STOCHASTIC MODELS FOR MANY-BODY SYSTEMS. I. INFINITE SYSTEMS IN THERMAL EQUILIBRIUM
Abstract
Some model Hamiltonians are proposed for quantummechanical many-body systems with pair forces. In the case of an infinite system in thermal equilibrium, they lead to temperature-domain propagator expansions which are expressible by closed, formally exact equations. The expansions are identical with infinite subclasses of terms from the propagator expansion for the true manybody problem. The two principal models introduced correspond, respectively, to ring and ladder summations from the true propagator expansions, but augmented by infinite classes of self-energy corrections. The latter are expected to yield damping of single-particle excitations. The eigenvalues of the ring and ladder model Hamiltonians are real, and they are bounded from below if the pair potential obeys certain conditions. The models are formulated for fermions, bosons, and distinguishable particles. In addition to the ring and ladder models, two simpler types are discussed, one of which yields the Hartree-Fock approximation to the true problem. A novel feature of all model Hamiltonians (except the Hartree-Fock) is that they contain an infinite number of parameters whose phases are fixed by random choices. Explicit closed expressions are obtained for the Helmholtz free energy of all the models in the classical limit. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1961
- Accession Number
- AD0264738
Entities
People
- Robert H. Kraichnan
Organizations
- New York University