Pre-requisites: PHY-106, 203, 204, 301

PART A

1. Classical Statistical Mechanics

• The scope of statistical physics
• Assemblies
• Phase Space and Phase Trajectory
• Volume in Phase Space
• Specification of States of a System
• Density of States and its General Behavior
• Liouville's theorem and its Consequences
• The Postulates of Classical Statistical Mechanics
• Stirling Approximation
• Thermodynamic Probability
• Statistical Equilibrium
• Macrostates and Microstates

2. Statistics and Thermodynamics

• Statistical concept of Temperature
• Ensembles: Microcanonical Ensemble, Canonical Ensemble- its Connection with thermodynamic parameters and grandcanonical ensemble
• Entropy
• Free energy and other thermodynamic functions and their equilibrium conditions
• Statistical Distribution Function
• The Boltzmann partition function
• Maxwell velocity distribution and mean values
• Maxwell-Boltzmann Statistics and its Applications
• Ideal monatomic gas
• Harmonic oscillator
• Specific heat of solids.

3. Quantum Statistical Mechanics

• Postulates of Quantum Statistical Mechanics
• Transition from Classical to Quantum Statistical Mechanics
• Particle Statistics: Principle of indistinguishability for quantum particles, Spin-statistics connection, Exchange degeneracy
• Average value and Quantum Statistics
• The Density Matrix
• Statistics of various Ensembles

PART B

4. Ferni Systems

• Fermi-Dirac distribution function
• Fermi-Dirac gas
• Fermi Energy
• Fermi Temperature
• Fermi Velocity and Mean Velocity of a free electron in Metal
• Degenerate Fermi systems
• Landau Diamagnetism
• Pauli Paramagnetism
• Thermionic Emission
• Statistical equilibrium in White Dwarfs

5. Bose Systems

• Bose-Einstein distribution function and it's application
• Planck’s radiation law
• The Photon Gas
• The Specific heat of Solids
• The Phonon gas
• Bose-Einstein Condensation
• Superfluidity in Liquid He
• Thermodynamics of Bose systems
• Thermodynamic Properties of Diatomic Molecules
• Nuclear Spin Effects in Diatomic Molecules.

6. The Condensed State

• Solids at low and high temperature
• Debye’s interpolation formula
• Thermal expansion of solids
• Quantum liquids with Bose-type spectrum
• Quantum liquids with Fermi-type spectrum
• The electronic spectra of metals
• The electronic spectra of solid dielectrics.

7. Transport Phenomena and Phase Transition

• Boltzmann transport equation
• $H$- theorem, validity of the equation
• Mean free path, Viscosity and Diffusion
• Electrical Conductivity, Brownian motion
• Thermodynamic classification of Phase transition
• Difference between first and second order phase transition
• Mean-field theory