Basic Statistical Physics

The following sections are included:

• Preface

• Notations and Fundamental Constants

• Contents

The following sections are included:

• Introduction

• Master Equation and Hypothesis of Equal á-priori Probability
  • Example of 3 Level Systems

• Phase Space, Phase Point, Phase Trajectory

• Statistical Distribution Function and Ergodic Hypothesis

• Statistical Fluctuation and Statistical Independence

• Statistical Fluctuation and Generalized Susceptibility

• Generalized Ornstein-Zernicke Relation

• Problems

The following sections are included:

• Integral Invariants

• Classical Liouville's Equation

• Role of Energy

• Quantum Mechanical Density Matrix

• Quantum Liouville's Equation

• Problems

The following sections are included:

• Microscopic and Macroscopic States

• Statistical Weight and Density of States

• Examples: Non-interacting One- and N-Particle Systems and Spin-½ Particles

• Entropy and Boltzmann's Principle

• Boltzmann's H-Theorem

• Problems

The following sections are included:

• Introduction

• Microcanonical Distribution Function

• Canonical (Gibbs) Distribution Function
  • Thermodynamic Temperature and Distribution Function
  • Spin-½ Particles and Negative Temperature
  • Partition Function and Different Thermodynamic Functions
  • System of Linear Harmonic Oscillators in Canonical Ensemble
  • Energy Fluctuation in Canonical Ensemble and Equivalence of Canonical and Microcanonical Ensembles

• Grandcanonical Distribution Function
  • Dependence of Thermodynamic Functions on Number of Particles
  • Chemical Potential and Distribution Function
  • Density Fluctuation in Grandcanonical Ensemble and Equivalence of Grandcanonical and Canonical Ensembles

• Problems

The following sections are included:

• Boltzmann Distribution

• Partition Function, Free Energy and Equation of State

• Specific Heat: Translational, Vibrational and Rotational Components

• Degeneracy Temperature

• Problems

The following sections are included:

• Conditions of Chemical Equilibrum

• Law of Mass Action

• Heat of Reaction and Direction of Reaction

• Ionization Equilibrium

• Saha Formula

• Problems

The following sections are included:

• Free Energy, Virial Equation of State

• Second Virial Coefficient and Applicability of Virial Equation

• Model Calculation and van-der-Waal's Equation of State

• Joule-Thomson Expansion and Inversion Temperature

• Problems

The following sections are included:

• Debye-Hückel Approximation, Debye Length

• Screened Coulomb Potential

• Equation of State and Osmotic Pressure

• Problems

The following sections are included:

• Bose and Fermi Distributions

• Quantum Gases of Elementary Particles: Number Density and Chemical Potential, Energy Density, Equation of State

• Black Body Radiation and Planck's Law

• Lattice Specific Heat and Phonons

• Degenerate Bose Gas, Bose Condensation

• Liquid He and Superfluidity
  • Systematics of Liquid ⁴He
  • Landau's 2-Fluid Model
  • Systematics of Liquid ³He

• Degenerate Fermi Gas, Degeneracy Pressure, Specific Heat

• Magnetism of Free Fermions
  • Preamble
  • Landau Diamagnetism
  • Pauli Paramagnetism

• Interacting Fermi System: Fermi Liquid Theory

• Relativistic Degenerate Fermi Gas

• Problems

The following sections are included:

• Introduction

• Trapping of Atoms

• Cooling of Atoms

• Problems

The following sections are included:

• Introduction

• Stars: Stability and Evolution

• High Temperature Dense Matter

• Neutron Stars and Black Holes

• Problems

The following sections are included:

• Systematics of Phase Transitions

• Ehrenfest's Classification of Phase Transitions

• Order Parameter, Continuous and Discontinuous Transitions

• Landau's Theory of Continuous Phase Transitions

• Continuity of Entropy and Discontinuity of Specific Heat

• Generalized Susceptibility

• Critical Exponents and Fluctuations of Order Parameter

• Ising Model
  • Zero-Field 1-Dimensional Case
  • Non-Zero-Field 1-Dimensional Case
  • Multi-Dimensional Case
  • 2-Dimensional Ising System

• Problems

The following sections are included:

• Introduction

• Linear Response Theory (Kubo Formalism)
  • Mechanical Process
  • Thermal Process

• Symmetry Relations

• Fluctuation-Dissipation Theorem

• Problems

The following sections are included:

• Beta and Gamma Functions

• Dirac Delta Function (Distribution)

• Functional Derivative

• Mathematical Identities

• Multiple Summation

• Pauli Matrices

• Probability Theory
  • Elementary Results of Probability Theory
  • Statistical Distributions
    • Binomial/Bernoulli Distribution
    • Poisson Distribution
    • Gaussian/Normal Distribution
    • Lorentzian/Cauchy Distribution
  • Central Limit Theorem

• Quantum Mechanics, A Retrospect

• Riemann, Bernoulli and Fourier
  • Riemann's ζ-Function
  • Bernoulli Numbers and Polynomials
  • Fourier Series
  • Integrals of Quantum Statistics

• Sanskrit Transliteration

• Stirling's Theorem

• Summation and Integration

• Volume of an N-Dimensional Sphere

The following sections are included:

• Bibliography

• Index