The limiting dynamics of an imperfect Bose gas

Abstract

For an imperfect Bose gas consisting of massive particles and interacting through a long-range pair potential in a mean-field approximation, both in equilibrium and far from equilibrium, the dynamics are derived in the thermodynamic limit. This is done in the framework of the operator algebraic quantum theory. The limiting dynamics is formulated in the Schrödinger picture as a group of affine transformations of certain folia of physical states. Similar to the mean-field models for spin lattices, the algebra of quasilocal observables is not invariant under the Heisenberg dynamics in the GNS representation of general time invariant states. It is known that above critical density the infinite system exhibits condensation, and the condensate is characterized by the classical parameters density and phase. For these parameters a classical nonlinear equation of motion is derived.