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Indian Institute of Science Education and Research Bhopal

PHY 604: Statistical Mechanics (4)

Prerequisite: PHY 303: Quantum Mechanics I, PHY 301: Mathematical Methods I, PHY 309: Thermal Physics      

Motivation : Why do we need statistical mechanics ? Thermodynamic description of a system. Microscopic origin of of thermodynamic results - introduction of statistical description. Introduction and definition of ensemble. Examples of ensembles.

Phase spac:  Introduction and definition of phase space. Examples. Phase space density Time average and ensemble average. Equivalence between time average and ensemble average - Postulate of statistical mechanics (Ergodic hypothesis). Liouville's equation.

Equilibrium Statistical mechanics

1. Definition.
2. Micro-canonical ensemble: Definition ,Volume of phase space, Definition of entropy, Definition of temperature, Physical interpretation of temperature. Validity of statistical description. Definition of pressure,1st law of thermodynamics. Statistical interpretation of entropy. Classical ideal gas in microcanonical ensemble. Gibbs paradox.
3. Canonical ensemble: Definition, Average in canonical ensemble, Partition function Equivalence between canonical and microcanonical ensemble average. Definition of free energy. Ideal gas in canonical ensemble.
4. Grand-canonical ensemble: Definition, Grand-canonical partition function, Definition of chemical potential, Equivalence between canonical and grand-canonical average. Ideal gas in grand canonical ensemble

Quantum statistical mechanics: Pure and mixed ensemble. Examples of pure and mixed ensemble. Quantum ensemble average. Introduction of density matrix. Properties of density matrix. Examples of density matrix. Micro-canonical ensemble, Canonical ensemble and Partition function, Grand-canonical ensemble and partition function.

Three different statistics Boltzmann statistics: Partition function for ideal Boltzmann gas.  Equation of state. Bose and Fermi statics/distribution

Ideal Fermi gas: Partition function. Equation of state. High temperature fermi gas. Low temperature fermi gas.  Fermi energy, fermi temperature and fermi surface. Pressure of low temperature fermi gas. Zero point pressure.

Magnetization: Dia-magnetization, Paramagnetization.

Ideal Bose gas: Partition function. Equation of state. Gas of photon - Black body radiation Lattice vibration : Specific heal, Einstein and Debye's model of specific heat.

Suggested Books:

• F. Reif, Fundamentals of Statistical and Thermal Physics.
• R.K. Pathria, Statistical Mechanics, 2nd Ed.
• M. Plischke and B. Bergersen, Equilibrium Statistical Physics.
• J. K. Bhattacharjee, Statistical Physics: Equilibrium and Non-Equilibrium Aspects.
• Kerson Huang, Statistical Mechanics.
• S-K. Ma, Statistical Mechanics.
• L. D. Landau and E. M. Lifshitz, Statistical Physics.
• R. Kubo, M. Toda and N. Hashitsume, Statistical Physics I and II.
• S-K. Ma, Modern Theory of Critical Phenomena.

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