Variational model for the thermodynamic properties of a bose fluid

Summary

The interacting Bose fluid is studied on the basis of a variational principle for the thermodynamic potential. The Hamiltonian for a gas of noninteracting excitations, with a temperatureindependent spectrum, is used as the model Hamiltonian which appears in the variational principle. The excitations are assumed to be phonons for Wave vectors up toK _c and Bogoliubov excitations forK > K _c. Two cases are considered: in the first the wave-vector cut-offk _c is assumed to be zero and in the secondK _c is considered to be a variational parameter. In both cases it is found that the phase transition between the lowtemperature phase with a condensate and the high-temperature normal phase is a continuous transition. This contrasts with the first-order nature of the transition found on the basis of several model Hamiltonians.

Riassunto

Si studia un sistema di bosoni interagenti sulla base di un principio variazionale per il Potenziale termodinamico. L’uso di tale principio suggerisce l’introduzione di una Hamiltoniana modello ad eccitazioni elementari non interagenti, contenente opportuni parametri liberi da determinare variazionalmente. Si assume che lo spettro di energia delle