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1.

図書

図書
Josef Honerkamp
出版情報: Berlin : Springer, c2002  xiv, 515 p. ; 24 cm
シリーズ名: Advanced texts in physics
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Statistical Physics Is More than Statistical Mechanics / 1:
Modeling of Statistical Systems / Part I:
Random Variables: Fundamentals of Probability Theory and Statistics / 2:
Probability and Random Variables / 2.1:
The Space of Events / 2.1.1:
Introduction of Probability / 2.1.2:
Random Variables / 2.1.3:
Multivariate Random Variables and Conditional Probabilities / 2.2:
Multidimensional Random Variables / 2.2.1:
Marginal Densities / 2.2.2:
Conditional Probabilities and Bayes' Theorem / 2.2.3:
Moments and Quantiles / 2.3:
Moments / 2.3.1:
Quantiles / 2.3.2:
The Entropy / 2.4:
Entropy for a Discrete Set of Events / 2.4.1:
Entropy for a Continuous Space of Events / 2.4.2:
Relative Entropy / 2.4.3:
Remarks / 2.4.4:
Applications / 2.4.5:
Computations with Random Variables / 2.5:
Addition and Multiplication of Random Variables / 2.5.1:
Further Important Random Variables / 2.5.2:
Limit Theorems / 2.5.3:
Stable Random Variables and Renormalization Transformations / 2.6:
Stable Random Variables / 2.6.1:
The Renormalization Transformation / 2.6.2:
Stability Analysis / 2.6.3:
Scaling Behavior / 2.6.4:
The Large Deviation Property for Sums of Random Variables / 2.7:
Random Variables in State Space: Classical Statistical Mechanics of Fluids / 3:
The Microcanonical System / 3.1:
Systems in Contact / 3.2:
Thermal Contact / 3.2.1:
Systems with Exchange of Volume and Energy / 3.2.2:
Systems with Exchange of Particles and Energy / 3.2.3:
Thermodynamic Potentials / 3.3:
Susceptibilities / 3.4:
Heat Capacities / 3.4.1:
Isothermal Compressibility / 3.4.2:
Isobaric Expansivity / 3.4.3:
Isochoric Tension Coefficient and Adiabatic Compressibility / 3.4.4:
A General Relation Between Response Functions / 3.4.5:
The Equipartition Theorem / 3.5:
The Radial Distribution Function / 3.6:
Approximation Methods / 3.7:
The Virial Expansion / 3.7.1:
Integral Equations for the Radial Distribution Function / 3.7.2:
Perturbation Theory / 3.7.3:
The van der Waals Equation / 3.8:
The Isotherms / 3.8.1:
The Maxwell Construction / 3.8.2:
Corresponding States / 3.8.3:
Critical Exponents / 3.8.4:
Some General Remarks about Phase Transitions and Phase Diagrams / 3.9:
Random Fields: Textures and Classical Statistical Mechanics of Spin Systems / 4:
Discrete Stochastic Fields / 4.1:
Markov Fields / 4.1.1:
Gibbs Fields / 4.1.2:
Equivalence of Gibbs and Markov Fields / 4.1.3:
Examples of Markov Random Fields / 4.2:
Model with Independent Random Variables / 4.2.1:
Auto Model / 4.2.2:
Multilevel Logistic Model / 4.2.3:
Gauss Model / 4.2.4:
Characteristic Quantities of Densities for Random Fields / 4.3:
Simple Random Fields / 4.4:
The White Random Field or the Ideal Paramagnetic System / 4.4.1:
The One-Dimensional Ising Model / 4.4.2:
Random Fields with Phase Transitions / 4.5:
The Curie-Weiss Model / 4.5.1:
The Mean Field Approximation / 4.5.2:
The Two-Dimensional Ising Model / 4.5.3:
The Landau Free Energy / 4.6:
The Renormalization Group Method for Random Fields and Scaling Laws / 4.7:
Scaling Laws / 4.7.1:
Time-Dependent Random Variables: Classical Stochastic Processes / 5:
Markov Processes / 5.1:
The Master Equation / 5.2:
Examples of Master Equations / 5.3:
Analytic Solutions of Master Equations / 5.4:
Equations for the Moments / 5.4.1:
The Equation for the Characteristic Function / 5.4.2:
Examples / 5.4.3:
Simulation of Stochastic Processes and Fields / 5.5:
The Fokker-Planck Equation / 5.6:
Fokker-Planck Equation with Linear Drift Term and Additive Noise / 5.6.1:
The Linear Response Function and the Fluctuation-Dissipation Theorem / 5.7:
The [Omega] Expansion / 5.8:
The One-Particle Picture / 5.8.2:
More General Stochastic Processes / 5.9:
Self-Similar Processes / 5.9.1:
Fractal Brownian Motion / 5.9.2:
Stable Levy Processes / 5.9.3:
Autoregressive Processes / 5.9.4:
Quantum Random Systems / 6:
Quantum-Mechanical Description of Statistical Systems / 6.1:
Ideal Quantum Systems: General Considerations / 6.2:
Expansion in the Classical Regime / 6.2.1:
First Quantum-Mechanical Correction Term / 6.2.2:
Relations Between the Thermodynamic Potential and Other System Variables / 6.2.3:
The Ideal Fermi Gas / 6.3:
The Fermi-Dirac Distribution / 6.3.1:
Determination of the System Variables at Low Temperatures / 6.3.2:
Applications of the Fermi-Dirac Distribution / 6.3.3:
The Ideal Bose Gas / 6.4:
Particle Number and the Bose-Einstein Distribution / 6.4.1:
Bose-Einstein Condensation / 6.4.2:
Pressure / 6.4.3:
Energy and Specific Heat / 6.4.4:
Entropy / 6.4.5:
Applications of Bose Statistics / 6.4.6:
The Photon Gas and Black Body Radiation / 6.5:
The Kirchhoff Law / 6.5.1:
The Stefan-Boltzmann Law / 6.5.2:
The Pressure of Light / 6.5.3:
The Total Radiative Power of the Sun / 6.5.4:
The Cosmic Background Radiation / 6.5.5:
Lattice Vibrations in Solids: The Phonon Gas / 6.6:
Systems with Internal Degrees of Freedom: Ideal Gases of Molecules / 6.7:
Magnetic Properties of Fermi Systems / 6.8:
Diamagnetism / 6.8.1:
Paramagnetism / 6.8.2:
Quasi-particles / 6.9:
Models for the Magnetic Properties of Solids / 6.9.1:
Superfluidity / 6.9.2:
Changes of External Conditions / 7:
Reversible State Transformations, Heat, and Work / 7.1:
Cyclic Processes / 7.2:
Exergy and Relative Entropy / 7.3:
Time Dependence of Statistical Systems / 7.4:
Analysis of Statistical Systems / Part II:
Estimation of Parameters / 8:
Samples and Estimators / 8.1:
Confidence Intervals / 8.2:
Propagation of Errors / 8.3:
The Maximum Likelihood Estimator / 8.4:
The Least-Squares Estimator / 8.5:
Signal Analysis: Estimation of Spectra / 9:
The Discrete Fourier Transform and the Periodogram / 9.1:
Filters / 9.2:
Filters and Transfer Functions / 9.2.1:
Filter Design / 9.2.2:
Consistent Estimation of Spectra / 9.3:
Frequency Distributions for Nonstationary Time Series / 9.4:
Filter Banks and Discrete Wavelet Transformations / 9.5:
Wavelets / 9.6:
Wavelets as Base Functions in Function Spaces / 9.6.1:
Wavelets and Filter Banks / 9.6.2:
Solutions of the Dilation Equation / 9.6.3:
Estimators Based on a Probability Distribution for the Parameters / 10:
Bayesian Estimator and Maximum a Posteriori Estimator / 10.1:
Marginalization of Nuisance Parameters / 10.2:
Numerical Methods for Bayesian Estimators / 10.3:
Identification of Stochastic Models from Observations / 11:
Hidden Systems / 11.1:
The Maximum a Posteriori (MAP) Estimator for the Inverse Problem / 11.2:
The Least-Squares Estimator as a Special MAP Estimator / 11.2.1:
Strategies for Choosing the Regularization Parameter / 11.2.2:
The Regularization Method / 11.2.3:
Examples of Estimating a Distribution Function by a Regularization Method / 11.2.4:
Estimating the Realization of a Hidden Process / 11.3:
The Viterbi Algorithm / 11.3.1:
The Kalman Filter / 11.3.2:
Estimating the Parameters of a Hidden Stochastic Model / 12:
The Expectation Maximization Method (EM Method) / 12.1:
Use of the EM Method for Estimation of the Parameters in Hidden Systems / 12.2:
Estimating the Parameters of a Hidden Markov Model / 12.3:
The Forward Algorithm / 12.3.1:
The Backward Algorithm / 12.3.2:
The Estimation Formulas / 12.3.3:
Estimating the Parameters in a State Space Model / 12.4:
Statistical Tests and Classification Methods / 13:
General Comments Concerning Statistical Tests / 13.1:
Test Quantity and Significance Level / 13.1.1:
Empirical Moments for a Test Quantity: The Bootstrap Method / 13.1.2:
The Power of a Test / 13.1.3:
Some Useful Tests / 13.2:
The z- and the t-Test / 13.2.1:
Test for the Equality of the Variances of Two Sets of Measurements, the F-Test / 13.2.2:
The x[superscript 2]-Test / 13.2.3:
The Kolmogorov-Smirnov Test / 13.2.4:
The F-Test for Least-Squares Estimators / 13.2.5:
The Likelihood-Ratio Test / 13.2.6:
Classification Methods / 13.3:
Classifiers / 13.3.1:
Estimation of Parameters That Arise in Classifiers / 13.3.2:
Automatic Classification (Cluster Analysis) / 13.3.3:
Random Number Generation for Simulating Realizations of Random Variables / Appendix:
Problems
Hints and Solutions
References
Index
Statistical Physics Is More than Statistical Mechanics / 1:
Modeling of Statistical Systems / Part I:
Random Variables: Fundamentals of Probability Theory and Statistics / 2:
2.

図書

図書
Jean-François Sadoc and Rémy Mosseri
出版情報: Cambridge ; New York : Cambridge University Press, 1999  xii, 307 p. ; 26 cm
シリーズ名: Collection Aléa-Saclay : monographs and texts in statistical physics
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Preface
Introduction to geometrical frustration / 1:
Ideal models / 2:
Finite structures / 3:
Decurving and disclinations / 4:
Hierarchical polytopes / 5:
Some physical properties / 6:
Periodic structures with large cells / 7:
Quasiperiodic order and frustration / 8:
Appendices
Bibliography
Index
Preface
Introduction to geometrical frustration / 1:
Ideal models / 2:
3.

図書

図書
edited by Massimo Picardello, Wolfgang Woess
出版情報: Cambridge : Cambridge University Press, 1999  viii, 361 p. ; 24 cm
シリーズ名: Symposia mathematica ; v. 39
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4.

図書

図書
Rosario N. Mantegna, H. Eugene Stanley
出版情報: Cambridge, U.K. : Cambridge University Press, 2000  ix, 148 p. ; 26 cm
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Preface
Introduction / 1:
Efficient market hypothesis / 2:
Random walk / 3:
Lévy stochastic processes and limit theorems / 4:
Scales in financial data / 5:
Stationarity and time correlation / 6:
Time correlation in financial time series / 7:
Stochastic models of price dynamics / 8:
Scaling and its breakdown / 9:
ARCH and GARCH processes / 10:
Financial markets and turbulence / 11:
Correlation and anti-correlation between stocks / 12:
Taxonomy of a stock portfolio / 13:
Options in idealized markets / 14:
Options in real markets / 15:
Notation guide / Appendix A:
Martingales / Appendix B:
References
Index
LFvy stochastic processes and limit theorems
Preface
Introduction / 1:
Efficient market hypothesis / 2:
5.

図書

図書
Walter E. Thirring ; with foreword by Elliott H. Lieb
出版情報: Providence, R.I. : American Mathematical Society, c1998  xiii, 729 p. ; 26 cm
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6.

図書

図書
R.A. Minlos
出版情報: Providence, RI : American Mathematical Society, c2000  vii, 103 p. ; 26 cm
シリーズ名: University lecture series ; v. 19
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7.

図書

図書
Nandita Rudra, P. Rudra
出版情報: Hackensack : World Scientific, c2010  xvii, 229 p. ; 24 cm
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Preface
Notations and Fundamental Constants
Basic Concepts / 1:
Introduction / 1.1:
Master Equation and Hypothesis of Equal á-priori Probability / 1.2:
Example of 3 Level Systems / 1.2.1:
Phase Space, Phase Point, Phase Trajectory / 1.3:
Statistical Distribution Function and Ergodic Hypothesis / 1.4:
Statistical Fluctuation and Statistical Independence / 1.5:
Statistical Fluctuation and Generalized Susceptibility / 1.6:
Generalized Ornstein-Zernicke Relation / 1.7:
Problems / 1.8:
Motion of Systems in Phase Space / 2:
Integral Invariants / 2.1:
Classical Liouville's Equation / 2.2:
Role of Energy / 2.3:
Quantum Mechanical Density Matrix / 2.4:
Quantum Liouville's Equation / 2.5:
States in Statistical Physics / 2.6:
Microscopic and Macroscopic States / 3.1:
Statistical Weight and Density of States / 3.2:
Examples: Non-interacting One- and N-Particle Systems and Spin-1/2 Particles / 3.3:
Entropy and Boltzmann's Principle / 3.4:
Boltzmann's H-Theorem / 3.5:
Statistical Ensembles / 3.6:
Microcanonical Distribution Function / 4.1:
Canonical (Gibbs) Distribution Function / 4.3:
Thermodynamic Temperature and Distribution Function / 4.3.1:
Spin-1/2 Particles and Negative Temperature / 4.3.2:
Partition Function and Different Thermodynamic Functions / 4.3.3:
System of Linear Harmonic Oscillators in Canonical Ensemble / 4.3.4:
Energy Fluctuation in Canonical Ensemble and Equivalence of Canonical and Microcanonical Ensembles / 4.3.5:
Grandcanonical Distribution Function / 4.4:
Dependence of Thermodynamic Functions on Number of Particles / 4.4.1:
Chemical Potential and Distribution Function / 4.4.2:
Density Fluctuation in Grandcanonical Ensemble and Equivalence of Grandcanonical and Canonical Ensembles / 4.4.3:
Ideal Gas / 4.5:
Boltzmann Distribution / 5.1:
Partition Function, Free Energy and Equation of State / 5.2:
Specific Heat: Translational, Vibrational and Rotational Components / 5.3:
Degeneracy Temperature / 5.4:
Chemical Reaction Equilibrium / 5.5:
Conditions of Chemical Equilibrum / 6.1:
Law of Mass Action / 6.2:
Heat of Reaction and Direction of Reaction / 6.3:
Ionization Equilibrium / 6.4:
Saha Formula / 6.5:
Real Gas / 6.6:
Free Energy, Virial Equation of State / 7.1:
Second Virial Coefficient and Applicability of Virial Equation / 7.2:
Model Calculation and van-der-Waal's Equation of State / 7.3:
Joule-Thomson Expansion and Inversion Temperature / 7.4:
Strong Electrolytes / 7.5:
Debye-Hückel Approximation, Debye Length / 8.1:
Screened Coulomb Potential / 8.2:
Equation of State and Osmotic Pressure / 8.3:
Quantum Statistics / 8.4:
Bose and Fermi Distributions / 9.1:
Quantum Gases of Elementary Particles: Number Density and Chemical Potential, Energy Density, Equation of State / 9.2:
Black Body Radiation and Planck's Law / 9.3:
Lattice Specific Heat and Phonons / 9.4:
Degenerate Bose Gas, Bose Condensation / 9.5:
Liquid He and Superfluidity / 9.6:
Systematics of Liquid 4He / 9.6.1:
Landau's 2-Fluid Model / 9.6.2:
Systematics of Liquid 3He / 9.6.3:
Degenerate Fermi Gas, Degeneracy Pressure, Specific Heat / 9.7:
Magnetism of Free Fermions / 9.8:
Preamble / 9.8.1:
Landau Diamagnetism / 9.8.2:
Pauli Paramagnetism / 9.8.3:
Interacting Fermi System: Fermi Liquid Theory / 9.9:
Relativistic Degenerate Fermi Gas / 9.10:
Bose-Einstein Condensate / 9.11:
Trapping of Atoms / 10.1:
Cooling of Atoms / 10.3:
Statistical Astrophysics / 10.4:
Stars: Stability and Evolution / 11.1:
High Temperature Dense Matter / 11.3:
Neutron Stars and Black Holes / 11.4:
Phase Transitions / 11.5:
Systematics of Phase Transitions / 12.1:
Ehrenfest's Classification of Phase Transitions / 12.2:
Order Parameter, Continuous and Discontinuous Transitions / 12.3:
Landau's Theory of Continuous Phase Transitions / 12.4:
Continuity of Entropy and Discontinuity of Specific Heat / 12.5:
Generalized Susceptibility / 12.6:
Critical Exponents and Fluctuations of Order Parameter / 12.7:
Ising Model / 12.8:
Zero-Field 1-Dimensional Case / 12.8.1:
Non-Zero-Field 1-Dimensional Case / 12.8.2:
Multi-Dimensional Case / 12.8.3:
2-Dimensional Ising System / 12.8.4:
Irreversible Processes / 12.9:
Linear Response Theory (Kubo Formalism) / 13.1:
Mechanical Process / 13.2.1:
Thermal Process / 13.2.2:
Symmetry Relations / 13.3:
Fluctuation-Dissipation Theorem / 13.4:
Mathematical Appendix / 13.5:
Beta and Gamma Functions / 14.1:
Dirac Delta Function (Distribution) / 14.2:
Functional Derivative / 14.3:
Mathematical Identities / 14.4:
Multiple Summation / 14.5:
Pauli Matrices / 14.6:
Probability Theory / 14.7:
Elementary Results of Probability Theory / 14.7.1:
Statistical Distributions / 14.7.2:
Central Limit Theorem / 14.7.3:
Quantum Mechanics, A Retrospect / 14.8:
Riemann, Bernoulli and Fourier / 14.9:
Riemann's ζ-Function / 14.9.1:
Bernoulli Numbers and Polynomials / 14.9.2:
Fourier Series / 14.9.3:
Integrals of Quantum Statistics / 14.9.4:
Sanskrit Transliteration / 14.10:
Stirling's Theorem / 14.11:
Summation and Integration / 14.12:
Volume of an N-Dimensional Sphere / 14.13:
Bibliography
Index
Preface
Notations and Fundamental Constants
Basic Concepts / 1:
8.

図書

図書
editor, H.J. Raveché
出版情報: Amsterdam ; New York : North-Holland Pub. Co. , New York : sole distributors for the U.S.A. Elsevier North-Holland, c1981  xxviii, 367 p. ; 23 cm
シリーズ名: Studies in statistical mechanics / edited by J. De Boer and G.E. Uhlenbeck ; v. 9
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9.

図書

図書
James Glimm, Arthur Jaffe
出版情報: New York : Springer-Verlag, c1981  xx, 417 p. ; 24 cm
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10.

図書

図書
A.I. Akhiezer and S.V. Peletminskii ; translated by M. Schukin
出版情報: Oxford ; New York : Pergamon Press, c1981  xv, 450 p. ; 23 cm
シリーズ名: International series in natural philosophy ; v. 104
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