Contributions to the theory of decaying states in a soluble quantum model

G.C. Stey, R. W. Gibberd

Luciano Fonda, G. C. Ghirardi

Luciano Fonda, G. C. Ghirardi

Marvin D. Girardeau

A soluble model of gas-liquid condensation is constructed by a quantum-mechanical extension of van Kampen's classical analysis. The Hamiltonian of a system of identical particles is separated into a ``core'' and a ``tail'' Hamiltonian. Following van Kampen, we simulate the actual core Hamiltonian by an effective Hamiltonian with the same free energy. The tail Hamiltonian is replaced by its diagonal part in a single-particle basis chosen self-consistently so that the thermodynamics is exactly soluble. The resultant free energy agrees with that of Lieb's quantum-mechanical extension of the van der Waals-Maxwell theory, without the necessity of taking the van der Waals limit of a suitably infinite-ranged and infinitely-weak attractive tail. However, the exchange contributions omitted from the model become negligible only in that limit.

Robert E. Parrott, Jay Lawrence

Quantum dynamics predicts that a metastable state should decay exponentially except at very early and very late times. We show through an exactly soluble model that if the decay products can interact weakly with their environment, then the exponential decay regime is prolonged to later times, while the exponential decay constant itself remains essentially unaffected . As the number of environmental degrees of freedom is increased, the asymptotic late-time decay follows higher powers of 1/ t and the exponential decay regime is extended without limit.

V. G. Emel'Yanov, Dimitri P. Kostomarov, V. I. Kukulin