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1.

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:
2.

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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3.

図書

図書
by E.M. Lifshitz and L.P. Pitaevskiĭ ; translated from the Russian by J.B. Sykes and M.J. Kearsley
出版情報: Oxford : Butterworth-Heinemann, 1995, c1980  x, 387 p. ; 25 cm
シリーズ名: Course of theoretical physics ; v. 9 . Statistical physics / L.D. Landau and E. M. Lifshitz ; pt. 2
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Fundamental principles of theoretical physics
The Gibbs distribution
Ideal gases
Solids
Non-ideal gases
Solutions
Chemical reactions
Fluctuations
Surfaces
Fundamental principles of theoretical physics
The Gibbs distribution
Ideal gases
4.

図書

図書
edited by Elizabeth Garber, Stephen G. Brush, and C.W.F. Everitt
出版情報: Cambridge, Mass. : MIT Press, c1986  xxvii, 565 p. ; 24 cm
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5.

図書

図書
出版情報: Malabar, Fla. : R.E. Krieger, 1986  xx, 520 p. ; 28 cm
シリーズ名: Statistical and thermal physics / by Shigeji Fujita ; pt. 1
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6.

図書

図書
by Yu.L. Klimontovich ; translated from the Russian by G. Pontecorvo
出版情報: Chur, Switzerland ; New York : Harwood Academic Publishers, c1986  xxvi, 734 p. ; 24 cm
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7.

図書

図書
Gregory H. Wannier
出版情報: New York : Dover Publications, 1987, c1966  xii, 532 p. ; 22 cm
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8.

図書

図書
Claude Itzykson, Jean-Michel Drouffe
出版情報: Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1989  xvi, 403 p. ; 24 cm
シリーズ名: Cambridge monographs on mathematical physics ; . Statistical field theory / Claude Itzykson, Jean-Michel Drouffe ; v. 1
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Contents of Volume 2
Preface
From Brownian motion to Euclidean fields / 1:
Brownian motion / 1.1:
Random walks / 1.1.1:
The sum over paths / 1.1.2:
The dimension two of Brownian curves / 1.1.3:
Euclidean fields / 1.2:
Free fields / 1.2.1:
Interacting fields and random walks / 1.2.2:
Self-avoiding walks and the limit n [right arrow] 0 / 1.2.3:
Comparison with the high temperature expansion / 1.2.4:
The one-dimensional case / 1.2.5:
Lattices / 1.A:
Notes
Grassmannian integrals and the two-dimensional Ising model / 2:
Grassmannian integrals / 2.1:
Anticommuting variables / 2.1.1:
Integrals / 2.1.2:
The two-dimensional Ising model / 2.2:
Duality / 2.2.1:
Transfer matrix / 2.2.2:
Fermionic representation / 2.2.3:
Free energy / 2.2.4:
Spontaneous magnetization / 2.2.5:
Correlation function in the high temperature phase / 2.2.6:
Surface tension / 2.2.7:
Critical continuous theory / 2.3:
Effective action / 2.3.1:
Correlation functions / 2.3.2:
Quadratic differences and Painleve equations / 2.A:
Spontaneous symmetry breaking, mean field / 3:
Mean field approximation / 3.1:
Dielectric constant of a polarizable medium / 3.1.1:
Classical spin model with a finite symmetry group / 3.1.2:
Continuous symmetry group / 3.1.3:
The Bethe approximation / 3.1.4:
Critical exponents / 3.1.5:
Lee-Yang zeroes / 3.2:
The Lee-Yang theorem / 3.2.1:
General properties / 3.2.2:
Zeroes in the temperature plane / 3.2.4:
Large n limit / 3.3:
Saddle point method / 3.3.1:
Factorization / 3.3.2:
Coupling to an external field / 3.3.3:
Corrections to mean field / 3.4:
Laplace transform / 3.4.1:
Scaling transformations and the XY-model / 4:
Scaling laws. Real space renormalization / 4.1:
Homogeneity and scale invariance / 4.1.1:
Recurrence relations in real space / 4.1.2:
Examples and approximations / 4.1.3:
The XY-model / 4.2:
High temperature behaviour / 4.2.1:
Low temperature expansion. Vortices / 4.2.2:
The Villain action / 4.2.3:
Correlations / 4.2.4:
Renormalization flow / 4.2.5:
Two-dimensional systems with continuous symmetry / 4.A:
Magnetization inequality / 4.A.1:
Correlation inequality / 4.A.2:
Phenomenological renormalization / 4.B:
Continuous field theory and the renormalization group / 5:
The Lagrangian and dimensional analysis / 5.1:
Introduction / 5.1.1:
Generating functionals and dimensional analysis / 5.1.2:
The perturbative method / 5.2:
Diagrammatic series / 5.2.1:
Loop expansion / 5.2.2:
Evaluation of integrals and dimensional continuation / 5.2.3:
Group theoretical factors / 5.2.4:
Power counting / 5.2.5:
Perturbative renormalization / 5.2.6:
The renormalization group / 5.3:
From the Gaussian ultraviolet fixed point to the infrared critical point in dimension less than four / 5.3.1:
Correlation functions at the critical point / 5.3.4:
Expansion near the critical point / 5.3.5:
Scaling laws below the critical temperature / 5.3.6:
Corrections to scaling laws / 5.4:
Deviation from the critical point in dimension lower than four / 5.4.1:
Logarithmic corrections in dimension four / 5.4.2:
Irrelevant operators / 5.4.3:
Numerical results / 5.5:
[varepsilon]-expansion of critical exponents / 5.5.1:
Equation of state / 5.5.2:
Amplitude ratios / 5.5.3:
Three-dimensional results / 5.5.4:
Multicritical points / 5.A:
Lattice gauge fields / 6:
Generalities / 6.1:
Presentation / 6.1.1:
The continuous limit / 6.1.2:
Order parameter and Elitzur's theorem / 6.1.3:
Structure of the phase diagram / 6.1.4:
Corrections to mean field and restoration of gauge invariance / 6.2.1:
Discrete groups: 1/d expansion / 6.2.3:
Continuous groups: computation of corrections / 6.2.4:
Strong coupling expansions / 6.3:
Convergence / 6.3.1:
Character expansions / 6.3.2:
String tension and roughening transition / 6.3.3:
Mass spectrum / 6.3.5:
Lattice fermions / 6.4:
The doubling problem / 6.4.1:
The Nielsen-Ninomiya theorem / 6.4.2:
Staggered fermions / 6.4.3:
Index
Grassmannian integrals and two-dimensional Ising models
Spontaneous symmetry breaking
Contents of Volume 2
Preface
From Brownian motion to Euclidean fields / 1:
9.

図書

図書
[by] B. Jancovici. Problems by Yves Archambault. translated from the French by L. J. Carroll
出版情報: London ; New York : McGraw-Hill, c1973  xi, 147 p. ; 23 cm
シリーズ名: European physics series
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10.

図書

図書
[by] Don C. Kelly
出版情報: New York : Academic Press, [1973]  xiii, 421 p. ; 24 cm
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