Mathematics Department Statistical Mechanics and Quantum Probability Group 



Research Activities
Manyparticle classical and quantum systems, or small systems interacting with such large systems, are studied using the methods of equilibrium statistical mechanics (David Lavis), scaling limits (Larry Landau), and the new methods of statistical dynamics (Ray Streater). In addition to standard physical systems, manyneuron systems and brain function are also studied (Ton Coolen). A general method for constructing nonlinear dynamical systems obeying the first and second laws of thermodynamics is developed in Statistical Dynamics, by Ray Streater (Imperial College Press, 1995). An essentialrole is played by the nonlinear irreversible mapping Q which is a generalization of the Boltzmann Stosszahlansatz. A number of research projects are available in the areas of nonlinear heat equations, complicated chemically reacting systems, and reactiondiffusion equations for dense fluids. The standard methods of equilibrium statistical mechanics are used to study phase transitions in lattice spin models, the computer package Maple being used to reduce the transfer matrix to block diagonal form. These methods are described in Statistical Mechanics of Lattice Systems, Volume I(2nd edition) and Volume II, by D.A.Lavis and G.Bell (Springer, 1998).
Large time or spacetime scaling limits of quantum systems yield irreversible and classical behavior: On the Weak Coupling Limit for a Fermi Gas in a Random Potential, Reviews in Mathematical Physics 5 (1993) and Macroscopic Observation of a Quantum Particle in a Slowly Varying Potential, Annals of Physics 246 (1996), by Larry Landau. The timeevolution of a free quantum particle on a lattice is described by Bessel functions and a detailed study has yielded new monotonicity properties and precise bounds: Bessel Functions: Monotonicity and Bounds, to be published. 
Staff:
Ton Coolen Larry Landau David Lavis Ray Streater
Recent Departmental preprints
in statistical mechanics and quantum probability:

