# Ensembles and simulations

## Classical Ensembles

Complete familiarity with these notions will be assumed. First try to solve the problems. If you cannot, then please study the notes before trying again. This material will be covered in break-neck speed. Apart from the reference books below, you can also check the lectures on statistical mechanics by Veytsman and Koteluanskii. See also a short note on entropy and probability.

## Quantum Ensembles

It will be assumed that these notions are familiar. Try to solve the problems, and study the notes if you do not succeed. This material will be covered very rapidly.

## Computer Simulations

For computer simulations of statistical systems we will use the Metropolis algorithm. This was invented by N.N. Metropolis and his collaborators in 1953, for evaluating high-dimensional integrals. The notions involved are new, but simple, once the material on probability is understood. This will be covered in detail. The assignment on writing your own Metropolis program is one of the first milestones in this course. Further information can be obtained on the web in the notes on Monte Carlo Methods by Coddington, or the notes on Monte Carlo by Hrothgar.

## General References

*Statistical Mechanics*by L. D. Landau and L. Lifschitz, Pergamon Press, 1977.*Statistical Mechanics*by R. K. Pathria, Pergamon Press, 1977.*Statistical Mechanics*by K. Huang, Wiley Eastern, 1988.*Pauli Lectures on Physics: Vol 4. Statistical Mechanics*by W. Pauli, ed. C.P. Enz, The MIT press, 1973.

© Sourendu Gupta. Created on Dec 11, 2001.