CLASSICAL STATISTICAL MECHANICS OF THE HARD-CORE POTENTIAL.
Abstract
The purpose of this work is to discuss the difficulties associated with representing the strong short ranged forces between the particles of a many-body system and to describe a method by which a more exact treatment of the N-body system becomes available without restricted domains or excluded volume regions provided that certain physical properties of the two-body scattering are retained. The method employed, that of an extended canonical point-transformation, is based on providing an equivalent nonsingular Hamiltonian which is both Hermitian and Fourier analyzable. The price of such a transformation is the introduction of non-local velocity dependent interactions between the particles. But such forms are well known in classical mechanics and can be treated in a statistical mechanical context without difficulty. This approach allows for an immediate means of analysis of the role of the hard-core interactions in a many-body system which may be treated by any of the conventional methods of statistical physics. Direct contact is made with the more usual expressions for a hard-sphere many-body system and it is explicitly demonstrated that the real advantage of this canonical reformulation of the strong interactions in terms of an equivalent momentum dependent potential lies in allowing the repulsion to be treated in the same manner as any weak long ranged interaction. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1966
- Accession Number
- AD0638830
Entities
People
- Martin J. Cooper
Organizations
- Brandeis University