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

L. I. Plimak·M. Fleischhauer·D. F. Walls
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Abstract

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

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L. I. Plimak, M. Fleischhauer, D. F. Walls. 1998-10-07. Thermal Properties of Interacting Bose Fields and Imaginary-Time Stochastic Differential Equations. https://doi.org/10.1209/epl%2Fi1998-00411-9

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