Thermal Properties of Interacting Bose Fields and Imaginary-Time Stochastic Differential Equations

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  • 17 December 1997
Abstract
Matsubara Green's functions for bosons interacting via a zero-range potential are expressed as statistical averages corresponding to a linear imaginary-time stochastic differential equation (SDE) with multiplicative noise. This makes direct numerical simulations applicable to the study of equilibrium quantum properties of bosons. We argue that the equation thus found is an Ito equation, based on a Pauli-Villars-type regularisation of the Matsubara diagram series. To verify this link between regularisations and stochastic calculus, we discuss an oscillator with quartic anharmonicity as a prototype model for an interacting Bose gas. We also study a finite version of the Higgs phase transition in the oscillator when its frequency becomes large and negative.

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