THERMAL-PROPERTIES OF INTERACTING BOSE FIELDS AND IMAGINARY-TIME STOCHASTIC DIFFERENTIAL-EQUATIONS

Matsubara Green's functions for interacting bosons are expressed as cl assical statistical averages corresponding to a linear imaginary-time stochastic differential equation. This makes direct numerical simulati ons applicable to the study of equilibrium quantum properties of boson s in the non-perturbative regime. To verify our results we discuss an oscillator with quartic anharmonicity as a prototype model for an inte racting Bose gas. An analytic expression for the characteristic functi on in a thermal state is derived and a Higgs-type phase transition dis cussed, which occurs when the oscillator frequency becomes negative.