# Accession Number:

## AD0676668

# Title:

## STATISTICAL MECHANICS OF EQUILIBRIUM, NON-EQUILIBRIUM AND QUANTUM MANY-BODY PROCESSES.

# Descriptive Note:

## Final rept. 1 Oct 65-1 Oct 67,

# Corporate Author:

## YESHIVA UNIV NEW YORK BELFER GRADUATE SCHOOL OF SCIENCE

# Personal Author(s):

# Report Date:

## 1967-12-01

# Pagination or Media Count:

## 16.0

# Abstract:

Several general results are obtained for a system of spins on a lattice in which the various lattice sites are occupied at random, and the spins, if present, interact via a general Heisenberg or Ising interaction decreasing sufficiently rapidly with distance. For a system of non-interacting particles which interact with randomly distributed scattering centers Feynmans path integral formulation of quantum statistics is used to derive some properties of the average partition function for one particle. A detailed study has been made of the time evolution of the distribution function of a labeled particle in a one-dimensional system of hard rods of diameter a. The stationary non-equilibrium Gibbsian ensemble representing a harmonic crystal in contact with several idealized heat reservoirs at different temperatures is shown to have a Gaussian gamma-space distribution for the case where the stochastic interaction between the system and heat reservoirs may be represented by Fokker-Planck type operators. The magnetic properties of a single non-degenerate band with short range intra-atomic electron interactions was studied. A generalized Hartree-Fock formalism was developed which gives closed expressions for all ordered magnetic states with constant local moments lying on a conical helix. Singlet-triplet pair Green functions were formulated and studied for the s-d exchange model of the dilute magnetic alloys for a single magnetic impurity. Author

# Descriptors:

# Subject Categories:

- Physical Chemistry
- Solid State Physics