Low temperature equilibrium correlation functions in dissipative quantum systems

TL;DR

This paper presents a novel theoretical method for analyzing dissipative quantum systems at low temperatures, using continuous unitary transformations to decouple the system from its environment and study correlation functions.

Contribution

A new approach employing infinitesimal unitary transformations to analyze dissipative quantum systems and their equilibrium correlation functions at low temperatures.

Findings

Effective description of the spin-boson model with super-Ohmic bath

Accurate results across various time scales at small temperatures

Validation via the generalized Shiba-relation within numerical errors

Abstract

We introduce a new theoretical approach to dissipative quantum systems. By means of a continuous sequence of infinitesimal unitary transformations, we decouple the small quantum system that one is interested in from its thermodynamically large environment. This yields a trivial final transformed Hamiltonian. Dissipation enters through the observation that generically observables ``decay'' completely under these unitary transformations, i.e. are completely transformed into other terms. As a nontrivial example the spin-boson model is discussed in some detail. For the super-Ohmic bath we obtain a very satisfactory description of short, intermediate and long time scales at small temperatures. This can be tested from the generalized Shiba-relation that is fulfilled within numerical errors.