Mathematical Methods of Statistical Mechanics of Model Systems

The main aim of statistical mechanics is the determination of a connection between the microscopic and macroscopic levels in studying nature. It is closely connected with mathematical methods and has initiated new branches in mathematics such as the ergodic theory and the Monte Carlo Method. This text looks for the common properties among wide classes of model problems. It is divided into two parts. Part 1 reviews the basic model problems of statistical mechanics, accounting for some general methods of equilibrium statistical mechanics. Topics specifically discussed include classical models, models of the theory of superconductivity and the concept of quasi-averages. In the second part, a number of nonequilibrium statistical mechanics are examined, including kenetic equations and green functions, hydrodynamics of hard spheres and dynamics of systems interacting with Bose fields. Detailed examples are included throughout the text.