Dissipative Quantum Systems in ThermoField Dynamics

TL;DR

This paper explores dissipative quantum systems interacting with thermal environments using ThermoField Dynamics, providing a framework for calculating observable averages in such systems.

Contribution

It introduces a novel approach combining Schwinger's Measurement Algebra with ThermoField Dynamics to analyze dissipative quantum systems in thermal equilibrium.

Findings

Established a method to compute statistical mean values as matrix elements in TFD.

Linked SMA operators with TFD vacuum states for dissipative systems.

Provided a theoretical foundation for future studies of quantum dissipation in thermal environments.

Abstract

We investigate a class of microscopic systems in interaction with a macroscopic system in thermal equilibrium, following the construction of Dalibard, Dupont-Roc and Cohen-Tannoudji (DDC). By considering self-adjoint operators as elements of Schwinger's Measurement Algebra (SMA), we construct statistical mean values of the relevant observables as matrix elements in a suitable operator basis, which correspond to the vacuum states of ThermoField Dynamics (TFD).