Basic Statistical Physics

By: Nandita Rudra, Prasanta Rudra

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Hardcover | 29 December 2009

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248 Pages

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22.86 x 15.24 x 1.6

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This is a masters/graduate level textbook on statistical physics. The basics of the discipline and its application in the current topics of interest like Bose-Einstein condensate, statistical astrophysics and phase transitions have been discussed with thoroughness.This is a systematic introduction and development of a course material tried successful over a number of years. Feedback from the students tells that it has immensely helped them in their later research.

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Non-Fiction Science Physics Mathematical Physics Statistical Physics Chemistry Physical Chemistry Engineering & Technology Biochemical Engineering Biotechnology Applied Physics Astrophysics

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Preface	p. vii
Notations and Fundamental Constants	p. xi
Basic Concepts	p. 1
Introduction	p. 1
Master Equation and Hypothesis of Equal á-priori Probability	p. 3
Example of 3 Level Systems	p. 4
Phase Space, Phase Point, Phase Trajectory	p. 4
Statistical Distribution Function and Ergodic Hypothesis	p. 5
Statistical Fluctuation and Statistical Independence	p. 7
Statistical Fluctuation and Generalized Susceptibility	p. 11
Generalized Ornstein-Zernicke Relation	p. 13
Problems	p. 15
Motion of Systems in Phase Space	p. 17
Integral Invariants	p. 17
Classical Liouville's Equation	p. 20
Role of Energy	p. 22
Quantum Mechanical Density Matrix	p. 22
Quantum Liouville's Equation	p. 24
Problems	p. 26
States in Statistical Physics	p. 27
Microscopic and Macroscopic States	p. 27
Statistical Weight and Density of States	p. 28
Examples: Non-interacting One- and N-Particle Systems and Spin-1/2 Particles	p. 29
Entropy and Boltzmann's Principle	p. 31
Boltzmann's H-Theorem	p. 34
Problems	p. 35
Statistical Ensembles	p. 37
Introduction	p. 37
Microcanonical Distribution Function	p. 37
Canonical (Gibbs) Distribution Function	p. 39
Thermodynamic Temperature and Distribution Function	p. 39
Spin-1/2 Particles and Negative Temperature	p. 40
Partition Function and Different Thermodynamic Functions	p. 41
System of Linear Harmonic Oscillators in Canonical Ensemble	p. 42
Energy Fluctuation in Canonical Ensemble and Equivalence of Canonical and Microcanonical Ensembles	p. 43
Grandcanonical Distribution Function	p. 44
Dependence of Thermodynamic Functions on Number of Particles	p. 44
Chemical Potential and Distribution Function	p. 47
Density Fluctuation in Grandcanonical Ensemble and Equivalence of Grandcanonical and Canonical Ensembles	p. 49
Problems	p. 50
Ideal Gas	p. 51
Boltzmann Distribution	p. 51
Partition Function, Free Energy and Equation of State	p. 52
Specific Heat: Translational, Vibrational and Rotational Components	p. 55
Degeneracy Temperature	p. 59
Problems	p. 61
Chemical Reaction Equilibrium	p. 63
Conditions of Chemical Equilibrum	p. 63
Law of Mass Action	p. 65
Heat of Reaction and Direction of Reaction	p. 66
Ionization Equilibrium	p. 68
Saha Formula	p. 70
Problems	p. 71
Real Gas	p. 73
Free Energy, Virial Equation of State	p. 73
Second Virial Coefficient and Applicability of Virial Equation	p. 76
Model Calculation and van-der-Waal's Equation of State	p. 78
Joule-Thomson Expansion and Inversion Temperature	p. 80
Problems	p. 83
Strong Electrolytes	p. 85
Debye-Hückel Approximation, Debye Length	p. 85
Screened Coulomb Potential	p. 88
Equation of State and Osmotic Pressure	p. 89
Problems	p. 90
Quantum Statistics	p. 91
Bose and Fermi Distributions	p. 91
Quantum Gases of Elementary Particles: Number Density and Chemical Potential, Energy Density, Equation of State	p. 94
Black Body Radiation and Planck's Law	p. 98
Lattice Specific Heat and Phonons	p. 100
Degenerate Bose Gas, Bose Condensation	p. 103
Liquid He and Superfluidity	p. 106
Systematics of Liquid ⁴He	p. 106
Landau's 2-Fluid Model	p. 111
Systematics of Liquid ³He	p. 117
Degenerate Fermi Gas, Degeneracy Pressure, Specific Heat	p. 118
Magnetism of Free Fermions	p. 124
Preamble	p. 124
Landau Diamagnetism	p. 124
Pauli Paramagnetism	p. 127
Interacting Fermi System: Fermi Liquid Theory	p. 129
Relativistic Degenerate Fermi Gas	p. 133
Problems	p. 136
Bose-Einstein Condensate	p. 139
Introduction	p. 139
Trapping of Atoms	p. 140
Cooling of Atoms	p. 142
Problems	p. 145
Statistical Astrophysics	p. 147
Introduction	p. 147
Stars: Stability and Evolution	p. 148
High Temperature Dense Matter	p. 152
Neutron Stars and Black Holes	p. 154
Problems	p. 156
Phase Transitions	p. 157
Systematics of Phase Transitions	p. 157
Ehrenfest's Classification of Phase Transitions	p. 159
Order Parameter, Continuous and Discontinuous Transitions	p. 160
Landau's Theory of Continuous Phase Transitions	p. 163
Continuity of Entropy and Discontinuity of Specific Heat	p. 165
Generalized Susceptibility	p. 167
Critical Exponents and Fluctuations of Order Parameter	p. 170
Ising Model	p. 173
Zero-Field 1-Dimensional Case	p. 175
Non-Zero-Field 1-Dimensional Case	p. 175
Multi-Dimensional Case	p. 177
2-Dimensional Ising System	p. 178
Problems	p. 181
Irreversible Processes	p. 183
Introduction	p. 183
Linear Response Theory (Kubo Formalism)	p. 184
Mechanical Process	p. 184
Thermal Process	p. 189
Symmetry Relations	p. 191
Fluctuation-Dissipation Theorem	p. 192
Problems	p. 196
Mathematical Appendix	p. 197
Beta and Gamma Functions	p. 197
Dirac Delta Function (Distribution)	p. 198
Functional Derivative	p. 200
Mathematical Identities	p. 201
Multiple Summation	p. 202
Pauli Matrices	p. 203
Probability Theory	p. 203
Elementary Results of Probability Theory	p. 203
Statistical Distributions	p. 204
Central Limit Theorem	p. 207
Quantum Mechanics, A Retrospect	p. 209
Riemann, Bernoulli and Fourier	p. 210
Riemann's ¿-Function	p. 210
Bernoulli Numbers and Polynomials	p. 211
Fourier Series	p. 212
Integrals of Quantum Statistics	p. 214
Sanskrit Transliteration	p. 216
Stirling's Theorem	p. 217
Summation and Integration	p. 219
Volume of an N-Dimensional Sphere	p. 220
Bibliography	p. 223
Index	p. 225
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Basic Statistical Physics

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Hardcover

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