PHY201: STATISTICAL MECHANICS
Course outlines
Elementary probability theory: Preliminary concepts, Random walk problem, Binomial distribution, mean values, standard deviation, various moments, Gaussian distribution, Poisson distribution, meanvalues. Probability density, probability for continuous variables. Extensive and intensive variables, laws of thermodynamics, Legendre transformations and thermodynamic potentials, Maxwell relations, applications of thermodynamics to (a) ideal gas, (b) magnetic material, and (c) dielectric material. The laws of thermodynamics and their consequences.
Statistical description of system of particles: State of a system, microstates, ensemble, basic postulates, behavior of density of states, density of state for ideal gas in classical limit, thermal and mechanical interactions, quasi-static process. Statistical thermodynamics: Irreversibility and attainment of equilibrium, Reversible and irreversible processes. Thermal interaction between macroscopic systems, approach to thermal equilibrium, dependence of density of states on external parameters, Statistical calculation of thermodynamic variables.
Classical statistical mechanics: Microcanonical ensembles and their Equivalence, Canonical and grand canonical ensembles, partition function, thermodynamic variables in terms of partition function and grand partition function, ideal gas, Gibbs paradox, validity of classical approximation, equipartition theorem. Maxwell-Boltzmann gas velocity and speed distribution. Chemical potential, Free energy and connection with thermodynamic variables, First and Second order phase transition; phase equilibrium. Formulation of quantum statistics, Density Matrix, ensembles in quantum statistical mechanics, simple applications of density matrix. The theory of simple gases: Maxwell-Boltzmann, Bose-Einstein, Fermi-Dirac gases. Statistics of occupation numbers, Evaluation of partition functions, Ideal gases in the classical limit.
Ideal Bose system: Thermodynamic behavior of an Ideal Bose gas, Bose-Einstein condensation. Thermodynamics of Black body radiation, Stefan-Boltzmann law, Wien’s displacement law. Specific heat of solids (Einstein and Debye models). Ideal Fermi System: Thermodynamic behavior of an ideal Fermi gas, degenerate Fermi gas, Fermi energy and mean energy, Fermi temperature, Fermi velocity of a particle of a degenerate gas.
References
Frederick Reif, Statistical Physics: Berkeley Physics Course, Volume 5, McGraw Hill Education (2010).
Frederick Reif, Fundamentals of Statistical and Thermal Physics, Waveland Press (2010).
Kerson Huang, Introduction to Statistical Physics (Second edition), Taylor & Francis (2009).
Kerson Huang, Statistical Mechanics (Second edition), Wiley (2008).
R. K. Pathria and Paul D. Beale, Statistical Mechanics (Third edition), Academic Press, (2011).
Harvey Gould and Jan Tobochnik, Statistical and Thermal Physics: With Computer Applications, Princeton University Press (2010).
L. D. Landau and E.M. Lifshitz, Statistical Physics: Course of Theoretical Physics, Volume 5 (Third edition), Butterworth-Heinemann, (1996).
Richard P. Feynman, Statistical Mechanics: A Set of Lectures (Advanced Books Classics), Second edition, Perseus Books (1998).
Mehran Kardar, Statistical Physics of Particles, Cambridge University Press (2007).
Mehran Kardar, Statistical Physics of Fields, Cambridge University Press (2007).
Daniel V. Schroeder, An Introduction to Thermal Physics, Pearson Education (2000).
James P. Sethna, Statistical Mechanics: Entropy, Order Parameters and Complexity, Oxford University Press (2006).
Assignments
Exams