Large Improved Wick Rotation Prescription in Stochastic Quantization of Dissipative Systems

TL;DR

This paper enhances the stochastic quantization method for dissipative systems at finite temperature by introducing an improved Wick rotation, clarifying its relation to the Caldeira-Leggett model and deriving a generalized fluctuation-dissipation theorem.

Contribution

It proposes a novel improved Wick rotation prescription in stochastic quantization, linking it to the Caldeira-Leggett model and deriving a generalized fluctuation-dissipation relation.

Findings

The improved Wick rotation aligns the Langevin system with ideal friction at low temperatures.

The approach clarifies the connection between stochastic quantization and dissipative quantum systems.

A general formula for fluctuation-dissipation theorem with higher derivatives is derived.

Abstract

We apply Stochastic Quantization Method to dissipative systems at finite temperature. Especially, the relation of SQM to the Caldeira-Leggett model is clarified ensuring that the naive Wick rotation is improved in this context. We show that the Langevin system obtained by the \lq\lq Improved Wick Rotation " prescription is equivalent to an ideal friction case ( low temperature limit) in the C-L model. We derive, based on our approach, a general formula on the fluctuation-dissipation theorem for higher derivative frictions.