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1.

図書
図書
1. Statistical physics : an advanced approach with applications : web-enhanced with problems and solutions. 2nd ed.
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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目次情報: 続きを見る
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
2. Geometrical frustration
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
3. Random walks and discrete potential theory : Cortona 1997
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
4. An introduction to econophysics : correlations and complexity in finance
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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目次情報: 続きを見る
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
5. Selected papers of Walter E. Thirring with commentaries
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
6. Introduction to mathematical statistical physics
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
7. Basic statistical physics
Nandita Rudra, P. Rudra
出版情報: Hackensack : World Scientific, c2010  xvii, 229 p. ; 24 cm
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目次情報: 続きを見る
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
8. Perspectives in statistical physics : M. S. Green memorial volume
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
9. Quantum physics : a functional integral point of view
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
10. Methods of statistical physics. 1st ed
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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