Faculty of Science

Objectives

To exploit tools and techniques that are used in the study of the collective nature of a many body system both in classical and in quantum mechanics.

Contents

Introduction: Basic principles- phase space, statistical ensemble, density matrix, Liouville’s theorem, quantum states and phase space; Canonical ensemble: entropy and probability distribution, Nernst’s heat theorem, canonical partition function, equipartition theorem, thermodynamic functions for canonical ensemble- classical system, quantum systems, energy fluctuations; Grand canonical ensemble: grand canonical distribution- classical systems, quantum systems, thermodynamic equivalence in grand canonical ensembles; Applications: ideal gases in microcanonical ensemble, in grand canonical ensemble, ideal Bose systems photon gas, phonons, Debye’s model of solids (revision), liquid helium, ideal Fermi systems- weakly degenerate, strongly degenerate , free electron theory of metals (revision), Interacting systems: classical- deviations of imperfect gases from ideal state, Vander Waal’s equation, virial expansion of equation of state, Quantum systems virial expansion. Phase transition: first order phase transition, Clausius-Clapeyron equation, second order phase transition, critical indices, and liquid-gas transition.