P556 Statistical Physics

Spring 2005, Indiana University

Charles J. Horowitz

Swain West 233, IUCF 1215

Email:  horowit "at" indiana.edu

Office hours: MWF 11-12 or by arrangement

Location:  Swain West 217

Lecture time:  MWF 10:10-11

Text:  Kerson Huang, “Statistical Mechanics” 2nd Ed, (Wiley, 1987)

Homework:  Problem sets will be handed out most WED. and due one week later.  Homework sets and solutions are posted here

Computer Project:  Each student will be asked to perform a Monte Carlo simulation of a liquid.  This will require writing a computer code in Fortran or C.

Fortran subroutine RAN3 is available here to generate uniform random numbers

Short Course Description:  The laws of thermodynamics, thermal equilibrium, entropy, and thermodynamic potentials.  Principles of classical and quantum statistical mechanics.  Partition functions and statistical ensembles.  Statistical basis of the laws of thermodynamics.  Elementary kinetic theory.

Mathematical Methods:  The department web site has a list of mathematical methods taught in the core graduate courses.  Listed for P556 are Combinatorial Probability: axioms for probabilities on finite sets, permutations, combinations, counting problems, Cauchy formula.  Stationary Phase Methods:  Estimates of multiple integrals and sums using the methods of stationary phase.

In addition we will discuss Monte Carlo Methods for multidimensional integrals, random variables, importance sampling and error estimates.

Other References:

If you would like more words than the text you may want to look at R.K. Pathria, “Statistical Mechanics” (Butterworth Heinemann, 1996)

P556         Outline

I.          Thermodynamics (~ 5 lectures)

1.  Introduction

2.  Basics concepts of thermodynamics

3.  Thermal Equilibrium, the Zeroth law, temperature

4.  The First Law.

5.  The Second Law.

6.  Thermodynamic Potentials; Maxwell Relations

7.  Specific Heats and the Tds Equations

8.  Thermodynamics of the Ideal Gas

II.         Statistical Physics (~ 5 lectures)

1.  Basic Ideas

2.  Hamilton’s Equations and Phase Space

3.  Canonical Transformations

4.  Invariance of Phase Space Volume Element

5.  Liouville’s Theorem

6.  Ensembles and Phase – Space Densities

7.  Ensemble Averages and the Basic Postulate of Statistical Mechanics

III.       Classical Statistical Mechanics (~ 6 lectures)

1.  Microcanonical Ensemble and Entropy, Temperature, and Derivation of

Thermodynamics, and Ideal Gas.

2.  Canonical Ensemble

3.  Viral Theorem and Equipartition

4.  Connection with Kinetic Theory of Gases

5.  Maxwell-Boltzmann Distribution

IV        Quantum Statistical Mechanics (~ 15 lectures)

1.  Density Matrix

2.  Quantal Canonical Distribution

3.  Derivation of Thermodynamics via Quantal Canonical Ensemble

4.  Paramagnetic Solids

5.  Entropy and information

6.  Maxwell Boltzmann Statistics

7.  Ideal Fermion gas

8.  3He gas, electrons in metals, white dwarf stars, Bose Gas, Bose condensation

Photon gas (black-body radiation solids)

V         Applications (~ 10 lectures)

1.  Co-existence of phases

2.  Viral expansion for imperfect gas

3.  Monte Carlo simulation of classical fluid

4.  Liquid He and superfluidity

5.  Ferromagnetism and Ising Model

6.  Critical Phenomena