Overview: Statistical mechanics applications


In this chapter you will begin to learn about statistical mechanics. Before delving too deeply into the theory you will do some computer programming exercises that will help you better understand the terminology and methods of statistical mechanics. You will be introduced to a number of simple Hamiltonians for lattice systems and will learn how to calculate ensemble averages and partition functions for these systems using both analytic methods and numerical methods. The principle aim of these exercises is to get used to the notion of a microstate and the notion that the state of the system includes information on the probability of being in each microstate.

Aims

  • You should be able to write computer programs to generate all possible microstates for a system consisting of particles on a lattice.
  • You should be able to write computer programs that evaluate the Hamiltonian for interacting and non-interacting particles on a lattice.
  • You should be able to evaluate the canonical partition function and the ensemble average of the energy for systems consisting of a small number of interacting or non-interacting particles on a lattice both by writing a computer program. You should also be able to discuss why this approach fails when the number of particles in the system is large.
  • You should be able to write computer programs to evaluate histograms and correlation functions.
  • You should be able to evaluate the partition function and ensemble average for a system of non-interacting particles on a lattice analytically.
  • You should be able to explain how mean field theories can be used to approximate the Hamiltonian for systems of interacting particles.

Contact Details

School of Mathematics and Physics,
Queen's University Belfast,
Belfast,
BT7 1NN

Email: g.tribello@qub.ac.uk
Website: mywebsite