Introduction To Statistical Mechanics

Overview

This is an introductory course in classical and quantum statistical mechanics which deals with the principle of ensembles, Classical, Fermi and Bose ideal gases, Pauli paramagnestim, Debye and Einstein’s theory of specific heat and the 1D Ising model.
INTENDED AUDIENCE: M.Sc. and beginning Ph.D. students and other interested individualsPREREQUISITES: Thermodynamics, Classical mechanics, Quantum mechanics

Syllabus

COURSE LAYOUT

Week 1: Review of thermodynamics, Hamiltonian mechanics of classical and quantum systems.Week 2: Microcanonical ensemble and the concept of entropy. Examples of systems with finite and infinitely many degrees of freedom. Counting of states and entropy in quantum systems.Week 3: Canonical ensemble and the concept of temperature. Relation between canonical and microcanonical ensembles and partition functions. Thermodynamic potentials and Legendre transformations. Examples from classical and quantum systems.Week 4: Other ensembles and their related thermodynamic potentials Concept of fugacity, pressure of an ideal gas. Equation of state of an ideal classical gas.Week 5: Equation of state of ideal Bose and Fermi gases. Bose Einstein condensation and Fermi degeneracy pressure.Week 6: Non-ideal gas: Van der Waals equation of state. Concept of phase diagramWeek 7: Magnetic insulators: Ising model, Potts model Solution on 1D lattice using transfer matrix method. Solution in large dimensions using mean field theory.Week 8: Pauli paramagnetism and temperature dependent susceptibility, electronic contribution to specific heat of solids. Deybe and Einstein theory of specific heat of solids