Models for local ohmic quantum dissipation

TL;DR

This paper develops local quantum dissipation models using Lindblad master equations that are linear, isotropic, and translationally invariant, providing a more general framework for understanding quantum decoherence and relaxation.

Contribution

It introduces a new class of Lindblad master equations for local ohmic quantum dissipation with specific symmetry constraints, expanding the modeling capabilities beyond traditional approaches.

Findings

Derived fluctuation-dissipation relations.

Analyzed relaxation to thermal equilibrium.

Compared with Dekker and Caldeira-Leggett models.

Abstract

We construct model master equations for local quantum dissipation. The master equations are in the form of Lindblad generators, with imposed constraints that the dissipations be strictly linear (i.e. ohmic), isotropic and translationally invariant. A particular form for is chosen to satisfy the constraints. The resulting master equations are given in both the Schr\"odinger and Heisenberg forms. We obtain fluctuation-dissipation relations, and discuss the relaxation of average kinetic energy to effective thermal equilibrium values. We compare our results to the Dekker and the Caldeira-Leggett master equations. These master equations allow a more general approach to quantum dissipation and the dynamics of quantum coherence to account for the nontrivial system-environment coupling in a local environment.