB)
Samuel, Mark
2003-06-25
The authors present rigorous proofs for several theorems on using Pade approximants to estimate coefficients in Perturbative Quantum Field Theory and Statistical Physics. As a result, they find new trigonometric and other identities where the estimates based on this approach are exact. They discuss hypergeometric functions, as well as series from both Perturbative Quantum Field Theory and Statistical Physics.
Quantum modeling of common sense.
Noori, Hamid R; Spanagel, Rainer
2013-06-01
Quantum theory is a powerful framework for probabilistic modeling of cognition. Strong empirical evidence suggests the context- and order-dependent representation of human judgment and decision-making processes, which falls beyond the scope of classical Bayesian probability theories. However, considering behavior as the output of underlying neurobiological processes, a fundamental question remains unanswered: Is cognition a probabilistic process at all?
Statistical Behavoirs of Quantum Spectra in Superheavy Nuclei
Institute of Scientific and Technical Information of China (English)
2001-01-01
From the point of view of the interplay between order and chaos, the most regular single-particle motion of neutrons has been found in the superheavy system of Z=120 and N=184 based on the Skyrme-Hartree-Fock model and in the system of Z=120 and N=\\12 based on the relativistic mean-field model. It has been shown that the statistical analysis of spectra indeed can give very valuable information about the stability of superheavy systems. The significance of this kind of study can go far beyond the investigation on the stability of superheavy systems and it may give a deep
Statistical Behaviors of Quantum Spectra in Superheavy Nuclei
Institute of Scientific and Technical Information of China (English)
WU Xi-Zhen; LI Zhu-Xia; WANG Ning; J.A. Maruhn
2003-01-01
From the point of view of the interplay between order and chaos, the most regular single-particle motion of neutrons has been found in the superheavy system with Z ＝ 120 and N ＝ 184 based on the Skyrme-Hartree-Fock model and in the system with Z ＝ 120 and N ＝ 172 based on the relativistic mean-field model. It has been shown that the statistical analysis of spectra can give valuable information about the stability of suprheavy systems. In addition it may yield deep insight into the single-particle motion in the mean field formed by the superheavy system.
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...
A Quantum Probability Model of Causal Reasoning
Trueblood, Jennifer S.; Busemeyer, Jerome R.
2012-01-01
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. PMID:22593747
A quantum probability model of causal reasoning.
Trueblood, Jennifer S; Busemeyer, Jerome R
2012-01-01
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.
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.
On a Quantum Model of Brain Activities
Fichtner, K.-H.; Fichtner, L.; Freudenberg, W.; Ohya, M.
2010-01-01
One of the main activities of the brain is the recognition of signals. A first attempt to explain the process of recognition in terms of quantum statistics was given in [6]. Subsequently, details of the mathematical model were presented in a (still incomplete) series of papers (cf. [7, 2, 5, 10]). In the present note we want to give a general view of the principal ideas of this approach. We will introduce the basic spaces and justify the choice of spaces and operations. Further, we bring the model face to face with basic postulates any statistical model of the recognition process should fulfill. These postulates are in accordance with the opinion widely accepted in psychology and neurology.
Fermi breakup and the statistical multifragmentation model
Energy Technology Data Exchange (ETDEWEB)
Carlson, B.V., E-mail: brett@ita.br [Departamento de Fisica, Instituto Tecnologico de Aeronautica - CTA, 12228-900 Sao Jose dos Campos (Brazil); Donangelo, R. [Instituto de Fisica, Universidade Federal do Rio de Janeiro, Cidade Universitaria, CP 68528, 21941-972, Rio de Janeiro (Brazil); Instituto de Fisica, Facultad de Ingenieria, Universidad de la Republica, Julio Herrera y Reissig 565, 11.300 Montevideo (Uruguay); Souza, S.R. [Instituto de Fisica, Universidade Federal do Rio de Janeiro, Cidade Universitaria, CP 68528, 21941-972, Rio de Janeiro (Brazil); Instituto de Fisica, Universidade Federal do Rio Grande do Sul, Av. Bento Goncalves 9500, CP 15051, 91501-970, Porto Alegre (Brazil); Lynch, W.G.; Steiner, A.W.; Tsang, M.B. [Joint Institute for Nuclear Astrophysics, National Superconducting Cyclotron Laboratory and the Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824 (United States)
2012-02-15
We demonstrate the equivalence of a generalized Fermi breakup model, in which densities of excited states are taken into account, to the microcanonical statistical multifragmentation model used to describe the disintegration of highly excited fragments of nuclear reactions. We argue that such a model better fulfills the hypothesis of statistical equilibrium than the Fermi breakup model generally used to describe statistical disintegration of light mass nuclei.
Quantum reversibility and a new model of quantum automaton
Ciamarra, M P
2001-01-01
This article is an attempt to generalize the classical theory of reversible computing, principally developed by Bennet [IBM J. Res. Develop., 17(1973)] and by Fredkin and Toffoli [Internat. J. Theoret. Phys., 21(1982)], to the quantum case. This is a fundamental step towards the construction of a quantum computer because a time efficient quantum computation is a reversible physical process. The paper is organized as follows. The first section reviews the classical theory of reversible computing. In the second section it is showed that the designs used in the classical framework to decrease the consumption of space cannot be generalized to the quantum case; it is also suggested that quantum computing is generally more demanding of space than classical computing. In the last section a new model of fully quantum and reversible automaton is proposed. The computational power of this automaton is at least equal to that of classical automata. Some conclusion are drawn in the last section.
A quantum mechanical model of "dark matter"
Belokurov, V V
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.
Quantum field theory, statistical physics, and information theory
Energy Technology Data Exchange (ETDEWEB)
Toyoda, Tadashi [Tokai Univ., Kanagawa (Japan)
2001-05-01
It is shown that the one-particle Matsubara temperature Green's function can be regarded as a Fisher information matrix on the basis of the quantum generalization of relative entropy due to Watanabe and Neumann.
Quantum statistical theory of semiconductor junctions in thermal equilibrium
Von Roos, O.
1977-01-01
Free carrier and electric field distributions of one-dimensional semiconductor junctions are evaluated using a quantum mechanical phase-space distribution and its corresponding Boltzmann equation. Attention is given to quantum and exchange corrections in cases of high doping concentrations when carrier densities become degenerate. Quantitative differences between degenerate and classical junction characteristics, e.g., maximum electric field and built-in voltage and carrier concentration within the transition region, are evaluated numerically.
Quantum Statistics of Surface Plasmon Polaritons in Metallic Stripe Waveguides
Di Martino, Giuliana; Kéna-Cohen, Stéphane; Tame, Mark; Özdemir, Şahin K; Kim, M S; Maier, Stefan A
2012-01-01
Single surface plasmon polaritons are excited using photons generated via spontaneous parametric down-conversion. The mean excitation rates, intensity correlations and Fock state populations are studied. The observed dependence of the second order coherence in our experiment is consistent with a linear uncorrelated Markovian environment in the quantum regime. Our results provide important information about the effect of loss for assessing the potential of plasmonic waveguides for future nanophotonic circuitry in the quantum regime.
Level statistics of a pseudo-Hermitian Dicke model.
Deguchi, Tetsuo; Ghosh, Pijush K; Kudo, Kazue
2009-08-01
A non-Hermitian operator that is related to its adjoint through a similarity transformation is defined as a pseudo-Hermitian operator. We study the level statistics of a pseudo-Hermitian Dicke Hamiltonian that undergoes quantum phase transition (QPT). We find that the level-spacing distribution of this Hamiltonian near the integrable limit is close to Poisson distribution, while it is Wigner distribution for the ranges of the parameters for which the Hamiltonian is nonintegrable. We show that the assertion in the context of the standard Dicke model that QPT is a precursor to a change in the level statistics is not valid in general.
Quantum Statistical Mechanics as an Exact Classical Expansion with Results for Lennard-Jones Helium
Attard, Phil
2016-01-01
The quantum states representing classical phase space are given, and these are used to formulate quantum statistical mechanics as a formally exact double perturbation expansion about classical statistical mechanics. One series of quantum contributions arises from the non-commutativity of the position and momentum operators. Although the formulation of the quantum states differs, the present results for separate averages of position operators and of momentum operators agree with Wigner (1932) and Kirkwood (1933). The second series arises from wave function symmetrization, and is given in terms of $l$-particle permutation loops in an infinite order re-summation. The series gives analytically the known exact result for the quantum ideal gas to all orders. The leading correction corrects a correction given by Kirkwood. The first four quantum corrections to the grand potential are calculated for a Lennard-Jones fluid using the hypernetted chain closure. For helium on liquid branch isotherms, the corrections range ...
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.
Govindarajan, T R
2016-01-01
Novel bound states are obtained for manifolds with singular potentials. These singular potentials require proper boundary conditions across boundaries. The number of bound states match nicely with what we would expect for black holes. Also they serve to model membrane mechanism for the black hole horizons in simpler contexts. The singular potentials can also mimic expanding boundaries elegantly, there by obtaining appropriately tuned radiation rates.
Tasaki, Hal
2016-04-29
Based on quantum statistical mechanics and microscopic quantum dynamics, we prove Planck's and Kelvin's principles for macroscopic systems in a general and realistic setting. We consider a hybrid quantum system that consists of the thermodynamic system, which is initially in thermal equilibrium, and the "apparatus" which operates on the former, and assume that the whole system evolves autonomously. This provides a satisfactory derivation of the second law for macroscopic systems.
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....
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....
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...
XYZ Quantum Heisenberg Models with p-Orbital Bosons
DEFF Research Database (Denmark)
Pinheiro, Fernanda; Bruun, Georg; Martikainen, Jani-Petri
2013-01-01
We demonstrate how the spin-1/2 XYZ quantum Heisenberg model can be realized with bosonic atoms loaded in the p band of an optical lattice in the Mott regime. The combination of Bose statistics and the symmetry of the p-orbital wave functions leads to a nonintegrable Heisenberg model...
Thermodynamics of ideal quantum gas with fractional statistics in D dimensions.
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.
On the Quantum Mechanical Scattering Statistics of Many Particles
Dürr, Detlef; Moser, Tilo; Römer, Sarah
2010-01-01
The probability of a quantum particle being detected in a given solid angle is determined by the $S$-matrix. The explanation of this fact in time dependent scattering theory is often linked to the quantum flux, since the quantum flux integrated against a (detector-) surface and over a time interval can be viewed as the probability that the particle crosses this surface within the given time interval. Regarding many particle scattering, however, this argument is no longer valid, as each particle arrives at the detector at its own random time. While various treatments of this problem can be envisaged, here we present a straightforward Bohmian analysis of many particle potential scattering from which the $S$-matrix probability emerges in the limit of large distances.
Quantum statistical mechanics of dense partially ionized hydrogen.
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.
Statistical Models and Methods for Lifetime Data
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,
Model dynamics for quantum computing
Tabakin, Frank
2017-08-01
A model master equation suitable for quantum computing dynamics is presented. In an ideal quantum computer (QC), a system of qubits evolves in time unitarily and, by virtue of their entanglement, interfere quantum mechanically to solve otherwise intractable problems. In the real situation, a QC is subject to decoherence and attenuation effects due to interaction with an environment and with possible short-term random disturbances and gate deficiencies. The stability of a QC under such attacks is a key issue for the development of realistic devices. We assume that the influence of the environment can be incorporated by a master equation that includes unitary evolution with gates, supplemented by a Lindblad term. Lindblad operators of various types are explored; namely, steady, pulsed, gate friction, and measurement operators. In the master equation, we use the Lindblad term to describe short time intrusions by random Lindblad pulses. The phenomenological master equation is then extended to include a nonlinear Beretta term that describes the evolution of a closed system with increasing entropy. An external Bath environment is stipulated by a fixed temperature in two different ways. Here we explore the case of a simple one-qubit system in preparation for generalization to multi-qubit, qutrit and hybrid qubit-qutrit systems. This model master equation can be used to test the stability of memory and the efficacy of quantum gates. The properties of such hybrid master equations are explored, with emphasis on the role of thermal equilibrium and entropy constraints. Several significant properties of time-dependent qubit evolution are revealed by this simple study.
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....
Fisher information and quantum-classical field theory: classical statistics similarity
Energy Technology Data Exchange (ETDEWEB)
Syska, J. [Department of Field Theory and Particle Physics, Institute of Physics, University of Silesia, Uniwersytecka 4, 40-007 Katowice (Poland)
2007-07-15
The classical statistics indication for the impossibility to derive quantum mechanics from classical mechanics is proved. The formalism of the statistical Fisher information is used. Next the Fisher information as a tool of the construction of a self-consistent field theory, which joins the quantum theory and classical field theory, is proposed. (copyright 2007 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Quantum biological channel modeling and capacity calculation.
Djordjevic, Ivan B
2012-12-10
Quantum mechanics has an important role in photosynthesis, magnetoreception, and evolution. There were many attempts in an effort to explain the structure of genetic code and transfer of information from DNA to protein by using the concepts of quantum mechanics. The existing biological quantum channel models are not sufficiently general to incorporate all relevant contributions responsible for imperfect protein synthesis. Moreover, the problem of determination of quantum biological channel capacity is still an open problem. To solve these problems, we construct the operator-sum representation of biological channel based on codon basekets (basis vectors), and determine the quantum channel model suitable for study of the quantum biological channel capacity and beyond. The transcription process, DNA point mutations, insertions, deletions, and translation are interpreted as the quantum noise processes. The various types of quantum errors are classified into several broad categories: (i) storage errors that occur in DNA itself as it represents an imperfect storage of genetic information, (ii) replication errors introduced during DNA replication process, (iii) transcription errors introduced during DNA to mRNA transcription, and (iv) translation errors introduced during the translation process. By using this model, we determine the biological quantum channel capacity and compare it against corresponding classical biological channel capacity. We demonstrate that the quantum biological channel capacity is higher than the classical one, for a coherent quantum channel model, suggesting that quantum effects have an important role in biological systems. The proposed model is of crucial importance towards future study of quantum DNA error correction, developing quantum mechanical model of aging, developing the quantum mechanical models for tumors/cancer, and study of intracellular dynamics in general.
Quantum Biological Channel Modeling and Capacity Calculation
Directory of Open Access Journals (Sweden)
Ivan B. Djordjevic
2012-12-01
Full Text Available Quantum mechanics has an important role in photosynthesis, magnetoreception, and evolution. There were many attempts in an effort to explain the structure of genetic code and transfer of information from DNA to protein by using the concepts of quantum mechanics. The existing biological quantum channel models are not sufficiently general to incorporate all relevant contributions responsible for imperfect protein synthesis. Moreover, the problem of determination of quantum biological channel capacity is still an open problem. To solve these problems, we construct the operator-sum representation of biological channel based on codon basekets (basis vectors, and determine the quantum channel model suitable for study of the quantum biological channel capacity and beyond. The transcription process, DNA point mutations, insertions, deletions, and translation are interpreted as the quantum noise processes. The various types of quantum errors are classified into several broad categories: (i storage errors that occur in DNA itself as it represents an imperfect storage of genetic information, (ii replication errors introduced during DNA replication process, (iii transcription errors introduced during DNA to mRNA transcription, and (iv translation errors introduced during the translation process. By using this model, we determine the biological quantum channel capacity and compare it against corresponding classical biological channel capacity. We demonstrate that the quantum biological channel capacity is higher than the classical one, for a coherent quantum channel model, suggesting that quantum effects have an important role in biological systems. The proposed model is of crucial importance towards future study of quantum DNA error correction, developing quantum mechanical model of aging, developing the quantum mechanical models for tumors/cancer, and study of intracellular dynamics in general.
Statistical Modeling of Bivariate Data.
1982-08-01
end identify by lock nsum br) joint density-quantile function, dependence-density, non-parametric bivariate density estimation, entropy , exponential...estimated, by autoregressive or exponential model estimators I with maximum entropy properties, is investigated in this thesis. The results provide...important and useful procedures for nonparametric bivariate density estimation. The thesis discusses estimators of the entropy H(d) of ul2) which seem to me
Lattice Models of Quantum Gravity
Bittner, E R; Holm, C; Janke, W; Markum, H; Riedler, J
1998-01-01
Standard Regge Calculus provides an interesting method to explore quantum gravity in a non-perturbative fashion but turns out to be a CPU-time demanding enterprise. One therefore seeks for suitable approximations which retain most of its universal features. The $Z_2$-Regge model could be such a desired simplification. Here the quadratic edge lengths $q$ of the simplicial complexes are restricted to only two possible values $q=1+\\epsilon\\sigma$, with Ising model. To test whether this simpler model still contains the essential qualities of the standard Regge Calculus, we study both models in two dimensions and determine several observables on the same lattice size. In order to compare expectation values, e.g. of the average curvature or the Liouville field susceptibility, we employ in both models the same functional integration measure. The phase structure is under current investigation using mean field theory and numerical simulation.
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 of t...
Statistical estimation of the quality of quantum-tomography protocols
Energy Technology Data Exchange (ETDEWEB)
Bogdanov, Yu. I.; Bukeev, I. D. [Institute of Physics and Technology, Russian Academy of Sciences, 117218, Moscow (Russian Federation); Brida, G.; Genovese, M.; Shurupov, A. P. [INRIM, Strada delle Cacce 91 I-10135, Torino (Italy); Kravtsov, K. S. [Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow, 119991 (Russian Federation); Kulik, S. P.; Soloviev, A. A. [Faculty of Physics, Moscow State University, 119992, Moscow (Russian Federation); Moreva, E. V. [Moscow National Research Nuclear University ' ' MEPHI' ' , 115409, Moscow (Russian Federation)
2011-10-15
We present a complete methodology for testing the performances of quantum tomography protocols. The theory is validated by several numerical examples and by the comparison with experimental results achieved with various protocols for whole families of polarization states of qubits and ququarts including pure, mixed, entangled, and separable.
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.
Bogdanov, Yu I; Gavrichenko, A K
2011-01-01
A throughout study of statistical characteristics of fidelity in different protocols of quantum tomography is given. We consider protocols based on geometry of platonic solids and other polyhedrons with high degree of symmetry such as fullerene and its dual polyhedron. Characteristics of fidelity in different protocols are compared to the theoretical level of the minimum possible level of fidelity loss. Tomography of pure and mixed states in Hilbert spaces of different dimension is analyzed. Results of this work could be used for a better control of quantum gates and quantum states in quantum information technologies.
QUANTUM THEORY FOR THE BINOMIAL MODEL IN FINANCE THEORY
Institute of Scientific and Technical Information of China (English)
CHEN Zeqian
2004-01-01
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 R3, 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 statistics of the system of N distinguishable particles.
Quasi-determinism of weak measurement statistics: Laplace's demon's quantum cousin
Hofmann, Holger F
2010-01-01
Weak measurements can provide a complete characterization of post-selected ensembles, including the uncertainties of observables. Interestingly, the average uncertainties for pure initial and final states are always zero, suggesting the kind of complete knowledge that would allow a knowledge of past, presence and future in the sense of Laplace's demon. However, the quantum version actually describes cancellations of positive and negative uncertainties made possible by the strangeness of weak values. In this paper, I take a closer look at the relation between statistics and causality in quantum mechanics, in an attempt to recover the traces of classical determinism in the statistical relations of quantum measurement outcomes.
Photon Statistics of Single-Photon Quantum States in Real Single Photon Detection
Institute of Scientific and Technical Information of China (English)
李刚; 李园; 王军民; 彭堃墀; 张天才
2004-01-01
@@ Single photon detection (SPD) with high quantum efficiency has been widely used for measurement of different quantum states with different photon distributions.Based on the direct single SPD and double-SPD of HBT configuration, we discuss the effect of a real SPD on the photon statistics measurement and it shows that the measured photon distributions for different quantum states are corrected in different forms.The results are confirmed by experiment with the strongly attenuated coherent light and thermal light.This system can be used to characterize the photon statistics of the fluorescence light from single atom or single molecular.
Parameter Estimation, Model Reduction and Quantum Filtering
Chase, Bradley A
2009-01-01
This dissertation explores the topics of parameter estimation and model reduction in the context of quantum filtering. Chapters 2 and 3 provide a review of classical and quantum probability theory, stochastic calculus and filtering. Chapter 4 studies the problem of quantum parameter estimation and introduces the quantum particle filter as a practical computational method for parameter estimation via continuous measurement. Chapter 5 applies these techniques in magnetometry and studies the estimator's uncertainty scalings in a double-pass atomic magnetometer. Chapter 6 presents an efficient feedback controller for continuous-time quantum error correction. Chapter 7 presents an exact model of symmetric processes of collective qubit systems.
A quantum-implementable neural network model
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.
Uncertainty the soul of modeling, probability & statistics
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...
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.
Accelerated life models modeling and statistical analysis
Bagdonavicius, Vilijandas
2001-01-01
Failure Time DistributionsIntroductionParametric Classes of Failure Time DistributionsAccelerated Life ModelsIntroductionGeneralized Sedyakin's ModelAccelerated Failure Time ModelProportional Hazards ModelGeneralized Proportional Hazards ModelsGeneralized Additive and Additive-Multiplicative Hazards ModelsChanging Shape and Scale ModelsGeneralizationsModels Including Switch-Up and Cycling EffectsHeredity HypothesisSummaryAccelerated Degradation ModelsIntroductionDegradation ModelsModeling the Influence of Explanatory Varia
Quantum-like Model of Unconscious-Conscious Dynamics
Directory of Open Access Journals (Sweden)
Andrei eKhrennikov
2015-08-01
Full Text Available 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 Schroder 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, 1933framework 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.
Multistructure Statistical Model Applied To Factor Analysis
Bentler, Peter M.
1976-01-01
A general statistical model for the multivariate analysis of mean and covariance structures is described. Matrix calculus is used to develop the statistical aspects of one new special case in detail. This special case separates the confounding of principal components and factor analysis. (DEP)
Will Quantum Cosmology Resurrect Chaotic Inflation Model?
Kim, Sang Pyo; Kim, Won
2016-07-01
The single field chaotic inflation model with a monomial power greater than one seems to be ruled out by the recent Planck and WMAP CMB data while Starobinsky model with a higher curvature term seems to be a viable model. Higher curvature terms being originated from quantum fluctuations, we revisit the quantum cosmology of the Wheeler-DeWitt equation for the chaotic inflation model. The semiclassical cosmology emerges from quantum cosmology with fluctuations of spacetimes and matter when the wave function is peaked around the semiclassical trajectory with quantum corrections a la the de Broglie-Bohm pilot theory.
Will quantum cosmology resurrect chaotic inflation model?
Kim, Sang Pyo
2016-01-01
The single field chaotic inflation model with a monomial power greater than one seems to be ruled out by the recent Planck and WMAP CMB data while Starobinsky model with a higher curvature term seems to be a viable model. Higher curvature terms being originated from quantum fluctuations, we revisit the quantum cosmology of the Wheeler-DeWitt equation for the chaotic inflation model. The semiclassical cosmology emerges from quantum cosmology with fluctuations of spacetimes and matter when the wave function is peaked around the semiclassical trajectory with quantum corrections a la the de Broglie-Bohm pilot theory.
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.
Sub-poissonian statistics as an experimental test for the contextuality of quantum theory
Arnoldus, H.F.; Dieks, Dennis; Nienhuis, G.
1984-01-01
It is argued that the phenomenon of sub-poissonian statistics can be regarded as experimental evidence for the contextual character of quantum theory. To this end, it is shown that the statistics predicted by non-contextual hidden-variable theories must satisfy certain inequalities which are a kind
Semantic Importance Sampling for Statistical Model Checking
2015-01-16
approach called Statistical Model Checking (SMC) [16], which relies on Monte - Carlo -based simulations to solve this verification task more scalably...Conclusion Statistical model checking (SMC) is a prominent approach for rigorous analysis of stochastic systems using Monte - Carlo simulations. In this... Monte - Carlo simulations, for computing the bounded probability that a specific event occurs during a stochastic system’s execution. Estimating the
Quantum Ising model coupled with conducting electrons
Energy Technology Data Exchange (ETDEWEB)
Yamashita, Yasufumi; Yonemitsu, Kenji [Institute for Molecular Science, 38 Nishigo-Naka, Myodaiji, Okazaki 444-8585 (Japan); Graduate University for Advanced studies, 38 Nishigo-Naka, Myodaiji, Okazaki 444-8585 (Japan)
2005-01-01
The effect of photo-doping on the quantum paraelectric SrTiO{sub 3} is studied by using the one-dimensional quantum Ising model, where the Ising spin describes the effective lattice polarization of an optical phonon. Two types of electron-phonon couplings are introduced through the modulation of transfer integral via lattice deformations. After the exact diagonalization and the perturbation studies, we find that photo-induced low-density carriers can drastically alter quantum fluctuations when the system locates near the quantum critical point between the quantum para- and ferro-electric phases.
Quantum Ising model coupled with conducting electrons
Yamashita, Yasufumi; Yonemitsu, Kenji
2005-01-01
The effect of photo-doping on the quantum paraelectric SrTiO3 is studied by using the one-dimensional quantum Ising model, where the Ising spin describes the effective lattice polarization of an optical phonon. Two types of electron-phonon couplings are introduced through the modulation of transfer integral via lattice deformations. After the exact diagonalization and the perturbation studies, we find that photo-induced low-density carriers can drastically alter quantum fluctuations when the system locates near the quantum critical point between the quantum para- and ferro-electric phases.
The Fractional Statistics of Generalized Haldane Wave Function in 4D Quantum Hall Effect
Institute of Scientific and Technical Information of China (English)
WANGKe-Lin; WANShao-Long; CHENQing; XUFei
2003-01-01
Recently, a generalization of Laughlin's wave function expressed in Haldane's spherical geometry is con-structed in 4D quantum Hall effect. In fact, it is a membrane wave function in CP3 space. In this article, we use non-Abelian Berry phase to anaJyze the statistics of this membrane wave function. Our results show that the membrane wave function obeys fractional statistics. It is the rare example to realize fractional statistics in higher-dimensiona space than 2D. And, it will help to make clear the unresolved problems in 4D quantum Hall effect.
The Fractional Statistics of Generalized Haldane Wave Function in 4D Quantum Hall Effect
Institute of Scientific and Technical Information of China (English)
XU Fei; WANG Ke-Lin; WAN Shao-Long; CHEN Qing
2003-01-01
Recently, a generalization of Laughlin's wave function expressed in Haldane's spherical geometry is con-structed in 4D quantum Hall effect. In fact, it is a membrane wave function in CP3 space. In this article, we usenon-Abelian Berry phase to analyze the statistics of this membrane wave function. Our results show that the membranewave function obeys fractional statistics. It is the rare example to realize fractional statistics in higher-dimensional spacethan 2D. And, it will help to make clear the unresolved problems in 4D quantum Hall effect.
Probability and Statistics in Sensor Performance Modeling
2010-12-01
transformed Rice- Nakagami distribution ......................................................................... 49 Report Documentation Page...acoustic or electromagnetic waves are scattered by both objects and turbulent wind. A version of the Rice- Nakagami model (specifically with a...Gaussian, lognormal, exponential, gamma, and the 2XX → transformed Rice- Nakagami —as well as a discrete model. (Other examples of statistical models
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...
Matrix Tricks for Linear Statistical Models
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
Methods of quantum field theory in statistical physics
Abrikosov, A A; Gorkov, L P; Silverman, Richard A
1975-01-01
This comprehensive introduction to the many-body theory was written by three renowned physicists and acclaimed by American Scientist as ""a classic text on field theoretic methods in statistical physics."
Statistical origin of classical mechanics and quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Chu, S. (Department of Physics, University of California, Riverside, California 92521 (United States))
1993-11-01
The classical action for interacting strings, obtained by generalizing the time-symmetric electrodynamics of Wheeler and Feynman, is exactly additive. The additivity of the string action suggests a connection between the area of the string world sheets and entropy. We find that the action principle of classical mechanics is the condition that the total entropy of the strings be at an extremum, and the path-integral representation of the quantum density matrix element is an approximation to the partition function of the string theory.
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.
A Process Model of Quantum Mechanics
Sulis, William
2014-01-01
A process model of quantum mechanics utilizes a combinatorial game to generate a discrete and finite causal space upon which can be defined a self-consistent quantum mechanics. An emergent space-time M and continuous wave function arise through a non-uniform interpolation process. Standard non-relativistic quantum mechanics emerges under the limit of infinite information (the causal space grows to infinity) and infinitesimal scale (the separation between points goes to zero). The model has th...
Distributions with given marginals and statistical modelling
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.
Random surfaces, solvable lattice models and discrete quantum gravity in two dimensions
Energy Technology Data Exchange (ETDEWEB)
Kostov, I.K. (CEA Centre d' Etudes Nucleaires de Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique)
1989-07-01
We give a review of the analytical results concerning dynamically triangulated surfaces and statistical models on a planar random lattice. The critical behaviour of these models is described by conformal field theories coupled to 2d quantum gravity. (orig.).
Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
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.
Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems.
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.
Light scattering and photon statistics of quantum emitters coupled to metallic nanoparticles
Directory of Open Access Journals (Sweden)
O. Di Stefano
2011-09-01
Full Text Available We study theoretically the quantum optical properties of hybrid artificial molecules composed of an individual quantum emitter and a metallic nanoparticle. The coupling between the two systems can give rise to a Fano interference effect which strongly influences the quantum statistical properties of the scattered photons: a small frequency shift of the incident light field may cause changes in the intensity correlation function of the scattered field of orders of magnitude. The system opens a good perspective for applications in active metamaterials and ultracompact single-photon devices. We also demonstrate with accurate scattering calculations that a system constituted by a single quantum emitter (a semiconductor quantum dot placed in the gap between two metallic nanoparticles can display the vacuum Rabi splitting.
Performance modeling, loss networks, and statistical multiplexing
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
Statistical Modeling for Radiation Hardness Assurance
Ladbury, Raymond L.
2014-01-01
We cover the models and statistics associated with single event effects (and total ionizing dose), why we need them, and how to use them: What models are used, what errors exist in real test data, and what the model allows us to say about the DUT will be discussed. In addition, how to use other sources of data such as historical, heritage, and similar part and how to apply experience, physics, and expert opinion to the analysis will be covered. Also included will be concepts of Bayesian statistics, data fitting, and bounding rates.
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......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....... 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...
Introduction to relativistic statistical mechanics classical and quantum
Hakim, Rémi
2011-01-01
This is one of the very few books focusing on relativistic statistical mechanics, and is written by a leading expert in this special field. It started from the notion of relativistic kinetic theory, half a century ago, exploding into relativistic statisti
QUANTUM STATISTICS OF AN ATOM LASER IN THEPRESENCE OF A STRONG INPUT LIGHT
Institute of Scientific and Technical Information of China (English)
JING HUI; MIAO YUAN-XIU; HAN YI-ANG
2001-01-01
Within the framework of quantum dynamical theory, we present a new method to control the quantum statistics of an atom laser by applying a powerful input light. Differing from the case in the rotating wave approximation, the non-classical properties can appear in the output atom laser beam with the evolution of time. By choosing a suitable phase of the input light, it is capable of realizing a steady and brighter output of coherent atom laser.
Advances in statistical models for data analysis
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.
Statistical Model Checking for Stochastic Hybrid Systems
DEFF Research Database (Denmark)
David, Alexandre; Du, Dehui; Larsen, Kim Guldstrand
2012-01-01
This paper presents novel extensions and applications of the UPPAAL-SMC model checker. The extensions allow for statistical model checking of stochastic hybrid systems. We show how our race-based stochastic semantics extends to networks of hybrid systems, and indicate the integration technique ap...
Quantum simulation of the t- J model
Yamaguchi, Fumiko; Yamamoto, Yoshihisa
2002-12-01
Computer simulation of a many-particle quantum system is bound to reach the inevitable limits of its ability as the system size increases. The primary reason for this is that the memory size used in a classical simulator grows polynomially whereas the Hilbert space of the quantum system does so exponentially. Replacing the classical simulator by a quantum simulator would be an effective method of surmounting this obstacle. The prevailing techniques for simulating quantum systems on a quantum computer have been developed for purposes of computing numerical algorithms designed to obtain approximate physical quantities of interest. The method suggested here requires no numerical algorithms; it is a direct isomorphic translation between a quantum simulator and the quantum system to be simulated. In the quantum simulator, physical parameters of the system, which are the fixed parameters of the simulated quantum system, are under the control of the experimenter. A method of simulating a model for high-temperature superconducting oxides, the t- J model, by optical control, as an example of such a quantum simulation, is presented.
Quantum statistical gravity: time dilation due to local information in many-body quantum systems
Sels, Dries; Wouters, Michiel
2017-08-01
We propose a generic mechanism for the emergence of a gravitational potential that acts on all classical objects in a quantum system. Our conjecture is based on the analysis of mutual information in many-body quantum systems. Since measurements in quantum systems affect the surroundings through entanglement, a measurement at one position reduces the entropy in its neighbourhood. This reduction in entropy can be described by a local temperature, that is directly related to the gravitational potential. A crucial ingredient in our argument is that ideal classical mechanical motion occurs at constant probability. This definition is motivated by the analysis of entropic forces in classical systems.
Probabilistic Model--Checking of Quantum Protocols
Gay, S; Papanikolaou, N; Gay, Simon; Nagarajan, Rajagopal; Papanikolaou, Nikolaos
2005-01-01
We establish fundamental and general techniques for formal verification of quantum protocols. Quantum protocols are novel communication schemes involving the use of quantum-mechanical phenomena for representation, storage and transmission of data. As opposed to quantum computers, quantum communication systems can and have been implemented using present-day technology; therefore, the ability to model and analyse such systems rigorously is of primary importance. While current analyses of quantum protocols use a traditional mathematical approach and require considerable understanding of the underlying physics, we argue that automated verification techniques provide an elegant alternative. We demonstrate these techniques through the use of PRISM, a probabilistic model-checking tool. Our approach is conceptually simpler than existing proofs, and allows us to disambiguate protocol definitions and assess their properties. It also facilitates detailed analyses of actual implemented systems. We illustrate our techniqu...
Electromagnetic phenomena in matter statistical and quantum approaches
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
On the completeness of quantum computation models
Arrighi, Pablo
2010-01-01
The notion of computability is stable (i.e. independent of the choice of an indexing) over infinite-dimensional vector spaces provided they have a finite "tensorial dimension". Such vector spaces with a finite tensorial dimension permit to define an absolute notion of completeness for quantum computation models and give a precise meaning to the Church-Turing thesis in the framework of quantum theory. (Extra keywords: quantum programming languages, denotational semantics, universality.)
Statistical moments of quantum-walk dynamics reveal topological quantum transitions
Cardano, Filippo; Maffei, Maria; Massa, Francesco; Piccirillo, Bruno; de Lisio, Corrado; de Filippis, Giulio; Cataudella, Vittorio; Santamato, Enrico; Marrucci, Lorenzo
2016-04-01
Many phenomena in solid-state physics can be understood in terms of their topological properties. Recently, controlled protocols of quantum walk (QW) are proving to be effective simulators of such phenomena. Here we report the realization of a photonic QW showing both the trivial and the non-trivial topologies associated with chiral symmetry in one-dimensional (1D) periodic systems. We find that the probability distribution moments of the walker position after many steps can be used as direct indicators of the topological quantum transition: while varying a control parameter that defines the system phase, these moments exhibit a slope discontinuity at the transition point. Numerical simulations strongly support the conjecture that these features are general of 1D topological systems. Extending this approach to higher dimensions, different topological classes, and other typologies of quantum phases may offer general instruments for investigating and experimentally detecting quantum transitions in such complex systems.
Statistical moments of quantum-walk dynamics reveal topological quantum transitions.
Cardano, Filippo; Maffei, Maria; Massa, Francesco; Piccirillo, Bruno; de Lisio, Corrado; De Filippis, Giulio; Cataudella, Vittorio; Santamato, Enrico; Marrucci, Lorenzo
2016-04-22
Many phenomena in solid-state physics can be understood in terms of their topological properties. Recently, controlled protocols of quantum walk (QW) are proving to be effective simulators of such phenomena. Here we report the realization of a photonic QW showing both the trivial and the non-trivial topologies associated with chiral symmetry in one-dimensional (1D) periodic systems. We find that the probability distribution moments of the walker position after many steps can be used as direct indicators of the topological quantum transition: while varying a control parameter that defines the system phase, these moments exhibit a slope discontinuity at the transition point. Numerical simulations strongly support the conjecture that these features are general of 1D topological systems. Extending this approach to higher dimensions, different topological classes, and other typologies of quantum phases may offer general instruments for investigating and experimentally detecting quantum transitions in such complex systems.
Cavallo, A; Cosenza, F; De Cesare, L
2008-05-01
We extend the formalism of the thermodynamic two-time Green's functions to nonextensive quantum statistical mechanics. Working in the optimal Lagrangian multiplier representation, the q -spectral properties and the methods for a direct calculation of the two-time q Green's functions and the related q -spectral density ( q measures the nonextensivity degree) for two generic operators are presented in strict analogy with the extensive (q=1) counterpart. Some emphasis is devoted to the nonextensive version of the less known spectral density method whose effectiveness in exploring equilibrium and transport properties of a wide variety of systems has been well established in conventional classical and quantum many-body physics. To check how both the equations of motion and the spectral density methods work to study the q -induced nonextensivity effects in nontrivial many-body problems, we focus on the equilibrium properties of a second-quantized model for a high-density Bose gas with strong attraction between particles for which exact results exist in extensive conditions. Remarkably, the contributions to several thermodynamic quantities of the q -induced nonextensivity close to the extensive regime are explicitly calculated in the low-temperature regime by overcoming the calculation of the q grand-partition function.
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.
Growth curve models and statistical diagnostics
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.
Three Generative, Lexicalised Models for Statistical Parsing
Collins, M
1997-01-01
In this paper we first propose a new statistical parsing model, which is a generative model of lexicalised context-free grammar. We then extend the model to include a probabilistic treatment of both subcategorisation and wh-movement. Results on Wall Street Journal text show that the parser performs at 88.1/87.5% constituent precision/recall, an average improvement of 2.3% over (Collins 96).
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)
2017-03-23
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.
Quantum decoration transformation for spin models
Braz, F. F.; Rodrigues, F. C.; de Souza, S. M.; Rojas, Onofre
2016-09-01
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.
Parallelism in computations in quantum and statistical mechanics
Clementi, E.; Corongiu, G.; Detrich, J. H.
1985-07-01
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 4341s 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.
Biphoton statistic of quantum light generated on a silicon chip
Lu, Xiyuan; Zhang, Jidong; Lin, Qiang
2016-01-01
We demonstrate a silicon-chip biphoton source with an unprecedented quantum cross correlation up to ${\\rm g_{si}^{(2)}(0) = (2.58 \\pm 0.16) \\times 10^4}$. The emitted biphotons are intrinsically single-mode, with self correlations of ${\\rm g_{ss}^{(2)}(0) = 1.90 \\pm 0.05}$ and ${\\rm g_{ii}^{(2)}(0) = 1.87 \\pm 0.06}$ for signal and idler photons, respectively. We observe the waveform asymmetry of cross correlation between signal and idler photons and reveal the identical and non-exponential nature of self correlations of individual signal and idler photon modes, which is a nature of cavity-enhanced nonlinear optical processes. The high efficiency and high purity of the biphoton source allow us to herald single photons with a conditional self correlation $\\rm g_{c}^{(2)}(0)$ as low as $\\rm 0.0059 \\pm 0.0014$ at a pair flux of $\\rm 1.95 \\times 10^5$ pairs/s, which remains below $\\rm 0.026 \\pm 0.001$ for a biphoton flux up to $\\rm 2.93 \\times 10^6$ pairs/s, with a photon preparation efficiency in the single-mode ...
Bayesian models a statistical primer for ecologists
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
An R companion to linear statistical models
Hay-Jahans, Christopher
2011-01-01
Focusing on user-developed programming, An R Companion to Linear Statistical Models serves two audiences: those who are familiar with the theory and applications of linear statistical models and wish to learn or enhance their skills in R; and those who are enrolled in an R-based course on regression and analysis of variance. For those who have never used R, the book begins with a self-contained introduction to R that lays the foundation for later chapters.This book includes extensive and carefully explained examples of how to write programs using the R programming language. These examples cove
Statistics of quantum transport in weakly nonideal chaotic cavities.
Rodríguez-Pérez, Sergio; Marino, Ricardo; Novaes, Marcel; Vivo, Pierpaolo
2013-11-01
We consider statistics of electronic transport in chaotic cavities where time-reversal symmetry is broken and one of the leads is weakly nonideal; that is, it contains tunnel barriers characterized by tunneling probabilities Γ(i). Using symmetric function expansions and a generalized Selberg integral, we develop a systematic perturbation theory in 1-Γ(i) valid for an arbitrary number of channels and obtain explicit formulas up to second order for the average and variance of the conductance and for the average shot noise. Higher moments of the conductance are considered to leading order.
Quantum game simulator, using the circuit model of quantum computation
Vlachos, Panagiotis; Karafyllidis, Ioannis G.
2009-10-01
We present a general two-player quantum game simulator that can simulate any two-player quantum game described by a 2×2 payoff matrix (two strategy games).The user can determine the payoff matrices for both players, their strategies and the amount of entanglement between their initial strategies. The outputs of the simulator are the expected payoffs of each player as a function of the other player's strategy parameters and the amount of entanglement. The simulator also produces contour plots that divide the strategy spaces of the game in regions in which players can get larger payoffs if they choose to use a quantum strategy against any classical one. We also apply the simulator to two well-known quantum games, the Battle of Sexes and the Chicken game. Program summaryProgram title: Quantum Game Simulator (QGS) Catalogue identifier: AEED_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEED_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3416 No. of bytes in distributed program, including test data, etc.: 583 553 Distribution format: tar.gz Programming language: Matlab R2008a (C) Computer: Any computer that can sufficiently run Matlab R2008a Operating system: Any system that can sufficiently run Matlab R2008a Classification: 4.15 Nature of problem: Simulation of two player quantum games described by a payoff matrix. Solution method: The program calculates the matrices that comprise the Eisert setup for quantum games based on the quantum circuit model. There are 5 parameters that can be altered. We define 3 of them as constant. We play the quantum game for all possible values for the other 2 parameters and store the results in a matrix. Unusual features: The software provides an easy way of simulating any two-player quantum games. Running time: Approximately
Universal and nonuniversal level statistics in a chaotic quantum spin chain.
Pineda, Carlos; Prosen, Tomaz
2007-12-01
We study the level statistics of an interacting multiqubit system, namely the kicked Ising spin chain, in the regime of quantum chaos. Long range quasienergy level statistics show effects analogous to the ones observed in semiclassical systems due to the presence of short classical periodic orbits, while short range level statistics display perfect statistical agreement with random matrix theory. Even though our system possesses no classical limit, our results suggest existence of an important nonuniversal system specific behavior at short time scale, which clearly goes beyond finite size effects in random matrix theory.
A Primary Quantum Model of Telepathy
Gao, Shan
2003-01-01
In this paper, we give a primary quantum theoretical model of telepathy based on the principle of quantum superluminal communication (QSC). Some feasible experimental suggestions are presented. The possible application of telepathy as one kind of new communication means is also discussed.
STATISTICAL MODELS OF REPRESENTING INTELLECTUAL CAPITAL
Directory of Open Access Journals (Sweden)
Andreea Feraru
2016-07-01
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.
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.
Statistical Modeling Efforts for Headspace Gas
Energy Technology Data Exchange (ETDEWEB)
Weaver, Brian Phillip [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-03-17
The purpose of this document is to describe the statistical modeling effort for gas concentrations in WIPP storage containers. The concentration (in ppm) of CO_{2} in the headspace volume of standard waste box (SWB) 68685 is shown. A Bayesian approach and an adaptive Metropolis-Hastings algorithm were used.
Nonperturbative approach to the modified statistical model
Energy Technology Data Exchange (ETDEWEB)
Magdy, M.A.; Bekmezci, A.; Sever, R. [Middle East Technical Univ., Ankara (Turkey)
1993-12-01
The modified form of the statistical model is used without making any perturbation. The mass spectra of the lowest S, P and D levels of the (Q{bar Q}) and the non-self-conjugate (Q{bar q}) mesons are studied with the Song-Lin potential. The authors results are in good agreement with the experimental and theoretical findings.
Quantum-statistical property of optical diode based on cavity QED
Li, Haozhen; Xu, Jingping; Wang, Da-Wei; Xia, Xiuwen; Yang, Yaping; Zhu, Shiyao
2017-07-01
An optical diode made of an asymmetric cavity containing a two-level atom is investigated. We focus on the quantum-statistical property of the transmitted field with nonclassical light input. Both coherent and squeezed light inputs have been considered. The results show that the transmitted contrast of such optical diode is independent of the statistical properties of the incident light but is only sensitive to its intensity. On the other hand, the quantum-statistical property, i.e., the squeezing, of the transmitted field strongly depends on the statistical properties and directions of the incident light. For squeezed light input, the degree of the squeezing of the transmitted field can be remarkably enhanced. Moreover, the squeezing of the amplitude quadrature of the incident light can be transferred to the phase quadrature due to the coupling of the light and the atom.
Quantum Model Theory (QMod): Modeling Contextual Emergent Entangled Interfering Entities
Aerts, Diederik
2012-01-01
In this paper we present 'Quantum Model Theory' (QMod), a theory we developed to model entities that entail the typical quantum effects of 'contextuality, 'superposition', 'interference', 'entanglement' and 'emergence'. This aim of QMod is to put forward a theoretical framework that has the technical power of standard quantum mechanics, namely it makes explicitly use of the standard complex Hilbert space and its quantum mechanical calculus, but is also more general than standard quantum mechanics, in the sense that it only uses this quantum calculus locally, i.e. for each context corresponding to a measurement. In this sense, QMod is a generalization of quantum mechanics, similar to how the general relativity manifold mathematical formalism is a generalization of special relativity and classical physics. We prove by means of a representation theorem that QMod can be used for any entity entailing the typical quantum effects mentioned above. Some examples of application of QMod in concept theory and macroscopic...
Janssens, Bas
2010-01-01
This PHD thesis is concerned with uncertainty relations in quantum probability theory, state estimation in quantum stochastics, and natural bundles in differential geometry. After some comments on the nature and necessity of decoherence in open systems and its absence in closed ones, we prove sharp, state-independent inequalities reflecting the Heisenberg principle, the necessity of decoherence and the impossibility of perfect joint measurement. These bounds are used to judge how far a particular measurement is removed from the optimal one. We do this for a qubit interacting with the quantized EM field, continually probed using homodyne detection. We calculate to which extent this joint measurement is optimal. We then propose a two-step strategy to determine the (possibly mixed) state of n identically prepared qubits, and prove that it is asymptotically optimal in a local minimax sense, using `Quantum Local Asymptotic Normality' for qubits. We propose a physical implementation of QLAN, based on interaction wi...
Quantum model for mode locking in pulsed semiconductor quantum dots
Beugeling, W.; Uhrig, Götz S.; Anders, Frithjof B.
2016-12-01
Quantum dots in GaAs/InGaAs structures have been proposed as a candidate system for realizing quantum computing. The short coherence time of the electronic quantum state that arises from coupling to the nuclei of the substrate is dramatically increased if the system is subjected to a magnetic field and to repeated optical pulsing. This enhancement is due to mode locking: oscillation frequencies resonant with the pulsing frequencies are enhanced, while off-resonant oscillations eventually die out. Because the resonant frequencies are determined by the pulsing frequency only, the system becomes immune to frequency shifts caused by the nuclear coupling and by slight variations between individual quantum dots. The effects remain even after the optical pulsing is terminated. In this work, we explore the phenomenon of mode locking from a quantum mechanical perspective. We treat the dynamics using the central-spin model, which includes coupling to 10-20 nuclei and incoherent decay of the excited electronic state, in a perturbative framework. Using scaling arguments, we extrapolate our results to realistic system parameters. We estimate that the synchronization to the pulsing frequency needs time scales in the order of 1 s .
Statistical Model Checking for Stochastic Hybrid Systems
DEFF Research Database (Denmark)
David, Alexandre; Du, Dehui; Larsen, Kim Guldstrand
2012-01-01
This paper presents novel extensions and applications of the UPPAAL-SMC model checker. The extensions allow for statistical model checking of stochastic hybrid systems. We show how our race-based stochastic semantics extends to networks of hybrid systems, and indicate the integration technique...... applied for implementing this semantics in the UPPAAL-SMC simulation engine. We report on two applications of the resulting tool-set coming from systems biology and energy aware buildings....
Statistical modeling of space shuttle environmental data
Tubbs, J. D.; Brewer, D. W.
1983-01-01
Statistical models which use a class of bivariate gamma distribution are examined. Topics discussed include: (1) the ratio of positively correlated gamma varieties; (2) a method to determine if unequal shape parameters are necessary in bivariate gamma distribution; (3) differential equations for modal location of a family of bivariate gamma distribution; and (4) analysis of some wind gust data using the analytical results developed for modeling application.
Performance modeling, stochastic networks, and statistical multiplexing
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
Statistical physical models of cellular motility
Banigan, Edward J.
Cellular motility is required for a wide range of biological behaviors and functions, and the topic poses a number of interesting physical questions. In this work, we construct and analyze models of various aspects of cellular motility using tools and ideas from statistical physics. We begin with a Brownian dynamics model for actin-polymerization-driven motility, which is responsible for cell crawling and "rocketing" motility of pathogens. Within this model, we explore the robustness of self-diffusiophoresis, which is a general mechanism of motility. Using this mechanism, an object such as a cell catalyzes a reaction that generates a steady-state concentration gradient that propels the object in a particular direction. We then apply these ideas to a model for depolymerization-driven motility during bacterial chromosome segregation. We find that depolymerization and protein-protein binding interactions alone are sufficient to robustly pull a chromosome, even against large loads. Next, we investigate how forces and kinetics interact during eukaryotic mitosis with a many-microtubule model. Microtubules exert forces on chromosomes, but since individual microtubules grow and shrink in a force-dependent way, these forces lead to bistable collective microtubule dynamics, which provides a mechanism for chromosome oscillations and microtubule-based tension sensing. Finally, we explore kinematic aspects of cell motility in the context of the immune system. We develop quantitative methods for analyzing cell migration statistics collected during imaging experiments. We find that during chronic infection in the brain, T cells run and pause stochastically, following the statistics of a generalized Levy walk. These statistics may contribute to immune function by mimicking an evolutionarily conserved efficient search strategy. Additionally, we find that naive T cells migrating in lymph nodes also obey non-Gaussian statistics. Altogether, our work demonstrates how physical
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.
Gulden, Tobias
Increased interest in non-Hermitian quantum systems calls for the development of efficient methods to treat these. This interest was sparked by the introduction of PT-symmetry and the study of mathematical mappings which map conventional statistical or quantum mechanics onto non-Hermitian quantum operators. One of the most common methods in quantum mechanics is the semiclassial approximation which requires integration along trajectories that solve classical equations of motion. However in non-Hermitian systems these solutions are rarely attainable. We borrow concepts from algebraic topology to develop methods to avoid solving the equations of motion and avoid straightforward integration altogether. We apply these methods to solve the semiclassical problem for three largely dierent systems and demonstrate their usefulness for Hermitian and non-Hermitian systems alike.
Quantum and classical statistics of the electromagnetic zero-point field
Ibison, M
1996-01-01
A classical electromagnetic zero-point field (ZPF) analogue of the vacuum of quantum field theory has formed the basis for theoretical investigations in the discipline known as random or stochastic electrodynamics (SED) wherein quantum measurements are imitated by the introduction of a stochastic classical background EM field. Random EM fluctuations are assumed to provide perturbations which can mimic some quantum phenomena while retaining a purely classical basis, e.g. the Casimir force, the Van-der-Waals force, the Lamb shift, spontaneous emission, the RMS radius of the harmonic oscillator, and the radius of the Bohr atom. This classical ZPF is represented as a homogeneous, isotropic ensemble of plane waves with fixed amplitudes and random phases. Averaging over the random phases is assumed to be equivalent to taking the ground-state expectation values of the corresponding quantum operator. We demonstrate that this is not precisely correct by examining the statistics of the classical ZPF in contrast to that...
Quantum, classical and semiclassical analyses of photon statistics in harmonic generation
Bajer, J; Bajer, Jiri; Miranowicz, Adam
2001-01-01
In this review, we compare different descriptions of photon-number statistics in harmonic generation processes within quantum, classical and semiclassical approaches. First, we study the exact quantum evolution of the harmonic generation by applying numerical methods including those of Hamiltonian diagonalization and global characteristics. We show explicitly that the harmonic generations can indeed serve as a source of nonclassical light. Then, we demonstrate that the quasi-stationary sub-Poissonian light can be generated in these quantum processes under conditions corresponding to the so-called no-energy-transfer regime known in classical nonlinear optics. By applying method of classical trajectories, we demonstrate that the analytical predictions of the Fano factors are in good agreement with the quantum results. On comparing second and higher harmonic generations in the no-energy-transfer regime, we show that the highest noise reduction is achieved in third-harmonic generation with the Fano-factor of the ...
Lee, Kai-Yan; Fung, Chi-Hang Fred; Chau, H. F.
2013-05-01
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.
Pitfalls in statistical landslide susceptibility modelling
Schröder, Boris; Vorpahl, Peter; Märker, Michael; Elsenbeer, Helmut
2010-05-01
The use of statistical methods is a well-established approach to predict landslide occurrence probabilities and to assess landslide susceptibility. This is achieved by applying statistical methods relating historical landslide inventories to topographic indices as predictor variables. In our contribution, we compare several new and powerful methods developed in machine learning and well-established in landscape ecology and macroecology for predicting the distribution of shallow landslides in tropical mountain rainforests in southern Ecuador (among others: boosted regression trees, multivariate adaptive regression splines, maximum entropy). Although these methods are powerful, we think it is necessary to follow a basic set of guidelines to avoid some pitfalls regarding data sampling, predictor selection, and model quality assessment, especially if a comparison of different models is contemplated. We therefore suggest to apply a novel toolbox to evaluate approaches to the statistical modelling of landslide susceptibility. Additionally, we propose some methods to open the "black box" as an inherent part of machine learning methods in order to achieve further explanatory insights into preparatory factors that control landslides. Sampling of training data should be guided by hypotheses regarding processes that lead to slope failure taking into account their respective spatial scales. This approach leads to the selection of a set of candidate predictor variables considered on adequate spatial scales. This set should be checked for multicollinearity in order to facilitate model response curve interpretation. Model quality assesses how well a model is able to reproduce independent observations of its response variable. This includes criteria to evaluate different aspects of model performance, i.e. model discrimination, model calibration, and model refinement. In order to assess a possible violation of the assumption of independency in the training samples or a possible
Quantum-statistical equilibrium and the ``law'' of constant Fermi potential
Le Coz, Yannick L.
2003-02-01
We apply the general quantum-statistical density-matrix formalism to an independent-electron gas within a space-dependent external electric potential, under equilibrium conditions. This problem is analogous to an ideal semiconductor homojunction diode. We solve the resulting equilibrium density-matrix equation using a perturbation theory. Next, we derive a first-order quantum correction to the classical Maxwell-Boltzmann density-potential formula. The correction appears as an added curvature term in external potential. It represents expected quantum-mechanical scattering against a spatially varying potential. Our results indicate that the commonly encountered thermodynamic or statistical-mechanical "law" of constant, equilibrium Fermi potential—with Fermi potential a parameter in the Maxwell-Boltzmann density-potential formula—is not fundamentally exact. In a general space-dependent potential, this "law," we prove, is simply a classical approximation.
The Green-Kubo formula and the Onsager reciprocity relations in quantum statistical mechanics
Jaksic, V; Pillet, C
2005-01-01
We study linear response theory in the general framework of algebraic quantum statistical mechanics and prove the Green-Kubo formula and the Onsager reciprocity relations for heat fluxes generated by temperature differentials. Our derivation is axiomatic and the key assumptions concern ergodic properties of non-equilibrium steady states.
Quantum Statistics of a Forced Oscillator with a Time-Dependent Driving Force
Institute of Scientific and Technical Information of China (English)
刘文森
2003-01-01
Quantum statistics of a forced harmonic oscillator acted upon by a time-dependent external force are derived using the Wilcox trick and the time-dependent inhomogeneous Bogoliubov transformation formalism.The internal energy,fluctuation of the particle-number average and entropy of this nonequilibrium system are presented explicitly.
Non-abelian quantum Hall states -- exclusion statistics, K-matrices and duality
Ardonne, E.; Bouwknegt, P.; Schoutens, K.
2001-01-01
We study excitations in edge theories for non-abelian quantum Hall states, focussing on the spin polarized states proposed by Read and Rezayi and on the spin singlet states proposed by two of the authors. By studying the exclusion statistics properties of edge-electrons and edge-quasiholes, we
Quantum Statistical Properties of Binomial Field Interacting with Two Entangled Atoms
Institute of Scientific and Technical Information of China (English)
JIAO Zhi-Yong; MA Jun-Mao; SHANG Yong-Tao; LI Ning; FU Xia
2008-01-01
Quantum statistical properties of the binomial field interacting with the two entangled atoms are investi-gated for the different initial conditions. It is found that the sub-Poissonian distribution and the antibunching effect can be presented for the certain ranges of the involved parameters.
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
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. A468, 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.
Equilibrium statistical mechanics of lattice models
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...
Statistical shape and appearance models of bones.
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.
Statistical Compressed Sensing of Gaussian Mixture Models
Yu, Guoshen
2011-01-01
A novel framework of compressed sensing, namely statistical compressed sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution, and achieving accurate reconstruction on average, is introduced. SCS based on Gaussian models is investigated in depth. For signals that follow a single Gaussian model, with Gaussian or Bernoulli sensing matrices of O(k) measurements, considerably smaller than the O(k log(N/k)) required by conventional CS based on sparse models, where N is the signal dimension, and with an optimal decoder implemented via linear filtering, significantly faster than the pursuit decoders applied in conventional CS, the error of SCS is shown tightly upper bounded by a constant times the best k-term approximation error, with overwhelming probability. The failure probability is also significantly smaller than that of conventional sparsity-oriented CS. Stronger yet simpler results further show that for any sensing matrix, the error of Gaussian SCS is u...
Quantum gravity and the standard model
Bilson-Thompson, S O; Smolin, L; Bilson-Thompson, Sundance O.; Markopoulou, Fotini; Smolin, Lee
2006-01-01
We show that a class of background independent models of quantum spacetime have local excitations that can be mapped to the first generation fermions of the standard model of particle physics. These states propagate coherently as they can be shown to be noiseless subsystems of the microscopic quantum dynamics. These are identified in terms of certain patterns of braiding of graphs, thus giving a quantum gravitational foundation for the topological preon model proposed by one of us. These results apply to a large class of theories in which the Hilbert space has a basis of states given by ribbon graphs embedded in a three-dimensional manifold up to diffeomorphisms, and the dynamics is given by local moves on the graphs, such as arise in the representation theory of quantum groups. For such models, matter appears to be already included in the microscopic kinematics and dynamics.
The Bipolar Quantum Drift-diffusion Model
Institute of Scientific and Technical Information of China (English)
Xiu Qing CHEN; Li CHEN
2009-01-01
A fourth order parabolic system, the bipolar quantum drift-diffusion model in semiconductor simulation, with physically motivated Dirichlet-Neumann boundary condition is studied in this paper. By semidiscretization in time and compactness argument, the global existence and semiclassical limit are obtained, in which semiclassical limit describes the relation between quantum and classical drift-diffusion models. Furthermore, in the case of constant doping, we prove the weak solution exponentially approaches its constant steady state as time increases to infinity.
Sakata, Toshio; Sumi, Toshio; Miyazaki, Mitsuhiro
2009-01-01
Quantum communication is concerned with the complexity of entanglement of a state and statistical data analysis is concerned with the complexity of a model. A common key word for both is "rank". In this paper we will show that both community is tracing the same target and that the methods used are slightly different. Two different methods, the range criterion method from quantum communication and the determinant polynomial method, are shown as an examples.
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....
Modeling Transmission Line Networks Using Quantum Graphs
Koch, Trystan; Antonsen, Thomas
Quantum graphs--one dimensional edges, connecting nodes, that support propagating Schrödinger wavefunctions--have been studied extensively as tractable models of wave chaotic behavior (Smilansky and Gnutzmann 2006, Berkolaiko and Kuchment 2013). Here we consider the electrical analog, in which the graph represents an electrical network where the edges are transmission lines (Hul et. al. 2004) and the nodes contain either discrete circuit elements or intricate circuit elements best represented by arbitrary scattering matrices. Including these extra degrees of freedom at the nodes leads to phenomena that do not arise in simpler graph models. We investigate the properties of eigenfrequencies and eigenfunctions on these graphs, and relate these to the statistical description of voltages on the transmission lines when driving the network externally. The study of electromagnetic compatibility, the effect of external radiation on complicated systems with numerous interconnected cables, motivates our research into this extension of the graph model. Work supported by the Office of Naval Research (N0014130474) and the Air Force Office of Scientific Research.
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.
Iwakoshi, Takehisa; Hirota, Osamu
2014-10-01
This study will test an interpretation in quantum key distribution (QKD) that trace distance between the distributed quantum state and the ideal mixed state is a maximum failure probability of the protocol. Around 2004, this interpretation was proposed and standardized to satisfy both of the key uniformity in the context of universal composability and operational meaning of the failure probability of the key extraction. However, this proposal has not been verified concretely yet for many years while H. P. Yuen and O. Hirota have thrown doubt on this interpretation since 2009. To ascertain this interpretation, a physical random number generator was employed to evaluate key uniformity in QKD. In this way, we calculated statistical distance which correspond to trace distance in quantum theory after a quantum measurement is done, then we compared it with the failure probability whether universal composability was obtained. As a result, the degree of statistical distance of the probability distribution of the physical random numbers and the ideal uniformity was very large. It is also explained why trace distance is not suitable to guarantee the security in QKD from the view point of quantum binary decision theory.
Inferring the statistical interpretation of quantum mechanics from the classical limit
Gottfried
2000-06-01
It is widely believed that the statistical interpretation of quantum mechanics cannot be inferred from the Schrodinger equation itself, and must be stated as an additional independent axiom. Here I propose that the situation is not so stark. For systems that have both continuous and discrete degrees of freedom (such as coordinates and spin respectively), the statistical interpretation for the discrete variables is implied by requiring that the system's gross motion can be classically described under circumstances specified by the Schrodinger equation. However, this is not a full-fledged derivation of the statistical interpretation because it does not apply to the continuous variables of classical mechanics.
Spin, angular momentum and spin-statistics for a relativistic quantum many body system
Horwitz, Lawrence
2012-01-01
The adaptation of Wigner's induced representation for a relativistic quantum theory making possible the construction of wavepackets and admitting covariant expectation values for the coordinate operator x^\\mu introduces a foliation on the Hilbert space of states. The spin-statistics relation for fermions and bosons implies the universality of the parametrization of orbits of the induced representation, implying that all particles within the identical particle sets transform under the same SU(2) subgroup of the Lorentz group, and therefore their spins and angular momentum states can be computed using the usual Clebsch-Gordon coefficients associated with angular momentum. Important consequences, such as entanglement for subsystems at unequal times, covariant statistical correlations in many body systems, and the construction of relativistic boson and fermion statistical ensembles, as well as implications for the foliation of the Fock space and for quantum field theory are discussed.
Hybrid Models in Loop Quantum Cosmology
Navascués, B Elizaga; Marugán, G A Mena
2016-01-01
In the framework of Loop Quantum Cosmology, inhomogeneous models are usually quantized by means of a hybrid approach that combines loop quantization techniques with standard quantum field theory methods. This approach is based on a splitting of the phase space in a homogeneous sector, formed by global, zero-modes, and an inhomogeneous sector, formed by the remaining, infinite number of modes, that describe the local degrees of freedom. Then, the hybrid quantization is attained by adopting a loop representation for the homogeneous gravitational sector, while a Fock representation is used for the inhomogeneities. The zero-mode of the Hamiltonian constraint operator couples the homogeneous and inhomogeneous sectors. The hybrid approach, therefore, is expected to provide a suitable quantum theory in regimes where the main quantum effects of the geometry are those affecting the zero-modes, while the inhomogeneities, still being quantum, can be treated in a more conventional way. This hybrid strategy was first prop...
Statistical modeling of geopressured geothermal reservoirs
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.
Statistical Language Model for Chinese Text Proofreading
Institute of Scientific and Technical Information of China (English)
张仰森; 曹元大
2003-01-01
Statistical language modeling techniques are investigated so as to construct a language model for Chinese text proofreading. After the defects of n-gram model are analyzed, a novel statistical language model for Chinese text proofreading is proposed. This model takes full account of the information located before and after the target word wi, and the relationship between un-neighboring words wi and wj in linguistic environment(LE). First, the word association degree between wi and wj is defined by using the distance-weighted factor, wj is l words apart from wi in the LE, then Bayes formula is used to calculate the LE related degree of word wi, and lastly, the LE related degree is taken as criterion to predict the reasonability of word wi that appears in context. Comparing the proposed model with the traditional n-gram in a Chinese text automatic error detection system, the experiments results show that the error detection recall rate and precision rate of the system have been improved.
Statistics, Computation, and Modeling in Cosmology
Jewell, Jeff; Guiness, Joe; SAMSI 2016 Working Group in Cosmology
2017-01-01
Current and future ground and space based missions are designed to not only detect, but map out with increasing precision, details of the universe in its infancy to the present-day. As a result we are faced with the challenge of analyzing and interpreting observations from a wide variety of instruments to form a coherent view of the universe. Finding solutions to a broad range of challenging inference problems in cosmology is one of the goals of the “Statistics, Computation, and Modeling in Cosmology” workings groups, formed as part of the year long program on ‘Statistical, Mathematical, and Computational Methods for Astronomy’, hosted by the Statistical and Applied Mathematical Sciences Institute (SAMSI), a National Science Foundation funded institute. Two application areas have emerged for focused development in the cosmology working group involving advanced algorithmic implementations of exact Bayesian inference for the Cosmic Microwave Background, and statistical modeling of galaxy formation. The former includes study and development of advanced Markov Chain Monte Carlo algorithms designed to confront challenging inference problems including inference for spatial Gaussian random fields in the presence of sources of galactic emission (an example of a source separation problem). Extending these methods to future redshift survey data probing the nonlinear regime of large scale structure formation is also included in the working group activities. In addition, the working group is also focused on the study of ‘Galacticus’, a galaxy formation model applied to dark matter-only cosmological N-body simulations operating on time-dependent halo merger trees. The working group is interested in calibrating the Galacticus model to match statistics of galaxy survey observations; specifically stellar mass functions, luminosity functions, and color-color diagrams. The group will use subsampling approaches and fractional factorial designs to statistically and
How to construct the optimal Bayesian measurement in quantum statistical decision theory
Tanaka, Fuyuhiko
Recently, much more attention has been paid to the study aiming at the application of fundamental properties in quantum theory to information processing and technology. In particular, modern statistical methods have been recognized in quantum state tomography (QST), where we have to estimate a density matrix (positive semidefinite matrix of trace one) representing a quantum system from finite data collected in a certain experiment. When the dimension of the density matrix gets large (from a few hundred to millions), it gets a nontrivial problem. While a specific measurement is often given and fixed in QST, we are also able to choose a measurement itself according to the purpose of QST by using qunatum statistical decision theory. Here we propose a practical method to find the best projective measurement in the Bayesian sense. We assume that a prior distribution (e.g., the uniform distribution) and a convex loss function (e.g., the squared error) are given. In many quantum experiments, these assumptions are not so restrictive. We show that the best projective measurement and the best statistical inference based on the measurement outcome exist and that they are obtained explicitly by using the Monte Carlo optimization. The Grant-in-Aid for Scientific Research (B) (No. 26280005).
A Holographic Model For Quantum Critical Responses
Myers, Robert C; Witczak-Krempa, William
2016-01-01
We analyze the dynamical response functions of strongly interacting quantum critical states described by conformal field theories (CFTs). We construct a self-consistent holographic model that incorporates the relevant scalar operator driving the quantum critical phase transition. Focusing on the finite temperature dynamical conductivity $\\sigma(\\omega,T)$, we study its dependence on our model parameters, notably the scaling dimension of the relevant operator. It is found that the conductivity is well-approximated by a simple ansatz proposed by Katz et al [1] for a wide range of parameters. We further dissect the conductivity at large frequencies $\\omega >> T$ using the operator product expansion, and show how it reveals the spectrum of our model CFT. Our results provide a physically-constrained framework to study the analytic continuation of quantum Monte Carlo data, as we illustrate using the O(2) Wilson-Fisher CFT. Finally, we comment on the variation of the conductivity as we tune away from the quantum cri...
Quantum Internal Model Principle: Decoherence Control
Ganesan, Narayan; 10.1109/CDC.2007.4434706
2010-01-01
In this article, we study the problem of Decoherence Control for quantum systems by employing a novel construction termed "the bait" and with techniques from geometric control theory, in order to successfully and completely decouple an open quantum system from its environment. We re-formulate the problem of Decoherence Control as a disturbance rejection scheme which also leads us to the idea of Internal Model Principle for quantum control systems which is first of its kind in the literature. Classical internal model principle provides the guidelines for designing linear controllers for perfect tracking in the presence of external disturbances, with the help of the internal model of the disturbance generator. The theory of Disturbance Decoupling of the output from external noises is another problem that is well studied for classical systems. The two problems focus on different aspects viz. perfect output tracking and complete decoupling of output in the presence of the noise respectively. However for quantum s...
Statistical assessment of predictive modeling uncertainty
Barzaghi, Riccardo; Marotta, Anna Maria
2017-04-01
When the results of geophysical models are compared with data, the uncertainties of the model are typically disregarded. We propose a method for defining the uncertainty of a geophysical model based on a numerical procedure that estimates the empirical auto and cross-covariances of model-estimated quantities. These empirical values are then fitted by proper covariance functions and used to compute the covariance matrix associated with the model predictions. The method is tested using a geophysical finite element model in the Mediterranean region. Using a novel χ2 analysis in which both data and model uncertainties are taken into account, the model's estimated tectonic strain pattern due to the Africa-Eurasia convergence in the area that extends from the Calabrian Arc to the Alpine domain is compared with that estimated from GPS velocities while taking into account the model uncertainty through its covariance structure and the covariance of the GPS estimates. The results indicate that including the estimated model covariance in the testing procedure leads to lower observed χ2 values that have better statistical significance and might help a sharper identification of the best-fitting geophysical models.
Anyonic behavior of an intermediate-statistics fermion gas model.
Algin, Abdullah; Irk, Dursun; Topcu, Gozde
2015-06-01
We study the high-temperature behavior of an intermediate-statistics fermionic gas model whose quantum statistical properties enable us to effectively deduce the details about both the interaction among deformed (quasi)particles and their anyonic behavior. Starting with a deformed fermionic grand partition function, we calculate, in the thermodynamical limit, several thermostatistical functions of the model such as the internal energy and the entropy by means of a formalism of the fermionic q calculus. For high temperatures, a virial expansion of the equation of state for the system is obtained in two and three dimensions and the first five virial coefficients are derived in terms of the model deformation parameter q. From the results obtained by the effect of fermionic deformation, it is found that the model parameter q interpolates completely between bosonlike and fermionic systems via the behaviors of the third and fifth virial coefficients in both two and three spatial dimensions and in addition it characterizes effectively the interaction among quasifermions. Our results reveal that the present deformed (quasi)fermion model could be very efficient and effective in accounting for the nonlinear behaviors in interacting composite particle systems.
Phase locking and quantum statistics in a parametrically driven nonlinear resonator
Hovsepyan, G. H.; Shahinyan, A. R.; Chew, Lock Yue; Kryuchkyan, G. Yu.
2016-04-01
We discuss phase-locking phenomenon at low-level of quanta and quantum statistics for parametrically driven nonlinear Kerr resonator (PDNR). Oscillatory mode of PDNR is created in the process of a degenerate down-conversion of photons under interaction with a train of external Gaussian pulses. We calculate the distribution of photon-number states, the second-order correlation function of photons, the Wigner functions of cavity mode showing two-fold symmetry in phase space, and we analyze formation of phase-locked states in the regular as well as the quantum chaotic regime of the PDNR.
Shiraishi, Maresuke; Hikage, Chiaki; Namba, Ryo; Namikawa, Toshiya; Hazumi, Masashi
2016-08-01
The B -mode polarization in the cosmic microwave background (CMB) anisotropies at large angular scales provides compelling evidence for the primordial gravitational waves (GWs). It is often stated that a discovery of the GWs establishes the quantum fluctuation of vacuum during the cosmic inflation. Since the GWs could also be generated by source fields, however, we need to check if a sizable signal exists due to such source fields before reaching a firm conclusion when the B mode is discovered. Source fields of particular types can generate non-Gaussianity (NG) in the GWs. Testing statistics of the B mode is a powerful way of detecting such NG. As a concrete example, we show a model in which gauge field sources chiral GWs via a pseudoscalar coupling and forecast the detection significance at the future CMB satellite LiteBIRD. Effects of residual foregrounds and lensing B mode are both taken into account. We find the B -mode bispectrum "BBB" is in particular sensitive to the source-field NG, which is detectable at LiteBIRD with a >3 σ significance. Therefore the search for the BBB will be indispensable toward unambiguously establishing quantum fluctuation of vacuum when the B mode is discovered. We also introduced the Minkowski functional to detect the NGs. While we find that the Minkowski functional is less efficient than the harmonic-space bispectrum estimator, it still serves as a useful cross-check. Finally, we also discuss the possibility of extracting clean information on parity violation of GWs and new types of parity-violating observables induced by lensing.
Parameter estimation, model reduction and quantum filtering
Chase, Bradley A.
This thesis explores the topics of parameter estimation and model reduction in the context of quantum filtering. The last is a mathematically rigorous formulation of continuous quantum measurement, in which a stream of auxiliary quantum systems is used to infer the state of a target quantum system. Fundamental quantum uncertainties appear as noise which corrupts the probe observations and therefore must be filtered in order to extract information about the target system. This is analogous to the classical filtering problem in which techniques of inference are used to process noisy observations of a system in order to estimate its state. Given the clear similarities between the two filtering problems, I devote the beginning of this thesis to a review of classical and quantum probability theory, stochastic calculus and filtering. This allows for a mathematically rigorous and technically adroit presentation of the quantum filtering problem and solution. Given this foundation, I next consider the related problem of quantum parameter estimation, in which one seeks to infer the strength of a parameter that drives the evolution of a probe quantum system. By embedding this problem in the state estimation problem solved by the quantum filter, I present the optimal Bayesian estimator for a parameter when given continuous measurements of the probe system to which it couples. For cases when the probe takes on a finite number of values, I review a set of sufficient conditions for asymptotic convergence of the estimator. For a continuous-valued parameter, I present a computational method called quantum particle filtering for practical estimation of the parameter. Using these methods, I then study the particular problem of atomic magnetometry and review an experimental method for potentially reducing the uncertainty in the estimate of the magnetic field beyond the standard quantum limit. The technique involves double-passing a probe laser field through the atomic system, giving
Statistical Seasonal Sea Surface based Prediction Model
Suarez, Roberto; Rodriguez-Fonseca, Belen; Diouf, Ibrahima
2014-05-01
The interannual variability of the sea surface temperature (SST) plays a key role in the strongly seasonal rainfall regime on the West African region. The predictability of the seasonal cycle of rainfall is a field widely discussed by the scientific community, with results that fail to be satisfactory due to the difficulty of dynamical models to reproduce the behavior of the Inter Tropical Convergence Zone (ITCZ). To tackle this problem, a statistical model based on oceanic predictors has been developed at the Universidad Complutense of Madrid (UCM) with the aim to complement and enhance the predictability of the West African Monsoon (WAM) as an alternative to the coupled models. The model, called S4CAST (SST-based Statistical Seasonal Forecast) is based on discriminant analysis techniques, specifically the Maximum Covariance Analysis (MCA) and Canonical Correlation Analysis (CCA). Beyond the application of the model to the prediciton of rainfall in West Africa, its use extends to a range of different oceanic, atmospheric and helth related parameters influenced by the temperature of the sea surface as a defining factor of variability.
Statistical modelling for falls count data.
Ullah, Shahid; Finch, Caroline F; Day, Lesley
2010-03-01
Falls and their injury outcomes have count distributions that are highly skewed toward the right with clumping at zero, posing analytical challenges. Different modelling approaches have been used in the published literature to describe falls count distributions, often without consideration of the underlying statistical and modelling assumptions. This paper compares the use of modified Poisson and negative binomial (NB) models as alternatives to Poisson (P) regression, for the analysis of fall outcome counts. Four different count-based regression models (P, NB, zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB)) were each individually fitted to four separate fall count datasets from Australia, New Zealand and United States. The finite mixtures of P and NB regression models were also compared to the standard NB model. Both analytical (F, Vuong and bootstrap tests) and graphical approaches were used to select and compare models. Simulation studies assessed the size and power of each model fit. This study confirms that falls count distributions are over-dispersed, but not dispersed due to excess zero counts or heterogeneous population. Accordingly, the P model generally provided the poorest fit to all datasets. The fit improved significantly with NB and both zero-inflated models. The fit was also improved with the NB model, compared to finite mixtures of both P and NB regression models. Although there was little difference in fit between NB and ZINB models, in the interests of parsimony it is recommended that future studies involving modelling of falls count data routinely use the NB models in preference to the P or ZINB or finite mixture distribution. The fact that these conclusions apply across four separate datasets from four different samples of older people participating in studies of different methodology, adds strength to this general guiding principle.
Quantum Stoner-Wohlfarth Model
Hatomura, Takuya; Barbara, Bernard; Miyashita, Seiji
2016-01-01
The quantum mechanical counterpart of the famous Stoner-Wohlfarth model—an easy-axis magnet in a tilted magnetic field—is studied theoretically and through simulations as a function of the spin size S in a sweeping longitudinal field. Beyond the classical Stoner-Wohlfarth transition, the sweeping field-induced adiabatic change of states slows down as S increases, leading to a dynamical quantum phase transition. This result gives us new insights to describe the collapse of the metastability from the viewpoint of a critical phenomenon associated with the Landau-Zener tunneling gaps. Furthermore, a beating of the amplitude of the magnetization (the spin-length fidelity) is discovered after the Stoner-Wohlfarth transition. The period of the beating, confirmed analytically, arises from a new type of quantum phase factor.
Quantum field theory competitive models
Tolksdorf, Jürgen; Zeidler, Eberhard
2009-01-01
For more than 70 years, quantum field theory (QFT) can be seen as a driving force in the development of theoretical physics. Equally fascinating is the fruitful impact which QFT had in rather remote areas of mathematics. The present book features some of the different approaches, different physically viewpoints and techniques used to make the notion of quantum field theory more precise. For example, the present book contains a discussion including general considerations, stochastic methods, deformation theory and the holographic AdS/CFT correspondence. It also contains a discussion of more recent developments like the use of category theory and topos theoretic methods to describe QFT. The present volume emerged from the 3rd 'Blaubeuren Workshop: Recent Developments in Quantum Field Theory', held in July 2007 at the Max Planck Institute of Mathematics in the Sciences in Leipzig/Germany. All of the contributions are committed to the idea of this workshop series: 'To bring together outstanding experts working in...
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
A survey of statistical network models
Goldenberg, Anna; Fienberg, Stephen E; Airoldi, Edoardo M
2009-01-01
Networks are ubiquitous in science and have become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation. Probability models on graphs date back to 1959. Along with empirical studies in social psychology and sociology from the 1960s, these early works generated an active network community and a substantial literature in the 1970s. This effort moved into the statistical literature in the late 1970s and 1980s, and the past decade has seen a burgeoning network literature in statistical physics and computer science. The growth of the World Wide Web and the emergence of online networking communities such as Facebook, MySpace, and LinkedIn, and a host of more specialized professional network communities has intensified interest in the study of networks and network data. Our goal in this review is to provide the reader with an entry poin...
Statistical Modelling of the Soil Dielectric Constant
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
Quantum protocols within Spekkens' toy model
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.
Werbos, P J
2003-01-01
Quantum Field Theory (QFT) makes predictions by combining two sets of assumptions: (1) quantum dynamics, such as a Schrodinger or Liouville equation; (2) quantum measurement, such as stochastic collapse to an eigenfunction of a measurement operator. A previous paper defined a classical density matrix R encoding the statistical moments of an ensemble of states of classical second-order Hamiltonian field theory. It proved Tr(RQ)=E(Q), etc., for the usual field operators as defined by Weinberg, and it proved that those observables of the classical system obey the usual Heisenberg dynamic equation. However, R itself obeys dynamics different from the usual Liouville equation! This paper derives those dynamics, and calculates the discrepancy between CFT and normal form QFT in predicting general observables g(Q,P). There is some preliminary evidence for the conjecture that the discrepancies disappear in equilibrium states (bound states and scattering states) for finite bosonic field theories. Even if not, they appea...
Ehrenfest-time dependence of quantum transport corrections and spectral statistics.
Waltner, Daniel; Kuipers, Jack
2010-12-01
The Ehrenfest-time scale in quantum transport separates essentially classical propagation from wave interference and here we consider its effect on the transmission and reflection through quantum dots. In particular, we calculate the Ehrenfest-time dependence of the next-to-leading-order quantum corrections to the transmission and reflection for dc and ac transport and check that our results are consistent with current conservation relations. Looking as well at spectral statistics in closed systems, we finally demonstrate how the contributions analyzed here imply changes in the calculation, given by Brouwer [Phys. Rev. E 74, 066208 (2006)], of the next-to-leading order of the spectral form factor. Our semiclassical result coincides with the result obtained by Tian and Larkin [Phys. Rev. B 70, 035305 (2004)] by field-theoretical methods.
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...
Fast Quantum Rabi Model with Trapped Ions
Moya-Cessa, Héctor M.
2016-12-01
We show how to produce a fast quantum Rabi model with trapped ions. Its importance resides not only in the acceleration of the phenomena that may be achieved with these systems, from quantum gates to the generation of nonclassical states of the vibrational motion of the ion, but also in reducing unwanted effects such as the decay of coherences that may appear in such systems.
Electronic noise modeling in statistical iterative reconstruction.
Xu, Jingyan; Tsui, Benjamin M W
2009-06-01
We consider electronic noise modeling in tomographic image reconstruction when the measured signal is the sum of a Gaussian distributed electronic noise component and another random variable whose log-likelihood function satisfies a certain linearity condition. Examples of such likelihood functions include the Poisson distribution and an exponential dispersion (ED) model that can approximate the signal statistics in integration mode X-ray detectors. We formulate the image reconstruction problem as a maximum-likelihood estimation problem. Using an expectation-maximization approach, we demonstrate that a reconstruction algorithm can be obtained following a simple substitution rule from the one previously derived without electronic noise considerations. To illustrate the applicability of the substitution rule, we present examples of a fully iterative reconstruction algorithm and a sinogram smoothing algorithm both in transmission CT reconstruction when the measured signal contains additive electronic noise. Our simulation studies show the potential usefulness of accurate electronic noise modeling in low-dose CT applications.
Statistical model with a standard Γ distribution
Patriarca, Marco; Chakraborti, Anirban; Kaski, Kimmo
2004-07-01
We study a statistical model consisting of N basic units which interact with each other by exchanging a physical entity, according to a given microscopic random law, depending on a parameter λ . We focus on the equilibrium or stationary distribution of the entity exchanged and verify through numerical fitting of the simulation data that the final form of the equilibrium distribution is that of a standard Gamma distribution. The model can be interpreted as a simple closed economy in which economic agents trade money and a saving criterion is fixed by the saving propensity λ . Alternatively, from the nature of the equilibrium distribution, we show that the model can also be interpreted as a perfect gas at an effective temperature T(λ) , where particles exchange energy in a space with an effective dimension D(λ) .
Statistical model with a standard Gamma distribution
Chakraborti, Anirban; Patriarca, Marco
2005-03-01
We study a statistical model consisting of N basic units which interact with each other by exchanging a physical entity, according to a given microscopic random law, depending on a parameter λ. We focus on the equilibrium or stationary distribution of the entity exchanged and verify through numerical fitting of the simulation data that the final form of the equilibrium distribution is that of a standard Gamma distribution. The model can be interpreted as a simple closed economy in which economic agents trade money and a saving criterion is fixed by the saving propensity λ. Alternatively, from the nature of the equilibrium distribution, we show that the model can also be interpreted as a perfect gas at an effective temperature T (λ), where particles exchange energy in a space with an effective dimension D (λ).
Statistical Decision-Tree Models for Parsing
Magerman, D M
1995-01-01
Syntactic natural language parsers have shown themselves to be inadequate for processing highly-ambiguous large-vocabulary text, as is evidenced by their poor performance on domains like the Wall Street Journal, and by the movement away from parsing-based approaches to text-processing in general. In this paper, I describe SPATTER, a statistical parser based on decision-tree learning techniques which constructs a complete parse for every sentence and achieves accuracy rates far better than any published result. This work is based on the following premises: (1) grammars are too complex and detailed to develop manually for most interesting domains; (2) parsing models must rely heavily on lexical and contextual information to analyze sentences accurately; and (3) existing {$n$}-gram modeling techniques are inadequate for parsing models. In experiments comparing SPATTER with IBM's computer manuals parser, SPATTER significantly outperforms the grammar-based parser. Evaluating SPATTER against the Penn Treebank Wall ...
Statistical Model Checking for Product Lines
DEFF Research Database (Denmark)
ter Beek, Maurice H.; Legay, Axel; Lluch Lafuente, Alberto
2016-01-01
average cost of products (in terms of the attributes of the products’ features) and the probability of features to be (un)installed at runtime. The product lines must be modelled in QFLan, which extends the probabilistic feature-oriented language PFLan with novel quantitative constraints among features......We report on the suitability of statistical model checking for the analysis of quantitative properties of product line models by an extended treatment of earlier work by the authors. The type of analysis that can be performed includes the likelihood of specific product behaviour, the expected...... and on behaviour and with advanced feature installation options. QFLan is a rich process-algebraic specification language whose operational behaviour interacts with a store of constraints, neatly separating product configuration from product behaviour. The resulting probabilistic configurations and probabilistic...
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.
Challenges in Dental Statistics: Data and Modelling
Directory of Open Access Journals (Sweden)
Domenica Matranga
2013-03-01
Full Text Available 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 topics of statistical methodology for the analysis of dental data, covering the analysis of hierarchically structured and over-dispersed data, the issue of calibration and reproducibility, as well as some problems related to survey methodology, such as the design and construction of unbiased statistical indicators and of well conducted clinical trials. This paper gathers some of the methodological topics discussed during the meeting, concerning multilevel and zero-inflated models for the analysis of caries data and methods for the training and calibration of raters in dental epidemiology.
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...... proved very useful for identifying interesting properties of biological systems. Our aim is to offer the best of the two worlds: optimal domain specific interfaces and formalisms suited to biology combined with powerful SMC analysis techniques for stochastic and hybrid systems. This goal is obtained...
Statistical shape and appearance models in osteoporosis.
Castro-Mateos, Isaac; Pozo, Jose M; Cootes, Timothy F; Wilkinson, J Mark; Eastell, Richard; Frangi, Alejandro F
2014-06-01
Statistical models (SMs) of shape (SSM) and appearance (SAM) have been acquiring popularity in medical image analysis since they were introduced in the early 1990s. They have been primarily used for segmentation, but they are also a powerful tool for 3D reconstruction and classification. All these tasks may be required in the osteoporosis domain, where fracture detection and risk estimation are key to reducing the mortality and/or morbidity of this bone disease. In this article, we review the different applications of SSMs and SAMs in the context of osteoporosis, and it concludes with a discussion of their advantages and disadvantages for this application.
A Statistical Model of Skewed Associativity
Michaud, Pierre
2002-01-01
This paper presents a statistical model of set-associativity, victim caching and skewed-associativity, with an emphasis on skewed-associativity. We show that set-associativity is not efficient when the working-set size is close to the cache size. We refer to this as the unit working-set problem. We show that victim-caching is not a practical solution to the unit working-se- t problem either, although victim caching emulates full associativity for working-sets much larger than the victim buffe...
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.
Shiraishi, Maresuke; Namba, Ryo; Namikawa, Toshiya; Hazumi, Masashi
2016-01-01
The B-mode polarization in the cosmic microwave background (CMB) anisotropies at large angular scales provides a smoking-gun evidence for the primordial gravitational waves (GWs). It is often stated that a discovery of the GWs establishes the quantum fluctuation of vacuum during the cosmic inflation. Since the GWs could also be generated by source fields, however, we need to check if a sizable signal exists due to such source fields before reaching a firm conclusion when the B-mode is discovered. Source fields of particular types can generate non-Gaussianity (NG) in the GWs. Testing statistics of the B-mode is a powerful way of detecting such NG. As a concrete example, we show a model in which a gauge field sources chiral GWs via a pseudoscalar coupling, and forecast the detection significance at the future CMB satellite LiteBIRD. Effects of residual foregrounds and lensing B-mode are both taken into account. We find the B-mode bispectrum "BBB" is in particular sensitive to the source-field NG, which is detec...
Jiang, Cong; Yu, Zong-Wen; Wang, Xiang-Bin
2017-03-01
We show how to calculate the secure final key rate in the four-intensity decoy-state measurement-device-independent quantum key distribution protocol with both source errors and statistical fluctuations with a certain failure probability. Our results rely only on the range of only a few parameters in the source state. All imperfections in this protocol have been taken into consideration without assuming any specific error patterns of the source.
Full counting statistics of level renormalization in electron transport through double quantum dots.
Luo, JunYan; Jiao, HuJun; Shen, Yu; Cen, Gang; He, Xiao-Ling; Wang, Changrong
2011-04-13
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.
Full counting statistics of level renormalization in electron transport through double quantum dots
Energy Technology Data Exchange (ETDEWEB)
Luo Junyan; Shen Yu; Cen Gang; He Xiaoling; Wang Changrong [School of Science, Zhejiang University of Science and Technology, Hangzhou 310023 (China); Jiao Hujun, E-mail: jyluo@zust.edu.cn [Department of Physics, Shanxi University, Taiyuan, Shanxi 030006 (China)
2011-04-13
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.
Two-time Green's functions and spectral density method in nonextensive quantum statistical mechanics
Cavallo, A.; Cosenza, F.; De Cesare, L.
2007-01-01
We extend the formalism of the thermodynamic two-time Green's functions to nonextensive quantum statistical mechanics. Working in the optimal Lagrangian multipliers representation, the $q$-spectral properties and the methods for a direct calculation of the two-time $q$% -Green's functions and the related $q$-spectral density ($q$ measures the nonextensivity degree) for two generic operators are presented in strict analogy with the extensive ($q=1$) counterpart. Some emphasis is devoted to the...
Theory, Methods and Tools for Statistical Testing of Pseudo and Quantum Random Number Generators
Jakobsson, Krister Sune
2014-01-01
Statistical random number testing is a well studied field focusing on pseudo-random number generators, that is to say algorithms that produce random-looking sequences of numbers. These generators tend to have certain kinds of flaws, which have been exploited through rigorous testing. Such testing has led to advancements, and today pseudo random number generators are both very high-speed and produce seemingly random numbers. Recent advancements in quantum physics have opened up new doors, wher...
Statistical pairwise interaction model of stock market
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.
Statistical tests of simple earthquake cycle models
DeVries, Phoebe M. R.; Evans, Eileen L.
2016-12-01
A central goal of observing and modeling the earthquake cycle is to forecast when a particular fault may generate an earthquake: a fault late in its earthquake cycle may be more likely to generate an earthquake than a fault early in its earthquake cycle. Models that can explain geodetic observations throughout the entire earthquake cycle may be required to gain a more complete understanding of relevant physics and phenomenology. Previous efforts to develop unified earthquake models for strike-slip faults have largely focused on explaining both preseismic and postseismic geodetic observations available across a few faults in California, Turkey, and Tibet. An alternative approach leverages the global distribution of geodetic and geologic slip rate estimates on strike-slip faults worldwide. Here we use the Kolmogorov-Smirnov test for similarity of distributions to infer, in a statistically rigorous manner, viscoelastic earthquake cycle models that are inconsistent with 15 sets of observations across major strike-slip faults. We reject a large subset of two-layer models incorporating Burgers rheologies at a significance level of α = 0.05 (those with long-term Maxwell viscosities ηM 4.6 × 1020 Pa s) but cannot reject models on the basis of transient Kelvin viscosity ηK. Finally, we examine the implications of these results for the predicted earthquake cycle timing of the 15 faults considered and compare these predictions to the geologic and historical record.
Projecting Policy Effects with Statistical Models Projecting Policy Effects with Statistical Models
Directory of Open Access Journals (Sweden)
Christopher Sims
1988-03-01
Full Text Available This paper attempts to briefly discus the current frontiers in quantitative modeling for forecastina and policy analvsis. It does so by summarizing some recent developmenrs in three areas: reduced form forecasting models; theoretical models including elements of stochastic optimization; and identification. In the process, the paper tries to provide some remarks on the direction we seem to be headed. Projecting Policy Effects with Statistical Models
Projected Dipole Model for Quantum Plasmonics
DEFF Research Database (Denmark)
Yan, Wei; Wubs, Martijn; Mortensen, N. Asger
2015-01-01
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...... 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 statistics and anharmonicity in the thermodynamics of spin waves in ferromagnetic metals
Wen, Haohua; Woo, C. H.
2016-09-01
The average energy needed to create a magnon is high in ferromagnetic metals due to the high-strength spin stiffness, which results in strong quantization effects that could be important even at thousands of degrees. To take into account quantum statistics at such high temperatures, the associated effects of anharmonicity of the spin vibrations must be taken into account. In addition to the complex nature of such effects, anharmonicity also affects the occupation of the density of state of the vibration states in the context of quantum statistics. Thus, an unoccupied vibration state might become occupied when its spring stiffness is substantially reduced with anharmonicity. Combined effects of quantum statistics and anharmonicity are expected. In this regard, the thermodynamics of ferromagnetic metals are investigated in this paper through the example of bcc iron between 10 and 1400 K. Theoretical analysis and spin-lattice dynamic simulations are performed, through which the physics behind the complex and dramatic temperature dependence of the thermodynamic functions of bcc iron is understood.
Total Quantum Statistical Entropy of Reissner-Nordstrom Black Holes: in Dirac Field Case
Institute of Scientific and Technical Information of China (English)
XU Dian-Yan
2005-01-01
The total quantum statistical entropy of Reissner-Nordstrom black holes in Dirac field case is evaluated in this article. The space-time of the black holes is divided into three regions: region 1 (r ＞ ro), region 2 (ro ＞ r ＞ ri),and region 3 (ri ＞ r ＞ 0), where ro is the radius of the outer event horizon, and ri is the radius of the inner event horizon. The total quantum statistical entropy of Reissner-Nordstrom black holes is S = S1 + S2 + S3, where Si(i ＝ 1, 2, 3) is the entropy, contributed by regions 1, 2, 3. The detailed calculation shows that S2 is neglectfully sma//.S1 = wt(π2/45)kb(Ao/ε2β3), S3 = -wt(π2/45)kb(Ai/ε2β3), where Ao and Ai are, respectively, the areas of the outer and inner event horizons, wt ＝ 2s[1 - 2-(s+1)], s ＝ d/2, d is the space-time dimension, here d ＝ 4, s ＝ 2. As ri approaches ro in the extreme case the total quantum statistical entropy of Reissner-Nordstrom black holes approaches zero.
Statistical Mechanical Models of Integer Factorization Problem
Nakajima, Chihiro H.; Ohzeki, Masayuki
2017-01-01
We formulate the integer factorization problem via a formulation of the searching problem for the ground state of a statistical mechanical Hamiltonian. The first passage time required to find a correct divisor of a composite number signifies the exponential computational hardness. The analysis of the density of states of two macroscopic quantities, i.e., the energy and the Hamming distance from the correct solutions, leads to the conclusion that the ground state (correct solution) is completely isolated from the other low-energy states, with the distance being proportional to the system size. In addition, the profile of the microcanonical entropy of the model has two peculiar features that are each related to two marked changes in the energy region sampled via Monte Carlo simulation or simulated annealing. Hence, we find a peculiar first-order phase transition in our model.
Statistical model semiquantitatively approximates arabinoxylooligosaccharides' structural diversity
DEFF Research Database (Denmark)
Dotsenko, Gleb; Nielsen, Michael Krogsgaard; Lange, Lene
2016-01-01
A statistical model describing the random distribution of substituted xylopyranosyl residues in arabinoxylooligosaccharides is suggested and compared with existing experimental data. Structural diversity of arabinoxylooligosaccharides of various length, originating from different arabinoxylans...... (wheat flour arabinoxylan (arabinose/xylose, A/X = 0.47); grass arabinoxylan (A/X = 0.24); wheat straw arabinoxylan (A/X = 0.15); and hydrothermally pretreated wheat straw arabinoxylan (A/X = 0.05)), is semiquantitatively approximated using the proposed model. The suggested approach can be applied...... not only for prediction and quantification of arabinoxylooligosaccharides' structural diversity, but also for estimate of yield and selection of the optimal source of arabinoxylan for production of arabinoxylooligosaccharides with desired structural features....
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.
XYZ quantum Heisenberg models with p-orbital bosons.
Pinheiro, Fernanda; Bruun, Georg M; Martikainen, Jani-Petri; Larson, Jonas
2013-11-15
We demonstrate how the spin-1/2 XYZ quantum Heisenberg model can be realized with bosonic atoms loaded in the p band of an optical lattice in the Mott regime. The combination of Bose statistics and the symmetry of the p-orbital wave functions leads to a nonintegrable Heisenberg model with antiferromagnetic couplings. Moreover, the sign and relative strength of the couplings characterizing the model are shown to be experimentally tunable. We display the rich phase diagram in the one-dimensional case and discuss finite size effects relevant for trapped systems. Finally, experimental issues related to preparation, manipulation, detection, and imperfections are considered.
Integrated statistical modelling of spatial landslide probability
Mergili, M.; Chu, H.-J.
2015-09-01
Statistical methods are commonly employed to estimate spatial probabilities of landslide release at the catchment or regional scale. Travel distances and impact areas are often computed by means of conceptual mass point models. The present work introduces a fully automated procedure extending and combining both concepts to compute an integrated spatial landslide probability: (i) the landslide inventory is subset into release and deposition zones. (ii) We employ a simple statistical approach to estimate the pixel-based landslide release probability. (iii) We use the cumulative probability density function of the angle of reach of the observed landslide pixels to assign an impact probability to each pixel. (iv) We introduce the zonal probability i.e. the spatial probability that at least one landslide pixel occurs within a zone of defined size. We quantify this relationship by a set of empirical curves. (v) The integrated spatial landslide probability is defined as the maximum of the release probability and the product of the impact probability and the zonal release probability relevant for each pixel. We demonstrate the approach with a 637 km2 study area in southern Taiwan, using an inventory of 1399 landslides triggered by the typhoon Morakot in 2009. We observe that (i) the average integrated spatial landslide probability over the entire study area corresponds reasonably well to the fraction of the observed landside area; (ii) the model performs moderately well in predicting the observed spatial landslide distribution; (iii) the size of the release zone (or any other zone of spatial aggregation) influences the integrated spatial landslide probability to a much higher degree than the pixel-based release probability; (iv) removing the largest landslides from the analysis leads to an enhanced model performance.
MSMBuilder: Statistical Models for Biomolecular Dynamics.
Harrigan, Matthew P; Sultan, Mohammad M; Hernández, Carlos X; Husic, Brooke E; Eastman, Peter; Schwantes, Christian R; Beauchamp, Kyle A; McGibbon, Robert T; Pande, Vijay S
2017-01-10
MSMBuilder is a software package for building statistical models of high-dimensional time-series data. It is designed with a particular focus on the analysis of atomistic simulations of biomolecular dynamics such as protein folding and conformational change. MSMBuilder is named for its ability to construct Markov state models (MSMs), a class of models that has gained favor among computational biophysicists. In addition to both well-established and newer MSM methods, the package includes complementary algorithms for understanding time-series data such as hidden Markov models and time-structure based independent component analysis. MSMBuilder boasts an easy to use command-line interface, as well as clear and consistent abstractions through its Python application programming interface. MSMBuilder was developed with careful consideration for compatibility with the broader machine learning community by following the design of scikit-learn. The package is used primarily by practitioners of molecular dynamics, but is just as applicable to other computational or experimental time-series measurements. Copyright © 2017 Biophysical Society. Published by Elsevier Inc. All rights reserved.
ZERODUR strength modeling with Weibull statistical distributions
Hartmann, Peter
2016-07-01
The decisive influence on breakage strength of brittle materials such as the low expansion glass ceramic ZERODUR is the surface condition. For polished or etched surfaces it is essential if micro cracks are present and how deep they are. Ground surfaces have many micro cracks caused by the generation process. Here only the depths of the micro cracks are relevant. In any case presence and depths of micro cracks are statistical by nature. The Weibull distribution is the model used traditionally for the representation of such data sets. It is based on the weakest link ansatz. The use of the two or three parameter Weibull distribution for data representation and reliability prediction depends on the underlying crack generation mechanisms. Before choosing the model for a specific evaluation, some checks should be done. Is there only one mechanism present or is it to be expected that an additional mechanism might contribute deviating results? For ground surfaces the main mechanism is the diamond grains' action on the surface. However, grains breaking from their bonding might be moved by the tool across the surface introducing a slightly deeper crack. It is not to be expected that these scratches follow the same statistical distribution as the grinding process. Hence, their description with the same distribution parameters is not adequate. Before including them a dedicated discussion should be performed. If there is additional information available influencing the selection of the model, for example the existence of a maximum crack depth, this should be taken into account also. Micro cracks introduced by small diamond grains on tools working with limited forces cannot be arbitrarily deep. For data obtained with such surfaces the existence of a threshold breakage stress should be part of the hypothesis. This leads to the use of the three parameter Weibull distribution. A differentiation based on the data set alone without preexisting information is possible but requires a
Statistical model for OCT image denoising
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.
Physical and Statistical Modeling of Saturn's Troposphere
Yanamandra-Fisher, Padmavati A.; Braverman, Amy J.; Orton, Glenn S.
2002-12-01
The 5.2-μm atmospheric window on Saturn is dominated by thermal radiation and weak gaseous absorption, with a 20% contribution from sunlight reflected from clouds. The striking variability displayed by Saturn's clouds at 5.2 μm and the detection of PH3 (an atmospheric tracer) variability near or below the 2-bar level and possibly at lower pressures provide salient constraints on the dynamical organization of Saturn's atmosphere by constraining the strength of vertical motions at two levels across the disk. We analyse the 5.2-μm spectra of Saturn by utilising two independent methods: (a) physical models based on the relevant atmospheric parameters and (b) statistical analysis, based on principal components analysis (PCA), to determine the influence of the variation of phosphine and the opacity of clouds deep within Saturn's atmosphere to understand the dynamics in its atmosphere.
Quantum Gravity models - brief conceptual summary
Lukierski, jerzy
2014-01-01
After short historical overview we describe the difficulties with application of standard QFT methods in quantum gravity (QG). The incompatibility of QG with the use of classical continuous space-time required conceptually new approach. We present briefly three proposals: loop quantum gravity (LQG), the field-theoretic framework on noncommutative space-time and QG models formulated on discretized (triangularized) space-time. We evaluate these models as realizing expected important properties of QG: background independence, consistent quantum diffeomorphisms, noncommutative or discrete structure of space-time at very short distances, finite/renormalizable QG corrections. We only briefly outline an important issue of embedding QG into larger geometric and dynamical frameworks (e.g. supergravity, (super)strings, p-branes, M-theory), with the aim to achieve full unification of all fundamental interactions.
New advances in statistical modeling and applications
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.
Javadi, A.; Maibom, S.; Sapienza, L.; Thyrrestrup Nielsen, H.; Garcia, P.D.; Lodahl, P.
2014-01-01
We present a statistical study of the Purcell enhancement of the light emission from quantum dots coupled to Anderson-localized cavities formed in disordered photonic-crystal waveguides. We measure the time-resolved light emission from both single quantum emitters coupled to Anderson-localized cavit
Hybrid models in loop quantum cosmology
Elizaga Navascués, Beatriz; Martín-Benito, Mercedes; Mena Marugán, Guillermo A.
2016-06-01
In the framework of Loop Quantum Cosmology (LQC), inhomogeneous models are usually quantized by means of a hybrid approach that combines loop quantization techniques with standard quantum field theory methods. This approach is based on a splitting of the phase space in a homogeneous sector, formed by global, zero-modes and an inhomogeneous sector, formed by the remaining, infinite number of modes, that describe the local degrees of freedom. Then, the hybrid quantization is attained by adopting a loop representation for the homogeneous gravitational sector, while a Fock representation is used for the inhomogeneities. The zero-mode of the Hamiltonian constraint operator couples the homogeneous and inhomogeneous sectors. The hybrid approach, therefore, is expected to provide a suitable quantum theory in regimes where the main quantum effects of the geometry are those affecting the zero-modes, while the inhomogeneities, still being quantum, can be treated in a more conventional way. This hybrid strategy was first proposed for the simplest cosmological midisuperspaces: the Gowdy models, and it has been later applied to the case of cosmological perturbations. This paper reviews the construction and main applications of hybrid LQC.
Optimal evolution models for quantum tomography
Czerwiński, Artur
2016-02-01
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.
Quantum statistics and squeezing for a microwave-driven interacting magnon system
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.
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...
Cafaro, C.; Ali, S. A.
2008-12-01
In this paper, we review our novel information-geometrodynamical approach to chaos (IGAC) on curved statistical manifolds and we emphasize the usefulness of our information-geometrodynamical entropy (IGE) as an indicator of chaoticity in a simple application. Furthermore, knowing that integrable and chaotic quantum antiferromagnetic Ising chains are characterized by asymptotic logarithmic and linear growths of their operator space entanglement entropies, respectively, we apply our IGAC to present an alternative characterization of such systems. Remarkably, we show that in the former case the IGE exhibits asymptotic logarithmic growth while in the latter case the IGE exhibits asymptotic linear growth. At this stage of its development, IGAC remains an ambitious unifying information-geometric theoretical construct for the study of chaotic dynamics with several unsolved problems. However, based on our recent findings, we believe that it could provide an interesting, innovative and potentially powerful way to study and understand the very important and challenging problems of classical and quantum chaos.
Quantum gravity and the standard model
Energy Technology Data Exchange (ETDEWEB)
Bilson-Thompson, Sundance O [CSSM, School of Chemistry and Physics, University of Adelaide, Adelaide SA 5005 (Australia); Markopoulou, Fotini [Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2J 2W9 (Canada); Smolin, Lee [Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2J 2W9 (Canada)
2007-08-21
We show that a class of background-independent models of quantum spacetime have local excitations that can be mapped to the first-generation fermions of the standard model of particle physics. These states propagate coherently as they can be shown to be noiseless subsystems of the microscopic quantum dynamics (Kribs and Markopoulou 2005 Preprint gr-qc/0510052, Markopoulou and Poulin unpublished). These are identified in terms of certain patterns of braiding of graphs, thus giving a quantum gravitational foundation for the topological preon model proposed by Bilson-Thompson (2005 Preprint hep-ph/0503213). These results apply to a large class of theories in which the Hilbert space has a basis of states given by ribbon graphs embedded in a three-dimensional manifold up to diffeomorphisms, and the dynamics is given by local moves on the graphs, such as arise in the representation theory of quantum groups. For such models, matter appears to be already included in the microscopic kinematics and dynamics.
Quantum gravity and the standard model
Bilson-Thompson, Sundance O.; Markopoulou, Fotini; Smolin, Lee
2007-08-01
We show that a class of background-independent models of quantum spacetime have local excitations that can be mapped to the first-generation fermions of the standard model of particle physics. These states propagate coherently as they can be shown to be noiseless subsystems of the microscopic quantum dynamics (Kribs and Markopoulou 2005 Preprint gr-qc/0510052, Markopoulou and Poulin unpublished). These are identified in terms of certain patterns of braiding of graphs, thus giving a quantum gravitational foundation for the topological preon model proposed by Bilson-Thompson (2005 Preprint hep-ph/0503213). These results apply to a large class of theories in which the Hilbert space has a basis of states given by ribbon graphs embedded in a three-dimensional manifold up to diffeomorphisms, and the dynamics is given by local moves on the graphs, such as arise in the representation theory of quantum groups. For such models, matter appears to be already included in the microscopic kinematics and dynamics.
Correlation Inequalities for the Quantum XY Model
Benassi, Costanza; Lees, Benjamin; Ueltschi, Daniel
2016-09-01
We show the positivity or negativity of truncated correlation functions in the quantum XY model with spin 1/2 (at any temperature) and spin 1 (in the ground state). These Griffiths-Ginibre inequalities of the second kind generalise an earlier result of Gallavotti.
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.
Processor core model for quantum computing.
Yung, Man-Hong; Benjamin, Simon C; Bose, Sougato
2006-06-09
We describe an architecture based on a processing "core," where multiple qubits interact perpetually, and a separate "store," where qubits exist in isolation. Computation consists of single qubit operations, swaps between the store and the core, and free evolution of the core. This enables computation using physical systems where the entangling interactions are "always on." Alternatively, for switchable systems, our model constitutes a prescription for optimizing many-qubit gates. We discuss implementations of the quantum Fourier transform, Hamiltonian simulation, and quantum error correction.
Modelling earthquake interaction and seismicity statistics
Steacy, S.; Hetherington, A.
2009-04-01
The effects of earthquake interaction and fault complexity on seismicity statistics are investigated in a 3D model composed of a number of cellular automata (each representing an individual fault) distributed in a volume. Each automaton is assigned a fractal distribution of strength. Failure occurs when the 3D Coulomb stress on any cell exceeds its strength and stress transfer during simulated earthquake rupture is via nearest-neighbor rules formulated to give realistic stress concentrations. An event continues until all neighboring cells whose stresses exceed their strengths have ruptured and the size of the event is determined from its area and stress drop. Long-range stress interactions are computed following the termination of simulated ruptures using a boundary element code. In practice, these stress perturbations are only computed for events above a certain size (e.g. a threshold length of 10 km) and stresses are updated on nearby structures. Events which occur as a result of these stress interactions are considered to be "triggered" earthquakes and they, in turn, can trigger further seismic activity. The threshold length for computing interaction stresses is a free parameter and hence interaction can be "turned off" by setting this to an unrealistically high value. We consider 3 synthetic fault networks of increasing degrees of complexity - modelled on the North Anatolian fault system, the structures in the San Francisco Bay Area, and the Southern California fault network. We find that the effect of interaction is dramatically different in networks of differing complexity. In the North Anatolian analogue, for example, interaction leads to a decreased number of events, increased b-values, and an increase in recurrence intervals. In the Bay Area model, by contrast, we observe that interaction increases the number of events, decreases the b-values, and has little effect on recurrence intervals. For all networks, we find that interaction can activate mis
Classical Ising model test for quantum circuits
Geraci, Joseph; Lidar, Daniel A.
2010-07-01
We exploit a recently constructed mapping between quantum circuits and graphs in order to prove that circuits corresponding to certain planar graphs can be efficiently simulated classically. The proof uses an expression for the Ising model partition function in terms of quadratically signed weight enumerators (QWGTs), which are polynomials that arise naturally in an expansion of quantum circuits in terms of rotations involving Pauli matrices. We combine this expression with a known efficient classical algorithm for the Ising partition function of any planar graph in the absence of an external magnetic field, and the Robertson-Seymour theorem from graph theory. We give as an example a set of quantum circuits with a small number of non-nearest-neighbor gates which admit an efficient classical simulation.
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
Pathway Model and Nonextensive Statistical Mechanics
Mathai, A. M.; Haubold, H. J.; Tsallis, C.
2015-12-01
The established technique of eliminating upper or lower parameters in a general hypergeometric series is profitably exploited to create pathways among confluent hypergeometric functions, binomial functions, Bessel functions, and exponential series. One such pathway, from the mathematical statistics point of view, results in distributions which naturally emerge within nonextensive statistical mechanics and Beck-Cohen superstatistics, as pursued in generalizations of Boltzmann-Gibbs statistics.
Statistical Ensemble Theory of Gompertz Growth Model
Directory of Open Access Journals (Sweden)
Takuya Yamano
2009-11-01
Full Text Available An ensemble formulation for the Gompertz growth function within the framework of statistical mechanics is presented, where the two growth parameters are assumed to be statistically distributed. The growth can be viewed as a self-referential process, which enables us to use the Bose-Einstein statistics picture. The analytical entropy expression pertain to the law can be obtained in terms of the growth velocity distribution as well as the Gompertz function itself for the whole process.
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.
Quantum Statistical Properties of the Exciton in a Leaky Quasi-Mode Cavity
Institute of Scientific and Technical Information of China (English)
YU Zhao-Xian; JIAO Zhi-Yong
2002-01-01
We have studied quantum statistical properties of the exciton in a leaky quasi-mode cavity. It is shown that when the exciton is initially in a squeezed coherent state whereas cavity initially in a vacuum state, there is energy exchange between the exciton and cavity. Both the exciton and cavity may exhibit sub-Poissonian distribution and exist quadrature squeezing. Calculation shows that correlation between the exciton and cavity is classical, which implies that there is not the violation of the Cauchy-Schwartz inequality.
An adaptive contextual quantum language model
Li, Jingfei; Zhang, Peng; Song, Dawei; Hou, Yuexian
2016-08-01
User interactions in search system represent a rich source of implicit knowledge about the user's cognitive state and information need that continuously evolves over time. Despite massive efforts that have been made to exploiting and incorporating this implicit knowledge in information retrieval, it is still a challenge to effectively capture the term dependencies and the user's dynamic information need (reflected by query modifications) in the context of user interaction. To tackle these issues, motivated by the recent Quantum Language Model (QLM), we develop a QLM based retrieval model for session search, which naturally incorporates the complex term dependencies occurring in user's historical queries and clicked documents with density matrices. In order to capture the dynamic information within users' search session, we propose a density matrix transformation framework and further develop an adaptive QLM ranking model. Extensive comparative experiments show the effectiveness of our session quantum language models.
Fisher-Schroedinger models for statistical encryption of covert information
Venkatesan, R. C.
2007-04-01
The theoretical framework for a principled procedure to encrypt/decrypt covert information (code)into/from the null spaces of a hierarchy of statistical distributions possessing ill-conditioned eigenstructures, is suggested. The statistical distributions are inferred using incomplete constraints, employing the generalized nonextensive thermostatistics (NET) Fisher information as the measure of uncertainty. The hierarchy of inferred statistical distributions possess a quantum mechanical connotation for unit values of the nonextensivity parameter. A systematic strategy to encrypt/decrypt code via unitary projections into the null spaces of the ill-conditioned eigenstructures, is presented.
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.
Haghshenasfard, Zahra; Cottam, Michael G
2017-03-20
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.
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.
Second Quantization of Cini Model for High Order Quantum Decoherence in Quantum Measurement
Zhou, D L; Sun, C P
2001-01-01
By making the second quantization for the Cini Model of quantum measurement without wave function collapse [M. Cini, Nuovo Cimento, B73 27(1983)], the second order quantum decoherence (SOQD) is studied with a two mode boson system interacting with an idealized apparatus composed by two quantum oscillators. In the classical limit that the apparatus is prepared in a Fock state with a very large quantum number, or in a coherent state with average quantum numbers large enough, the SOQD phenomenon appears similar to the first order case of quantum decoherence.
Quantum correlation and quantum phase transition in the one-dimensional extended Ising model
Zhang, Xi-Zheng; Guo, Jin-Liang
2017-09-01
Quantum phase transitions can be understood in terms of Landau's symmetry-breaking theory. Following the discovery of the quantum Hall effect, a new kind of quantum phase can be classified according to topological rather than local order parameters. Both phases coexist for a class of exactly solvable quantum Ising models, for which the ground state energy density corresponds to a loop in a two-dimensional auxiliary space. Motivated by this we study quantum correlations, measured by entanglement and quantum discord, and critical behavior seen in the one-dimensional extended Ising model with short-range interaction. We show that the quantum discord exhibits distinctive behaviors when the system experiences different topological quantum phases denoted by different topological numbers. Quantum discords capability to detect a topological quantum phase transition is more reliable than that of entanglement at both zero and finite temperatures. In addition, by analyzing the divergent behaviors of quantum discord at the critical points, we find that the quantum phase transitions driven by different parameters of the model can also display distinctive critical behaviors, which provides a scheme to detect the topological quantum phase transition in practice.
Metastability in an open quantum Ising model
Rose, Dominic C.; Macieszczak, Katarzyna; Lesanovsky, Igor; Garrahan, Juan P.
2016-11-01
We apply a recently developed theory for metastability in open quantum systems to a one-dimensional dissipative quantum Ising model. Earlier results suggest this model features either a nonequilibrium phase transition or a smooth but sharp crossover, where the stationary state changes from paramagnetic to ferromagnetic, accompanied by strongly intermittent emission dynamics characteristic of first-order coexistence between dynamical phases. We show that for a range of parameters close to this transition or crossover point the dynamics of the finite system displays pronounced metastability, i.e., the system relaxes first to long-lived metastable states before eventual relaxation to the true stationary state. From the spectral properties of the quantum master operator we characterize the low-dimensional manifold of metastable states, which are shown to be probability mixtures of two, paramagnetic and ferromagnetic, metastable phases. We also show that for long times the dynamics can be approximated by a classical stochastic dynamics between the metastable phases that is directly related to the intermittent dynamics observed in quantum trajectories and thus the dynamical phases.
Promoting Conceptual Coherence in Quantum Learning through Computational Models
Lee, Hee-Sun
2012-02-01
In order to explain phenomena at the quantum level, scientists use multiple representations in verbal, pictorial, mathematical, and computational forms. Conceptual coherence among these multiple representations is used as an analytical framework to describe student learning trajectories in quantum physics. A series of internet-based curriculum modules are designed to address topics in quantum mechanics, semiconductor physics, and nano-scale engineering applications. In these modules, students are engaged in inquiry-based activities situated in a highly interactive computational modeling environment. This study was conducted in an introductory level solid state physics course. Based on in-depth interviews with 13 students, methods for identifying conceptual coherence as a function of students' level of understanding are presented. Pre-post test comparisons of 20 students in the course indicate a statistically significant improvement in students' conceptual coherence of understanding quantum phenomena before and after the course, Effect Size = 1.29 SD. Additional analyses indicate that students who responded to the modules more coherently improved their conceptual coherence to a greater extent than those who did less to the modules after controlling for their course grades.
Statistical theory of relaxation of high-energy electrons in quantum Hall edge states
Lunde, Anders Mathias; Nigg, Simon E.
2016-07-01
We investigate theoretically the energy exchange between the electrons of two copropagating, out-of-equilibrium edge states with opposite spin polarization in the integer quantum Hall regime. A quantum dot tunnel coupled to one of the edge states locally injects electrons at high energy. Thereby a narrow peak in the energy distribution is created at high energy above the Fermi level. A second downstream quantum dot performs an energy-resolved measurement of the electronic distribution function. By varying the distance between the two dots, we are able to follow every step of the energy exchange and relaxation between the edge states, even analytically under certain conditions. In the absence of translational invariance along the edge, e.g., due to the presence of disorder, energy can be exchanged by non-momentum-conserving two-particle collisions. For weakly broken translational invariance, we show that the relaxation is described by coupled Fokker-Planck equations. From these we find that relaxation of the injected electrons can be understood statistically as a generalized drift-diffusion process in energy space for which we determine the drift velocity and the dynamical diffusion parameter. Finally, we provide a physically appealing picture in terms of individual edge-state heating as a result of the relaxation of the injected electrons.
Bond diluted anisotropic quantum Heisenberg model
Energy Technology Data Exchange (ETDEWEB)
Akıncı, Ümit, E-mail: umit.akinci@deu.edu.tr
2013-10-15
Effects of the bond dilution on the critical temperatures, phase diagrams and the magnetization behaviors of the isotropic and anisotropic quantum Heisenberg model have been investigated in detail. For the isotropic case, bond percolation threshold values have been determined for several numbers of two (2D) and three (3D) dimensional lattices. In order to investigate the effect of the anisotropy in the exchange interaction on the results obtained for the isotropic model, a detailed investigation has been made on a honeycomb lattice. Some interesting results, such as second order reentrant phenomena in the phase diagrams have been found. - Highlights: • Anisotropic quantum Heisenberg model with bond dilution investigated. • Bond percolation threshold values given for 2D and 3D lattices in isotropic case. • Phase diagrams and ground state magnetizations investigated in detail. • Variation of the bond percolation threshold values with anisotropy determined.
Internal quantum efficiency modeling of silicon photodiodes.
Gentile, T R; Brown, S W; Lykke, K R; Shaw, P S; Woodward, J T
2010-04-01
Results are presented for modeling of the shape of the internal quantum efficiency (IQE) versus wavelength for silicon photodiodes in the 400 nm to 900 nm wavelength range. The IQE data are based on measurements of the external quantum efficiencies of three transmission optical trap detectors using an extensive set of laser wavelengths, along with the transmittance of the traps. We find that a simplified version of a previously reported IQE model fits the data with an accuracy of better than 0.01%. These results provide an important validation of the National Institute of Standards and Technology (NIST) spectral radiant power responsivity scale disseminated through the NIST Spectral Comparator Facility, as well as those scales disseminated by other National Metrology Institutes who have employed the same model.
Lee, Myoung-Jae; Jung, Young-Dae
2017-09-01
The physical properties of the Washimi-Karpman ponderomotive magnetization are investigated in relativistically degenerate quantum Fermi-Dirac plasmas including the influence of quantum statistical degeneracy pressure. The induced magnetization and power radiation due to the Washimi-Karpman ponderomotive interaction are obtained in Fermi-Dirac plasmas. It is found that the ponderomotive magnetization decreases with an increase of the relativistic degeneracy parameter. It is also shown that the quantum statistical degeneracy pressure effect is more significant in small frequency and large wave number domains than that in large frequency and small wave number domains. In addition, it is found that the ponderomotive power radiation decreases with an increase of the relativistic degeneracy parameter in Fermi-Dirac plasmas. The variations of the Washimi-Karpman magnetization and power radiation due to the physical characteristics of degenerate quantum Fermi-Dirac plasmas are also discussed.
Quantum chaos and holographic tensor models
Krishnan, Chethan; Sanyal, Sambuddha; Subramanian, P. N. Bala
2017-03-01
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.
Online Statistical Modeling (Regression Analysis) for Independent Responses
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.
Full counting statistics of renormalized dynamics in open quantum transport system
Energy Technology Data Exchange (ETDEWEB)
Luo, JunYan, E-mail: jyluo@zust.edu.cn [School of Science, Zhejiang University of Science and Technology, Hangzhou, 310023 (China); Shen, Yu; He, Xiao-Ling [School of Science, Zhejiang University of Science and Technology, Hangzhou, 310023 (China); Li, Xin-Qi [Department of Chemistry, Hong Kong University of Science and Technology, Kowloon, Hong Kong SAR (China); State Key Laboratory for Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083 (China); Department of Physics, Beijing Normal University, Beijing 100875 (China); Yan, YiJing [Department of Chemistry, Hong Kong University of Science and Technology, Kowloon, Hong Kong SAR (China)
2011-11-28
The internal dynamics of a double quantum dot system is renormalized due to coupling respectively with transport electrodes and a dissipative heat bath. Their essential differences are identified unambiguously in the context of full counting statistics. The electrode coupling caused level detuning renormalization gives rise to a fast-to-slow transport mechanism, which is not resolved at all in the average current, but revealed uniquely by pronounced super-Poissonian shot noise and skewness. The heat bath coupling introduces an interdot coupling renormalization, which results in asymmetric Fano factor and an intriguing change of line shape in the skewness. -- Highlights: ► We study full counting statistics of electron transport through double quantum dots. ► Essential differences due to coupling to the electrodes and heat bath are identified. ► Level detuning induced by electrodes results in strongly enhanced shot noise and skewness. ► Interdot coupling renormalization due to heat bath leads to asymmetric noise and intriguing skewness.
Directory of Open Access Journals (Sweden)
Arkady Plotnitsky
2017-06-01
Full Text Available 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, that may be helpful or even necessary there or in physics itself. I shall, in closing, suggest one possible type of such models, singularized probabilistic models, SP-models, some
Modelling of multidimensional quantum systems by the numerical functional integration
Energy Technology Data Exchange (ETDEWEB)
Lobanov, Yu.Yu.; Zhidkov, E.P. (Joint Inst. for Nuclear Research, Dubna (USSR)); Shahbagian, R.R. (Yerevan Physics Inst., Erevan (USSR))
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. The comparison of numerical results with the data obtained by the other authors which used the Monte Carlo method combined with iterative algorithms indicates that our formulas provide the higher efficiency of computations.
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......Software is in increasing fashion embedded within safety- and business critical processes of society. Errors in these embedded systems can lead to human casualties or severe monetary loss. Model checking technology has proven formal methods capable of finding and correcting errors in software....... However, software is approaching the boundary in terms of the complexity and size that model checking can handle. Furthermore, software systems are nowadays more frequently interacting with their environment hence accurately modelling such systems requires modelling the environment as well - resulting...
Dimer Models, Free Fermions and Super Quantum Mechanics
Dijkgraaf, R; Reffert, S
2007-01-01
This note relates topics in statistical mechanics, graph theory and combinatorics, lattice quantum field theory, super quantum mechanics and string theory. We give a precise relation between the dimer model on a graph embedded on a torus and the massless free Majorana fermion living on the same lattice. A loop expansion of the fermion determinant is performed, where the loops turn out to be compositions of two perfect matchings. These loop states are sorted into co-chain groups using categorification techniques similar to the ones used for categorifying knot polynomials. The Euler characteristic of the resulting co-chain complex recovers the Newton polynomial of the dimer model. We re-interpret this system as supersymmetric quantum mechanics, where configurations with vanishing net winding number form the ground states. Finally, we make use of the quiver gauge theory - dimer model correspondence to obtain an interpretation of the loops in terms of the physics of D-branes probing a toric Calabi-Yau singularity...
A minimalist pilot-wave model for quantum electrodynamics
National Research Council Canada - National Science Library
W Struyve; H Westman
2007-01-01
We present a way to construct a pilot-wave model for quantum electrodynamics. The idea is to introduce beables corresponding only to the bosonic and not to the fermionic degrees of freedom of the quantum state...
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
The simplest possible bouncing quantum cosmological model
Peter, Patrick
2016-01-01
We present and expand the simplest possible quantum cosmological model already discussed in a previous work: the trajectory formulation of quantum mechanics applied to cosmology in the FLRW minisuperspace without spatial curvature. The initial conditions that were assumed there were such that the wave function would not change its functional form but instead provide a dynamics to its parameters. Here, we consider a more general situation, in practice consisting of modified Gaussian wave functions, aiming at obtaining a bounce from a contracting phase. Whereas previous works consistently obtain very symmetric bounces, we find that it is possible to produce highly non symmetric solutions, and even cases for which multiple bounces naturally occur. We also introduce a means of treating the shear in this category of models by quantizing in the Bianchi I minisuperpace.
The simplest possible bouncing quantum cosmological model
Peter, Patrick; Vitenti, Sandro D. P.
2016-06-01
We present and expand the simplest possible quantum cosmological bouncing model already discussed in previous works: the trajectory formulation of quantum mechanics applied to cosmology (through the Wheeler-De Witt equation) in the Friedmann-Lemaître-Robertson-Walker (FLRW) minisuperspace without spatial curvature. The initial conditions that were previously assumed were such that the wave function would not change its functional form but instead provide a dynamics to its parameters. Here, we consider a more general situation, in practice consisting of modified Gaussian wave functions, aiming at obtaining a nonsingular bounce from a contracting phase. Whereas previous works consistently obtain very symmetric bounces, we find that it is possible to produce highly non-symmetric solutions, and even cases for which multiple bounces naturally occur. We also introduce a means of treating the shear in this category of models by quantizing in the Bianchi I minisuperspace.
General Quantum Modeling of Combining Concepts: A Quantum Field Model in Fock Space
Aerts, Diederik
2007-01-01
We extend a quantum model in Hilbert space developed in Aerts (2007a) into a quantum field theoric model in Fock space for the modeling of the combination of concepts. Items and concepts are represented by vectors in Fock space and membership weights of items are modeled by quantum probabilities. We apply this theory to model the disjunction of concepts and show that the predictions of our theory for the membership weights of items regarding the disjunction of concepts match with great accuracy the complete set of results of an experiment conducted by Hampton (1988b). It are the quantum effects of interference and superposition of that are at the origin of the effects of overextension and underextension observed by Hampton as deviations from a classical use of the disjunction. It is essential for the perfect matches we obtain between the predictions of the quantum field model and Hampton's experimental data that items can be in superpositions of `different numbers states' which proves that the genuine structu...
Quantum Dynamics of the HMF Model
Plestid, Ryan; Mahon, Perry; O'Dell, Duncan
2016-01-01
We study the dynamics of the quantized Hamiltonian Mean Field (HMF) model assuming a gas of bosons in the large N limit. We characterize the full set of stationary states, and study the dynamics of the model numerically focussing on competition between classical and quantum effects. We make contact with the existing literature on the HMF model as a classical system, and stress universal features which can be inferred in the semi-classical limit.In particular we show that the characteristic ch...
Quantum error-correction failure distributions: Comparison of coherent and stochastic error models
Barnes, Jeff P.; Trout, Colin J.; Lucarelli, Dennis; Clader, B. D.
2017-06-01
We compare failure distributions of quantum error correction circuits for stochastic errors and coherent errors. We utilize a fully coherent simulation of a fault-tolerant quantum error correcting circuit for a d =3 Steane and surface code. We find that the output distributions are markedly different for the two error models, showing that no simple mapping between the two error models exists. Coherent errors create very broad and heavy-tailed failure distributions. This suggests that they are susceptible to outlier events and that mean statistics, such as pseudothreshold estimates, may not provide the key figure of merit. This provides further statistical insight into why coherent errors can be so harmful for quantum error correction. These output probability distributions may also provide a useful metric that can be utilized when optimizing quantum error correcting codes and decoding procedures for purely coherent errors.
Integer Set Compression and Statistical Modeling
DEFF Research Database (Denmark)
Larsson, N. Jesper
2014-01-01
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...... 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...
Statistical models and methods for reliability and survival analysis
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
The one-way quantum computer - a non-network model of quantum computation
Raussendorf, R; Briegel, H J; Raussendorf, Robert; Browne, Daniel E.; Briegel, Hans J.
2001-01-01
A one-way quantum computer works by only performing a sequence of one-qubit measurements on a particular entangled multi-qubit state, the cluster state. No non-local operations are required in the process of computation. Any quantum logic network can be simulated on the one-way quantum computer. On the other hand, the network model of quantum computation cannot explain all ways of processing quantum information possible with the one-way quantum computer. In this paper, two examples of the non-network character of the one-way quantum computer are given. First, circuits in the Clifford group can be performed in a single time step. Second, the realisation of a particular circuit --the bit-reversal gate-- on the one-way quantum computer has no network interpretation. (Submitted to J. Mod. Opt, Gdansk ESF QIT conference issue.)
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.
Exact infinite-time statistics of the Loschmidt echo for a quantum quench
Venuti, Lorenzo Campos; Santra, Siddhartha; Zanardi, Paolo
2011-01-01
The equilibration dynamics of a closed quantum system is encoded in the long-time distribution function of generic observables. In this paper 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, quasi-critical 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.
Quantum measurement as a driven phase transition: An exactly solvable model
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 con
Theodoropoulos, K.; Ntalaperas, D.; Petras, I.; Tsakalidis, A.; Konofaos, N.
2005-06-01
In this paper a quantum computer based on the recombination processes happening in semiconductor devices is presented. A "data element" and a "computational element" are derived based on Schokley-Read-Hall statistics and they can later be used in order to manifest a simple and known quantum algorithm. Such a paradigm is shown by the application of the proposed technology onto the Shor's period-finding algorithm.
Rank-based model selection for multiple ions quantum tomography
Guţă, Mădălin; Kypraios, Theodore; Dryden, Ian
2012-10-01
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 χ2 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.
Minimal model for spontaneous quantum synchronization
Benedetti, Claudia; Galve, Fernando; Mandarino, Antonio; Paris, Matteo G. A.; Zambrini, Roberta
2016-11-01
We show the emergence of spontaneous synchronization between a pair of detuned quantum oscillators within a harmonic network. Our model does not involve any nonlinearity, driving, or external dissipation, thus providing the simplest scenario for the occurrence of local coherent dynamics in an extended harmonic system. A sufficient condition for synchronization is established by building upon the Rayleigh normal mode approach to vibrational systems. Our results show that mechanisms favoring synchronization, even between oscillators that are not directly coupled to each other, are transient energy depletion and crosstalk. We also address the possible buildup of quantum correlations during synchronization and show that indeed entanglement may be generated in detuned systems, starting from uncorrelated states and without any direct coupling between the two oscillators.
A fully quantum model of Big Bang
Maydanyuk, Sergei P; Olkhovsky, Vladislav S
2013-01-01
In the paper the closed Friedmann-Robertson-Walker model with quantization in the presence of the positive cosmological constant and radiation is studied. For analysis of tunneling probability for birth of an asymptotically deSitter, inflationary Universe as a function of the radiation energy a new definition of a "free" wave propagating inside strong fields is proposed. On such a basis, tunneling boundary condition is corrected, penetrability and reflection concerning to the barrier are calculated in fully quantum stationary approach. For the first time non-zero interference between the incident and reflected waves has been taken into account which turns out to play important role inside cosmological potentials and could be explained by non-locality of barriers in quantum mechanics. Inside whole region of energy of radiation the tunneling probability for the birth of the inflationary Universe is found to be close to its value obtained in semiclassical approach. The reflection from the barrier is determined f...
Statistical Compressive Sensing of Gaussian Mixture Models
Yu, Guoshen
2010-01-01
A new framework of compressive sensing (CS), namely statistical compressive sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution and achieving accurate reconstruction on average, is introduced. For signals following a Gaussian distribution, with Gaussian or Bernoulli sensing matrices of O(k) measurements, considerably smaller than the O(k log(N/k)) required by conventional CS, where N is the signal dimension, and with an optimal decoder implemented with linear filtering, significantly faster than the pursuit decoders applied in conventional CS, the error of SCS is shown tightly upper bounded by a constant times the k-best term approximation error, with overwhelming probability. The failure probability is also significantly smaller than that of conventional CS. Stronger yet simpler results further show that for any sensing matrix, the error of Gaussian SCS is upper bounded by a constant times the k-best term approximation with probability one, and the ...
Comparison of Statistical Models for Regional Crop Trial Analysis
Institute of Scientific and Technical Information of China (English)
ZHANG Qun-yuan; KONG Fan-ling
2002-01-01
Based on the review and comparison of main statistical analysis models for estimating varietyenvironment cell means in regional crop trials, a new statistical model, LR-PCA composite model was proposed, and the predictive precision of these models were compared by cross validation of an example data. Results showed that the order of model precision was LR-PCA model ＞ AMMI model ＞ PCA model ＞ Treatment Means (TM) model ＞ Linear Regression (LR) model ＞ Additive Main Effects ANOVA model. The precision gain factor of LR-PCA model was 1.55, increasing by 8.4% compared with AMMI.
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...
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 primar
Exact diagonalization of quantum-spin models
Lin, H. Q.
1990-10-01
We have developed a technique to replace hashing in implementing the Lanczös method for exact diagonalization of quantum-spin models that enables us to carry out numerical studies on substantially larger lattices than previously studied. We describe the algorithm in detail and present results for the ground-state energy, the first-excited-state energy, and the spin-spin correlations on various finite lattices for spins S=1/2, 1, 3/2, and 2. Results for an infinite system are obtained by extrapolation. We also discuss the generalization of our method to other models.
Quantum dimer model for the pseudogap metal
Punk, Matthias; Allais, Andrea; Sachdev, Subir
2015-01-01
We propose a quantum dimer model for the metallic state of the hole-doped cuprates at low hole density, p. The Hilbert space is spanned by spinless, neutral, bosonic dimers and spin S=1/2, charge +e fermionic dimers. The model realizes a “fractionalized Fermi liquid” with no symmetry breaking and small hole pocket Fermi surfaces enclosing a total area determined by p. Exact diagonalization, on lattices of sizes up to 8×8, shows anisotropic quasiparticle residue around the pocket Fermi surfaces. We discuss the relationship to experiments. PMID:26195771
Quantum dimer model for the pseudogap metal.
Punk, Matthias; Allais, Andrea; Sachdev, Subir
2015-08-04
We propose a quantum dimer model for the metallic state of the hole-doped cuprates at low hole density, p. The Hilbert space is spanned by spinless, neutral, bosonic dimers and spin S = 1/2, charge +e fermionic dimers. The model realizes a "fractionalized Fermi liquid" with no symmetry breaking and small hole pocket Fermi surfaces enclosing a total area determined by p. Exact diagonalization, on lattices of sizes up to 8 × 8, shows anisotropic quasiparticle residue around the pocket Fermi surfaces. We discuss the relationship to experiments.
Cosmological constraints on non-standard inflationary quantum collapse models
Landau, Susana J; Sudarsky, Daniel
2011-01-01
We briefly review an important shortcoming --unearthed in previous works-- of the standard version of the inflationary model for the emergence of the seeds of cosmic structure. We consider here some consequences emerging from a proposal inspired on ideas of Penrose and Di\\'osi about a quantum-gravity induced reduction of the wave function, which has been put forward to address the shortcomings, arguing that its effect on the inflaton field is what can lead to the emergence of the seeds of cosmic structure. The proposal leads to a deviation of the primordial spectrum from the scale-invariant Harrison-Zel'dovich one, and consequently, to a different CMB power spectrum. We perform statistical analyses to test two quantum collapse schemes with recent data from the CMB, including the 7-yr release of WMAP and the matter power spectrum measured using LRGs by the Sloan Digital Sky Survey. Results from the statistical analyses indicate that several collapse models are compatible with CMB and LRG data, and establish co...
Quantum Computation and Non-Abelian Statistics in Chern-Simons-Higgs Theory
Brozeguini, J C
2013-01-01
We naturally obtain the NOT and CNOT logic gates, which are key pieces of quantum computing algorithms, in the framework of the non-Abelian Chern-Simons-Higgs theory in two spatial dimensions. For that, we consider the anyonic quantum vortex topological excitations occurring in this system and show that self-adjoint (Majorana-like) combinations of these vortices and anti-vortices have in general non-Abelian statistics. The associated unitary monodromy braiding matrices become the required logic gates in the special case when the vortex spin is $s=1/4$. We explicitly construct the vortex field operators, show that they carry both magnetic flux and charge and obtain their euclidean correlation functions by using the method of quantization of topological excitations, which is based on the order-disorder duality. These correlators are in general multivalued, the number of sheets being determined by the vortex spin. This, by its turn, is proportional to the vacuum expectation value of the Higgs field and therefore...
Hasegawa, Hiroshi
1997-02-01
The differential-geometric formulation of statistics (the so-called information geometry) concerning the structure of a smooth manifold in the parameter space Θ of classical probabilities, S = { p(·, θ), θɛΘ}, discussed by Amari, is extended to the same manifold but for quantum states (density matrices), S = { ϱ( θ); θɛΘ} in N × N matrix algebras. This is done by introducing an n-tuple of tangent vectors { δ} ni = 1 in analogy to the classical ones { ∂i} ni = 1 . On this basis, a special problem of quantum information geometry is treated; namely, the analysis of the exponential and the mixture families defined, respectively, as (e) ϱ(θ) = exp(θ i A i - ψ(θ)). θ ɛ Θ = R n. A i ɛ B s(H N) . (m) ϱ(θ) = θ iA i + θ 0 A 0. θ ɛ Θ = (0,1) n + 1. limit∑i=0nθ i=1. A i ɛ B +(H N) Tr A i = 1 (the tensorial summation convention for repeated indices is used). We prove some of the basic theorems known in the classical information geometry by extending the formulation to a non-commutative smooth manifold. We establish the existence of a pair of dual affine coordinate systems in (e) or (m) and a projection theorem in order to ensure the Cramer-Rao inequality and an identification of the efficient estimator.
Quantum Statistical Behaviors of Interaction of an Atomic Bose-Einstein Condensate with Laser
Institute of Scientific and Technical Information of China (English)
YU Zhao-Xian; JIAO Zhi-Yong
2001-01-01
We have investigated quantum statistical behaviors of photons and atoms in interaction of an atomic Bose Einstein condensate with quantized laser field. When the quantized laser field is initially prepared in a superposition state which exhibits holes in its photon-number distribution, while the atomic field is initially in a Fock state, it is found that there is energy exchange between photons and atoms. For the input and output states, the photons and atoms may exhibit the sub-Poissonian distribution. The input and output laser fields may exhibit quadrature squeezing, but for the atomic field, only the output state exhibits quadrature squeezing. It is shown that there exists the violation of the Cauchy-Schwartz inequality, which means that the correlation between photons and atoms is nonclassical.``
Cafaro, C
2008-01-01
In this paper, we review our novel information geometrodynamical approach to chaos (IGAC) on curved statistical manifolds and we emphasize the usefulness of our information-geometrodynamical entropy (IGE) as an indicator of chaoticity in a simple application. Furthermore, knowing that integrable and chaotic quantum antiferromagnetic Ising chains are characterized by asymptotic logarithmic and linear growths of their operator space entanglement entropies, respectively, we apply our IGAC to present an alternative characterization of such systems. Remarkably, we show that in the former case the IGE exhibits asymptotic logarithmic growth while in the latter case the IGE exhibits asymptotic linear growth. At this stage of its development, IGAC remains an ambitious unifying information-geometric theoretical construct for the study of chaotic dynamics with several unsolved problems. However, based on our recent findings, we believe it could provide an interesting, innovative and potentially powerful way to study and...
Physics colloquium: Single-electron counting in quantum metrology and in statistical mechanics
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...
Statistical models of shape optimisation and evaluation
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.
Quantum Rabi model in the Brillouin zone with ultracold atoms
Felicetti, Simone; Rico, Enrique; Sabin, Carlos; Ockenfels, Till; Koch, Johannes; Leder, Martin; Grossert, Christopher; Weitz, Martin; Solano, Enrique
2017-01-01
The quantum Rabi model describes the interaction between a two-level quantum system and a single bosonic mode. We propose a method to perform a quantum simulation of the quantum Rabi model, introducing an implementation of the two-level system provided by the occupation of Bloch bands in the first Brillouin zone by ultracold atoms in tailored optical lattices. The effective qubit interacts with a quantum harmonic oscillator implemented in an optical dipole trap. Our realistic proposal allows one to experimentally investigate the quantum Rabi model for extreme parameter regimes, which are not achievable with natural light-matter interactions. When the simulated wave function exceeds the validity region of the simulation, we identify a generalized version of the quantum Rabi model in a periodic phase space.
de Martini, Francesco; Santamato, Enrico
2016-04-01
The traditional standard theory of quantum mechanics is unable to solve the spin-statistics problem, i.e. to justify the utterly important “Pauli Exclusion Principle” but by the adoption of the complex standard relativistic quantum field theory. In a recent paper [E. Santamato and F. D. De Martini, Found. Phys. 45 (2015) 858] we presented a complete proof of the spin-statistics problem in the nonrelativistic approximation on the basis of the “Conformal Quantum Geometrodynamics” (CQG). In this paper, by the same theory, the proof of the spin-statistics theorem (SST) is extended to the relativistic domain in the scenario of curved spacetime. No relativistic quantum field operators are used in the present proof and the particle exchange properties are drawn from rotational invariance rather than from Lorentz invariance. Our relativistic approach allows to formulate a manifestly step-by-step Weyl gauge invariant theory and to emphasize some fundamental aspects of group theory in the demonstration. As in the nonrelativistic case, we find once more that the “intrinsic helicity” of the elementary particles enters naturally into play. It is therefore this property, not considered in the standard quantum mechanics (SQM), which determines the correct spin-statistics connection observed in Nature.
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.
Statistics-based investigation on typhoon transition modeling
DEFF Research Database (Denmark)
Zhang, Shuoyun; Nishijima, Kazuyoshi
and the seasonality are taken into account by developing the models for different spatial grids and seasons separately. An appropriate size of spatial grids is investigated. The statistical characteristics of the random residual terms in the models are also examined. Finally, Monte Carlo simulations are performed......The present study revisits the statistical modeling of typhoon transition. The objective of the study is to provide insights on plausible statistical typhoon transition models based on extensive statistical analysis. First, the correlation structures of the typhoon transition are estimated in terms...
The computer-based model of quantum measurements
Sevastianov, L. A.; Zorin, A. V.
2017-07-01
Quantum theory of measurements is an extremely important part of quantum mechanics. Currently perturbations by quantum measurements of observable quantities of atomic systems are rarely taken into account in computing algorithms and calculations. In the previous studies of the authors, constructive model of quantum measurements has been developed and implemented in the form of symbolic and numerical calculations for the hydrogen-like atoms. This work describes a generalization of these results to the alkali metal atoms.
Statistical image processing and multidimensional modeling
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
Statistical Tests for Mixed Linear Models
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
Low-Energy Effective Theories of Quantum Link and Quantum Spin Models
Schlittgen, B
2001-01-01
Quantum spin and quantum link models provide an unconventional regularization of field theory in which classical fields arise via dimensional reduction of discrete variables. This D-theory regularization leads to the same continuum theories as the conventional approach. We show this by deriving the low-energy effective Lagrangians of D-theory models using coherent state path integral techniques. We illustrate our method for the $(2+1)$-d Heisenberg quantum spin model which is the D-theory regularization of the 2-d O(3) model. Similarly, we prove that in the continuum limit a $(2+1)$-d quantum spin model with $SU(N)_L\\times SU(N)_R\\times U(1)_{L=R}$ symmetry is equivalent to the 2-d principal chiral model. Finally, we show that $(4+1)$-d SU(N) quantum link models reduce to ordinary 4-d Yang-Mills theory.
Are quantum-mechanical-like models possible, or necessary, outside quantum physics?
Plotnitsky, Arkady
2014-12-01
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.
On Complexity of the Quantum Ising Model
Bravyi, Sergey; Hastings, Matthew
2017-01-01
We study complexity of several problems related to the Transverse field Ising Model (TIM). First, we consider the problem of estimating the ground state energy known as the Local Hamiltonian Problem (LHP). It is shown that the LHP for TIM on degree-3 graphs is equivalent modulo polynomial reductions to the LHP for general k-local `stoquastic' Hamiltonians with any constant {k ≥ 2}. This result implies that estimating the ground state energy of TIM on degree-3 graphs is a complete problem for the complexity class {StoqMA} —an extension of the classical class {MA}. As a corollary, we complete the complexity classification of 2-local Hamiltonians with a fixed set of interactions proposed recently by Cubitt and Montanaro. Secondly, we study quantum annealing algorithms for finding ground states of classical spin Hamiltonians associated with hard optimization problems. We prove that the quantum annealing with TIM Hamiltonians is equivalent modulo polynomial reductions to the quantum annealing with a certain subclass of k-local stoquastic Hamiltonians. This subclass includes all Hamiltonians representable as a sum of a k-local diagonal Hamiltonian and a 2-local stoquastic Hamiltonian.
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
A Toy Model of Quantum Electrodynamics in (1 + 1) Dimensions
Boozer, A. D.
2008-01-01
We present a toy model of quantum electrodynamics (QED) in (1 + 1) dimensions. The QED model is much simpler than QED in (3 + 1) dimensions but exhibits many of the same physical phenomena, and serves as a pedagogical introduction to both QED and quantum field theory in general. We show how the QED model can be derived by quantizing a toy model of…
Multivariate statistical modelling based on generalized linear models
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...
Blinking in quantum dots: The origin of the grey state and power law statistics
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.
Statistical Model of Exotic Rotational Correlations in Emergent Space-Time
Hogan, Craig; Richardson, Jonathan
2016-01-01
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 s...
12th Workshop on Stochastic Models, Statistics and Their Applications
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.
Equilibrium statistical mechanics
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
Functional summary statistics for the Johnson-Mehl model
DEFF Research Database (Denmark)
Møller, Jesper; Ghorbani, Mohammad
of functional summary statistics. This paper therefore invents four functional summary statistics adapted to the Johnson-Mehl model, with two of them based on the second-order properties and the other two on the nuclei-boundary distances for the associated Johnson-Mehl tessellation. The functional summary...... statistics theoretical properties are investigated, non-parametric estimators are suggested, and their usefulness for model checking is examined in a simulation study. The functional summary statistics are also used for checking fitted parametric Johnson-Mehl models for a neurotransmitters dataset....
Decoding Beta-Decay Systematics: A Global Statistical Model for Beta^- Halflives
Costiris, N J; Gernoth, K A; Clark, J W
2008-01-01
Statistical modeling of nuclear data provides a novel approach to nuclear systematics complementary to established theoretical and phenomenological approaches based on quantum theory. Continuing previous studies in which global statistical modeling is pursued within the general framework of machine learning theory, we implement advances in training algorithms designed to improved generalization, in application to the problem of reproducing and predicting the halflives of nuclear ground states that decay 100% by the beta^- mode. More specifically, fully-connected, multilayer feedforward artificial neural network models are developed using the Levenberg-Marquardt optimization algorithm together with Bayesian regularization and cross-validation. The predictive performance of models emerging from extensive computer experiments is compared with that of traditional microscopic and phenomenological models as well as with the performance of other learning systems, including earlier neural network models as well as th...
An Electrostatic Model of Split-Gate Quantum Wires
Sun, Yinlong; Kirczenow, George; Sachrajda, Andrew. S.; Feng, Yan
1995-01-01
We present a theoretical model of split-gate quantum wires that are fabricated from GaAs-AlGaAs heterostructures. The model is built on the physical properties of donors and of semiconductor surfaces, and considerations of equilibrium in such systems. Based on the features of this model, we have studied different ionization regimes of quantum wires, provided a method to evaluate the shallow donor density, and calculated the depletion and pinchoff voltages of quantum wires both before and afte...
Statistical modeling and recognition of surgical workflow.
Padoy, Nicolas; Blum, Tobias; Ahmadi, Seyed-Ahmad; Feussner, Hubertus; Berger, Marie-Odile; Navab, Nassir
2012-04-01
In this paper, we contribute to the development of context-aware operating rooms by introducing a novel approach to modeling and monitoring the workflow of surgical interventions. We first propose a new representation of interventions in terms of multidimensional time-series formed by synchronized signals acquired over time. We then introduce methods based on Dynamic Time Warping and Hidden Markov Models to analyze and process this data. This results in workflow models combining low-level signals with high-level information such as predefined phases, which can be used to detect actions and trigger an event. Two methods are presented to train these models, using either fully or partially labeled training surgeries. Results are given based on tool usage recordings from sixteen laparoscopic cholecystectomies performed by several surgeons.
Statistical modelling of fine red wine production
María Rosa Castro; Marcelo Eduardo Echegaray; Rosa Ana Rodríguez; Stella Maris Udaquiola
2010-01-01
Producing wine is a very important economic activity in the province of San Juan in Argentina; it is therefore most important to predict production regarding the quantity of raw material needed. This work was aimed at obtaining a model relating kilograms of crushed grape to the litres of wine so produced. Such model will be used for predicting precise future values and confidence intervals for determined quantities of crushed grapes. Data from a vineyard in the province of San Juan was ...
On the Logical Development of Statistical Models.
1983-12-01
parameters t2 . Type I models include scalar and vectorial probability distributions. Usually, the noise has an expected value equal to zero, so that...qualitative variables. As might be expected, the vectorial representation of all these types of models lagged behind the scaler forms. The first...1978). "Modelos con parametros variables en el analisis de series temporales" Questiio, 4, 2, 75-87. [25] Seal, H. L. (1967). "The historical
Book review: Statistical Analysis and Modelling of Spatial Point Patterns
DEFF Research Database (Denmark)
Møller, Jesper
2009-01-01
Statistical Analysis and Modelling of Spatial Point Patterns by J. Illian, A. Penttinen, H. Stoyan and D. Stoyan. Wiley (2008), ISBN 9780470014912......Statistical Analysis and Modelling of Spatial Point Patterns by J. Illian, A. Penttinen, H. Stoyan and D. Stoyan. Wiley (2008), ISBN 9780470014912...
Rabi model as a quantum coherent heat engine: From quantum biology to superconducting circuits
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.
Quantum Aspects of the GP Model.
Wood, William Robert
In this thesis, the possibility that the description of Nature provided by the theories of general relativity and quantum mechanics may be made more complete by incorporating the ideas of the causal interpretation of quantum mechanics into a conformally invariant theory in Weyl space is investigated. The unified theory of gravitation and electromagnetism provided by the Gregorash-Papini (GP) model is shown to support both the particle and wave aspects required in the causal interpretation, as well as a nonlinear Klein-Gordon wave equation. The Gauss-Mainardi-Codazzi formalism is developed in Weyl geometry and then used to construct a particle model in terms of a spherically symmetric thin shell with a scalar-field-induced surface stress-energy tensor. By breaking the interior Weyl invariance at the microscopic scale, a new means by which Weyl's geometric interpretation of the exterior electromagnetic field may be reconciled with atomic standards of length becomes possible. In addition, the properties of the resulting interior anti-de Sitter space may prove to play an important role in accounting for the nonlocal effects that are necessarily present in any causal interpretation. The particle, which is represented by the thin shell, is embedded in the exterior Madelung fluid of the GP model such that de Broglie's guidance principle is satisfied. It is argued that a proper analysis of the guidance mechanism hypothesized in the causal interpretation is possible only in a geometrical formulation. The possibility that the causal theory that is developed in Weyl space requires a maximal acceleration is also investigated. A limiting acceleration has recently been shown to arise in other theories when aspects of quantum mechanics, such as the uncertainty relations, are employed. A controversial derivation based on the time-energy uncertainty relation is clarified and two new arguments for a maximal acceleration are presented. Finally, the demonstration that the causal
A statistical model of facial attractiveness.
Said, Christopher P; Todorov, Alexander
2011-09-01
Previous research has identified facial averageness and sexual dimorphism as important factors in facial attractiveness. The averageness and sexual dimorphism accounts provide important first steps in understanding what makes faces attractive, and should be valued for their parsimony. However, we show that they explain relatively little of the variance in facial attractiveness, particularly for male faces. As an alternative to these accounts, we built a regression model that defines attractiveness as a function of a face's position in a multidimensional face space. The model provides much more predictive power than the averageness and sexual dimorphism accounts and reveals previously unreported components of attractiveness. The model shows that averageness is attractive in some dimensions but not in others and resolves previous contradictory reports about the effects of sexual dimorphism on the attractiveness of male faces.
Fluctuations of offshore wind generation: Statistical modelling
DEFF Research Database (Denmark)
Pinson, Pierre; Christensen, Lasse E.A.; Madsen, Henrik
2007-01-01
The magnitude of power fluctuations at large offshore wind farms has a significant impact on the control and management strategies of their power output. If focusing on the minute scale, one observes successive periods with smaller and larger power fluctuations. It seems that different regimes...... production averaged at a 1, 5, and 10-minute rate. The exercise consists in one-step ahead forecasting of these time-series with the various regime-switching models. It is shown that the MSAR model, for which the succession of regimes is represented by a hidden Markov chain, significantly outperforms...
Statistical modelling of traffic safety development
DEFF Research Database (Denmark)
Christens, Peter
2004-01-01
: - Statistisk modellering af trafik uheld, Trafikdage på Ålborg Univeristet, 2001. - Sociale karakteristika hos trafikofre, Danish Transport Research Institute, 2001. - Models for traffic accidents, FERSI Young Researchers' Seminar, 2001. - Evaluation of the Danish Automatic Mobile Speed Camera Project...... 2000 dræbte trafikuheld over 40.000 i EU og skadede over 1.7 millioner. I Danmark i 2001 var der 6861 politirapporteret trafikuheld med tilskadekomst. De resulterede i 4519 lettere tilskadekomne, 3946 alvorligt tilskadekomne og 431 dræbte. Det generelle formål med dette forskningsarbejde er at forbedre...
Exponential order statistic models of software reliability growth
Miller, D. R.
1986-01-01
Failure times of a software reliability growth process are modeled as order statistics of independent, nonidentically distributed exponential random variables. The Jelinsky-Moranda, Goel-Okumoto, Littlewood, Musa-Okumoto Logarithmic, and Power Law models are all special cases of Exponential Order Statistic Models, but there are many additional examples also. Various characterizations, properties and examples of this class of models are developed and presented.
Spin foam models for quantum gravity
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
Statistical Modeling of Large-Scale Scientific Simulation Data
Energy Technology Data Exchange (ETDEWEB)
Eliassi-Rad, T; Baldwin, C; Abdulla, G; Critchlow, T
2003-11-15
With the advent of massively parallel computer systems, scientists are now able to simulate complex phenomena (e.g., explosions of a stars). Such scientific simulations typically generate large-scale data sets over the spatio-temporal space. Unfortunately, the sheer sizes of the generated data sets make efficient exploration of them impossible. Constructing queriable statistical models is an essential step in helping scientists glean new insight from their computer simulations. We define queriable statistical models to be descriptive statistics that (1) summarize and describe the data within a user-defined modeling error, and (2) are able to answer complex range-based queries over the spatiotemporal dimensions. In this chapter, we describe systems that build queriable statistical models for large-scale scientific simulation data sets. In particular, we present our Ad-hoc Queries for Simulation (AQSim) infrastructure, which reduces the data storage requirements and query access times by (1) creating and storing queriable statistical models of the data at multiple resolutions, and (2) evaluating queries on these models of the data instead of the entire data set. Within AQSim, we focus on three simple but effective statistical modeling techniques. AQSim's first modeling technique (called univariate mean modeler) computes the ''true'' (unbiased) mean of systematic partitions of the data. AQSim's second statistical modeling technique (called univariate goodness-of-fit modeler) uses the Andersen-Darling goodness-of-fit method on systematic partitions of the data. Finally, AQSim's third statistical modeling technique (called multivariate clusterer) utilizes the cosine similarity measure to cluster the data into similar groups. Our experimental evaluations on several scientific simulation data sets illustrate the value of using these statistical models on large-scale simulation data sets.
Links to sources of cancer-related statistics, including the Surveillance, Epidemiology and End Results (SEER) Program, SEER-Medicare datasets, cancer survivor prevalence data, and the Cancer Trends Progress Report.
Advanced data analysis in neuroscience integrating statistical and computational models
Durstewitz, Daniel
2017-01-01
This book is intended for use in advanced graduate courses in statistics / machine learning, as well as for all experimental neuroscientists seeking to understand statistical methods at a deeper level, and theoretical neuroscientists with a limited background in statistics. It reviews almost all areas of applied statistics, from basic statistical estimation and test theory, linear and nonlinear approaches for regression and classification, to model selection and methods for dimensionality reduction, density estimation and unsupervised clustering. Its focus, however, is linear and nonlinear time series analysis from a dynamical systems perspective, based on which it aims to convey an understanding also of the dynamical mechanisms that could have generated observed time series. Further, it integrates computational modeling of behavioral and neural dynamics with statistical estimation and hypothesis testing. This way computational models in neuroscience are not only explanat ory frameworks, but become powerfu...
Statistical Model of the 3-D Braided Composites Strength
Institute of Scientific and Technical Information of China (English)
XIAO Laiyuan; ZUO Weiwei; CAI Ganwei; LIAO Daoxun
2007-01-01
Based on the statistical model for the tensile statistical strength of unidirectional composite materials and the stress analysis of 3-D braided composites, a new method is proposed to calculate the tensile statistical strength of the 3-D braided composites. With this method, the strength of 3-D braided composites can be calculated with very large accuracy, and the statistical parameters of 3-D braided composites can be determined. The numerical result shows that the tensile statistical strength of 3-D braided composites can be predicted using this method.
Quantum Brownian motion model for the stock market
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.
Eigenfunction statistics in the localized Anderson model
Killip, R
2006-01-01
We consider the localized region of the Anderson model and study the distribution of eigenfunctions simultaneously in space and energy. In a natural scaling limit, we prove convergence to a Poisson process. This provides a counterpoint to recent work, which proves repulsion of the localization centres in a subtly different regime.
Statistical modelling of fine red wine production
Directory of Open Access Journals (Sweden)
María Rosa Castro
2010-05-01
Full Text Available Producing wine is a very important economic activity in the province of San Juan in Argentina; it is therefore most important to predict production regarding the quantity of raw material needed. This work was aimed at obtaining a model relating kilograms of crushed grape to the litres of wine so produced. Such model will be used for predicting precise future values and confidence intervals for determined quantities of crushed grapes. Data from a vineyard in the province of San Juan was thus used in this work. The sampling coefficient of correlation was calculated and a dispersion diagram was then constructed; this indicated a li- neal relationship between the litres of wine obtained and the kilograms of crushed grape. Two lineal models were then adopted and variance analysis was carried out because the data came from normal populations having the same variance. The most appropriate model was obtained from this analysis; it was validated with experimental values, a good approach being obtained.
Structured Statistical Models of Inductive Reasoning
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…
Probing NWP model deficiencies by statistical postprocessing
DEFF Research Database (Denmark)
Rosgaard, Martin Haubjerg; Nielsen, Henrik Aalborg; Nielsen, Torben S.
2016-01-01
numerical weather prediction (NWP) model generating global weather forecasts four times daily, with numerous users worldwide. The analysis is based on two years of hourly wind speed time series measured at three locations; offshore, in coastal and flat terrain, and inland in complex topography, respectively...
Energy Technology Data Exchange (ETDEWEB)
Madsen, Marianne Sloth [Department of Chemistry, H.C. Orsted Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen O (Denmark); Danish Meteorological Institute, Lyngbyvej 100, DK-2100 Copenhagen O (Denmark)], E-mail: msm@dmi.dk; Gross, Allan [Department of Chemistry, H.C. Orsted Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen O (Denmark); Danish Meteorological Institute, Lyngbyvej 100, DK-2100 Copenhagen O (Denmark); Falsig, Hanne [Department of Chemistry, H.C. Orsted Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen O (Denmark); Kongsted, Jacob [Department of Theoretical Chemistry, Chemical Center, University of Lund, P.O. Box 124, S-22100 Lund (Sweden); Osted, Anders; Mikkelsen, Kurt V. [Department of Chemistry, H.C. Orsted Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen O (Denmark); Christiansen, Ove [Department of Chemistry, University of Aarhus, Langelandsgade 140, DK-8000 Aarhus C (Denmark)
2008-06-02
We present a combined quantum mechanics/molecular mechanics and quantum statistical investigation of the interactions between a molecule (SO{sub 2}) and an aerosol particle including rate constants for the uptake process. A coupled cluster/molecular mechanics method including explicit polarization is used along with a quantum statistical method for calculating sticking coefficients. The importance of the polarization of the classical subsystem (the aerosol particle), the size of the classical subsystem and the size of one-electron basis sets are studied. The interaction energy is divided into van der Waals, electrostatic and polarization contributions. Relevant binding sites for the evaluation of the sticking coefficient are identified. These are classified into three groups according to the strength of the molecule-aerosol particle interaction energy. The identification of binding sites provides relevant information used in the quantum statistical method and thereby knowledge of the magnitude of the sticking coefficients for the different binding sites along with the total rates for the uptake processes between the aerosol particle and the SO{sub 2} molecule.
Spectral classification of coupling regimes in the quantum Rabi model
Rossatto, Daniel Z.; Villas-Bôas, Celso J.; Sanz, Mikel; Solano, Enrique
2017-07-01
The quantum Rabi model is in the scientific spotlight due to the recent theoretical and experimental progress. Nevertheless, a full-fledged classification of its coupling regimes remains as a relevant open question. We propose a spectral classification dividing the coupling regimes into three regions based on the validity of perturbative criteria on the quantum Rabi model, which allows us the use of exactly solvable effective Hamiltonians. These coupling regimes are (i) the perturbative ultrastrong coupling regime which comprises the Jaynes-Cummings model, (ii) a region where nonperturbative ultrastrong and nonperturbative deep strong coupling regimes coexist, and (iii) the perturbative deep strong coupling regime. We show that this spectral classification depends not only on the ratio between the coupling strength and the natural frequencies of the unperturbed parts, but also on the energy to which the system can access. These regimes additionally discriminate the completely different behaviors of several static physical properties, namely the total number of excitations, the photon statistics of the field, and the cavity-qubit entanglement. Finally, we explain the dynamical properties which are traditionally associated with the deep strong coupling regime, such as the collapses and revivals of the state population, in the frame of the proposed spectral classification.
A microscopic model for quantum optomechanics
Sinha, Kanupriya
We study a microscopic model, the Mirror-Oscillator-Field (MOF) model proposed in [1], for describing optomechanical interactions. In contrast with the conventional approach where the mirror-field interaction is understood as arising from the radiation pressure of an optical field inducing the motion of the mirror's CoM, the MOF model incorporates the dynamics of the internal degrees of freedom of the mirror that couple to the optical field directly. Considering the mirror's internal and mechanical degrees of freedom as two separate degrees of freedom we derive the optomechanical properties of the coupled mirror and field system. The major advantage in this approach is that it provides a self-consistent treatment of the three relevant subsystems (the mirror's motion, its internal degrees of freedom and the field) including their back-actions on each other, thereby giving a more accurate account of the coupled internal and external dynamics. The optical and the mechanical properties of a mirror arising from its dynamical interaction with the field are obtained without imposing any boundary conditions on the field additionally, as is done in the conventional way. We find that our results agree with those from the boundary condition approach in the appropriate limits and more generally the model provides a framework within which one can study optomechanical elements with different internal structures and mechanical properties, which makes it suited for studying hybrid systems. Considering the quantum dynamics of the coupled subsystems we look at the entanglement between the mirror's motion and the field, showing that the internal degrees of the mirror, in the appropriate parameter regimes, can act as a means to coherently transfer quantum correlations between the field and the mechanics thus leading to a larger optomechanical entanglement. We then use the MOF model to study the entanglement between the motion of an atom and a field for the setup in [95] and find a
Modeling quantum fluid dynamics at nonzero temperatures
Berloff, Natalia G.; Brachet, Marc; Proukakis, Nick P.
2014-03-01
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.
Molecular model with quantum mechanical bonding information.
Bohórquez, Hugo J; Boyd, Russell J; Matta, Chérif F
2011-11-17
The molecular structure can be defined quantum mechanically thanks to the theory of atoms in molecules. Here, we report a new molecular model that reflects quantum mechanical properties of the chemical bonds. This graphical representation of molecules is based on the topology of the electron density at the critical points. The eigenvalues of the Hessian are used for depicting the critical points three-dimensionally. The bond path linking two atoms has a thickness that is proportional to the electron density at the bond critical point. The nuclei are represented according to the experimentally determined atomic radii. The resulting molecular structures are similar to the traditional ball and stick ones, with the difference that in this model each object included in the plot provides topological information about the atoms and bonding interactions. As a result, the character and intensity of any given interatomic interaction can be identified by visual inspection, including the noncovalent ones. Because similar bonding interactions have similar plots, this tool permits the visualization of chemical bond transferability, revealing the presence of functional groups in large molecules.
Mathematical model I. Electron and quantum mechanics
Gadre, Nitin Ramchandra
2011-03-01
The basic particle electron obeys various theories like electrodynamics, quantum mechanics and special relativity. Particle under different experimental conditions behaves differently, allowing us to observe different characteristics which become basis for these theories. In this paper, we have made an attempt to suggest a classical picture by studying the requirements of these three modern theories. The basic presumption is: There must be certain structural characteristics in a particle like electron which make it obey postulates of modern theories. As it is `difficult' to find structure of electron experimentally, we make a mathematical attempt. For a classical approach, we require well defined systems and we have studied a system with two charged particles, proton and electron in a hydrogen atom. An attempt has been made to give a model to describe electron as seen by the proton. We then discuss how the model can satisfy the requirements of the three modern theories in a classical manner. The paper discusses basic aspects of relativity and electrodynamics. However the focus of the paper is on quantum mechanics.
Mathematical model I. Electron and quantum mechanics
Directory of Open Access Journals (Sweden)
Nitin Ramchandra Gadre
2011-03-01
Full Text Available The basic particle electron obeys various theories like electrodynamics, quantum mechanics and special relativity. Particle under different experimental conditions behaves differently, allowing us to observe different characteristics which become basis for these theories. In this paper, we have made an attempt to suggest a classical picture by studying the requirements of these three modern theories. The basic presumption is: There must be certain structural characteristics in a particle like electron which make it obey postulates of modern theories. As it is ‘difficult’ to find structure of electron experimentally, we make a mathematical attempt. For a classical approach, we require well defined systems and we have studied a system with two charged particles, proton and electron in a hydrogen atom. An attempt has been made to give a model to describe electron as seen by the proton. We then discuss how the model can satisfy the requirements of the three modern theories in a classical manner. The paper discusses basic aspects of relativity and electrodynamics. However the focus of the paper is on quantum mechanics.
Network Data: Statistical Theory and New Models
2016-02-17
Using AERONET DRAGON Campaign Data, IEEE Transactions on Geoscience and Remote Sensing, (08 2015): 0. doi: 10.1109/TGRS.2015.2395722 Geoffrey...are not viable, i.e. the fruit fly dies after the knock-out of the gene. Further examination of the ftz stained embryos indicates that the lack of...our approach for spatial gene expression analysis for early stage fruit fly embryos, we are in a process to extend it to model later stage gene
Non-Canonical Statistics of a Spin-Boson Model: Theory and Exact Monte-Carlo Simulations
Lee, Chee Kong; Gong, Jiangbin
2012-01-01
Equilibrium canonical distribution in statistical mechanics assumes weak system-bath coupling (SBC). In real physical situations this assumption can be invalid and equilibrium quantum statistics of the system may be non-canonical. By exploiting both polaron transformation and perturbation theory in a spin-boson model, an analytical treatment is advocated to study non-canonical statistics of a two-level system at arbitrary temperature and for arbitrary SBC strength, yielding theoretical results in agreement with exact Monte-Carlo simulations. In particular, the eigen-representation of system's reduced density matrix is used to quantify non-canonical statistics as well as the quantumness of the open system. For example, it is found that irrespective of SBC strength, non-canonical statistics enhances as temperature decreases but vanishes at high temperature.
Modeling fluid dynamics on type II quantum computers
Scoville, James; Weeks, David; Yepez, Jeffrey
2006-03-01
A quantum algorithm is presented for modeling the time evolution of density and flow fields governed by classical equations, such as the diffusion equation, the nonlinear Burgers equation, and the damped wave equation. The algorithm is intended to run on a type-II quantum computer, a parallel quantum computer consisting of a lattice of small type I quantum computers undergoing unitary evolution and interacting via information interchanges represented by an orthogonal matrices. Information is effectively transferred between adjacent quantum computers over classical communications channels because of controlled state demolition following local quantum mechanical qubit-qubit interactions within each quantum computer. The type-II quantum algorithm presented in this paper describes a methodology for generating quantum logic operations as a generalization of classical operations associated with finite-point group symmetries. The quantum mechanical evolution of multiple qubits within each node is described. Presented is a proof that the parallel quantum system obeys a finite-difference quantum Boltzman equation at the mesoscopic scale, leading in turn to various classical linear and nonlinear effective field theories at the macroscopic scale depending on the details of the local qubit-qubit interactions.
Simple Quantum Model of Learning Explains the Yerkes-Dodson Law in Psychology
Vol, E D
2012-01-01
We propose the simple model of learning based on which we derive and explain the Yerkes-Dodson law - one of the oldest laws of experimental psychology. The approach uses some ideas of quantum theory of open systems (QTOS) and develops the method of statistical description of psychological systems that was proposed by author earlier.
S-matrix Fluctuations in a model with Classical Diffusion and Quantum Localization
Borgonovi, F; Borgonovi, Fausto; Guarneri, Italo
1993-01-01
Abstract: The statistics of S-matrix fluctuations are numerically investigated on a model for irregular quantum scattering in which a classical chaotic diffusion takes place within the interaction region. Agreement with various random-matrix theoretic predictions is discussed in the various regimes (ballistic, diffusive, localized).
Behavioral and Statistical Models of Educational Inequality
DEFF Research Database (Denmark)
Holm, Anders; Breen, Richard
2016-01-01
This article addresses the question of how students and their families make educational decisions. We describe three types of behavioral model that might underlie decision-making, and we show that they have consequences for what decisions are made. Our study, thus, has policy implications if we...... wish to encourage students and their families to make better educational choices. We also establish the conditions under which empirical analysis can distinguish between the three sorts of decision-making, and we illustrate our arguments using data from the National Educational Longitudinal Study....
Behavioral and Statistical Models of Educational Inequality
DEFF Research Database (Denmark)
Holm, Anders; Breen, Richard
2016-01-01
This paper addresses the question of how students and their families make educational decisions. We describe three types of behavioral model that might underlie decision-making and we show that they have consequences for what decisions are made. Our study thus has policy implications if we wish...... to encourage students and their families to make better educational choices. We also establish the conditions under which empirical analysis can distinguish between the three sorts of decision-making and we illustrate our arguments using data from the National Educational Longitudinal Study....
Quantum monadology: a consistent world model for consciousness and physics.
Nakagomi, Teruaki
2003-04-01
The NL world model presented in the previous paper is embodied by use of relativistic quantum mechanics, which reveals the significance of the reduction of quantum states and the relativity principle, and locates consciousness and the concept of flowing time consistently in physics. This model provides a consistent framework to solve apparent incompatibilities between consciousness (as our interior experience) and matter (as described by quantum mechanics and relativity theory). Does matter have an inside? What is the flowing time now? Does physics allow the indeterminism by volition? The problem of quantum measurement is also resolved in this model.
Loop quantum cosmology of Bianchi type IX models
Wilson-Ewing, Edward
2010-01-01
The loop quantum cosmology "improved dynamics" of the Bianchi type IX model are studied. The action of the Hamiltonian constraint operator is obtained via techniques developed for the Bianchi type I and type II models, no new input is required. It is shown that the big bang and big crunch singularities are resolved by quantum gravity effects. We also present the effective equations which provide modifications to the classical equations of motion due to quantum geometry effects.
Loop quantum cosmology of Bianchi type IX models
Wilson-Ewing, Edward
2010-08-01
The loop quantum cosmology “improved dynamics” of the Bianchi type IX model are studied. The action of the Hamiltonian constraint operator is obtained via techniques developed for the Bianchi type I and type II models, no new input is required. It is shown that the big bang and big crunch singularities are resolved by quantum gravity effects. We also present effective equations which provide quantum geometry corrections to the classical equations of motion.
Statistical modelling in biostatistics and bioinformatics selected papers
Peng, Defen
2014-01-01
This book presents selected papers on statistical model development related mainly to the fields of Biostatistics and Bioinformatics. The coverage of the material falls squarely into the following categories: (a) Survival analysis and multivariate survival analysis, (b) Time series and longitudinal data analysis, (c) Statistical model development and (d) Applied statistical modelling. Innovations in statistical modelling are presented throughout each of the four areas, with some intriguing new ideas on hierarchical generalized non-linear models and on frailty models with structural dispersion, just to mention two examples. The contributors include distinguished international statisticians such as Philip Hougaard, John Hinde, Il Do Ha, Roger Payne and Alessandra Durio, among others, as well as promising newcomers. Some of the contributions have come from researchers working in the BIO-SI research programme on Biostatistics and Bioinformatics, centred on the Universities of Limerick and Galway in Ireland and fu...
The Standard Model Coupled to Quantum Gravitodynamics
Aldabe, Fermin
2016-01-01
We show that the renormalizable SO(4) X U (1) X SU (2) X SU (3) Yang Mills coupled to matter and the Higgs field fits all the experimentally observed differential cross sections known in nature. This extended Standard Model reproduces the experimental gravitational differential cross sections without resorting to the graviton field and instead by exchanging SO(4) gauge fields. By construction, each SO(4) generator in quantum gravitodynamics does not commute with the Dirac gamma matrices. This produces additional interactions absent to non-Abelian gauge fields in the Standard Model. The contributions from these new terms yield differential cross sections consistent with the Newtonian and post Newtonian interactions derived from General Relativity. Dimensional analysis of the Lagrangian shows that all its terms have total dimensionality four or less and therefore that all physical quantities in the theory renormalize by finite amounts. These properties make QGD the only renormalizable 4-dimensional theory descr...
The standard model coupled to quantum gravitodynamics
Aldabe, Fermin
2017-01-01
We show that the renormalizable SO(4)× U(1)× SU(2)× SU(3) Yang-Mills coupled to matter and the Higgs field fits all the experimentally observed differential cross sections known in nature. This extended Standard Model reproduces the experimental gravitational differential cross sections without resorting to the graviton field and instead by exchanging SO(4) gauge fields. By construction, each SO(4) generator in quantum gravitodynamics does not commute with the Dirac gamma matrices. This produces additional interactions absent to non-Abelian gauge fields in the Standard Model. The contributions from these new terms yield differential cross sections consistent with the Newtonian and post-Newtonian interactions derived from General Relativity. Dimensional analysis of the Lagrangian shows that all its terms have total dimensionality four or less and therefore that all physical quantities in the theory renormalize by finite amounts. These properties make QGD the only renormalizable four-dimensional theory describing gravitational interactions.