Computer Simulation of Collapsing Systems

Abstract

In statistical mechanics one is usually concerned with mechanically stable N-particle systems for which the Hamiltonian H _N is assumed to be bounded from below by a constant ~ N. Theoretically this property can be proved¹ if (a) the system is treated quantum mechanically, (b) the particles of one sign of charge are all fermions, and (c) gravitation is neglected. Mechanical stability manifests itself in a positive micro canonical specific heat c _v . Systems for which c _v is negative are mechanically unstable, implying that for large N the relativistic Hamiltonian becomes unbounded from below and the system collapses². The gravitational collapse of stars after exhaustion of their nuclear fuel serves as an example which was given considerable attention in the past³. In view of the fact that the coupling of such systems to an external thermal bath is weak, the use of a micro canonical ensemble for the description of such phenomena seems to be a natural choice.