STOCHASTIC MODELS FOR MANY-BODY SYSTEMS. II. FINITE SYSTEMS AND STATISTICAL NON-EQUILIBRIUM
Some model Hamiltonians proposed for quantummechanical many-body systems with pair forces are considered. For infinite systems in thermal equilibrium, they lead to temperature-domain propagator expansions that are formally summable and expressible by closed equations. These expansions are identical with infinite subclasses of terms from the propagator expansion for the true many-body problem. The two principal models correspond to ring- and ladder-diagram summations from the true propagator expansion, augmented by infinite classes of self-energy corrections. The model Hamiltonians are called stochastic because they contain parameters whose phases are fixed by random choices. More general models are formulated that yield formally summable propagator expansions for finite systems. The analysis is extended to correlation and Green's functions defined for nonequilibrium ensembles. The nonequilibrium treatment is developed in the Heisenberg representation in such a way that unlinked diagrams do not arise. A basic convergence question associated with the formal closed equations for the model propagators and correlation functions is examined by means of finite-difference integration of the Heisenberg equations of motion. This procedure appears to converge independently of whether the perturbation expansions for the propagators and correlation functions converge. It yields substantial support for the validity of the formal closed model equations. (auth)
- Research Organization:
- New York Univ., New York
- Sponsoring Organization:
- USDOE
- NSA Number:
- NSA-16-022769
- OSTI ID:
- 4811754
- Journal Information:
- J. Math. Phys., Vol. Vol: 3; Other Information: Orig. Receipt Date: 31-DEC-62
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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