Unitary perturbation theory approach to real-time evolution problems

TL;DR

This paper introduces a new analytical method based on continuous unitary transformations to study real-time evolution in quantum many-body systems, effectively handling dissipative dynamics and non-equilibrium correlations.

Contribution

It extends the framework of continuous unitary transformations to solve Heisenberg equations of motion, providing a novel approach for dissipative quantum systems.

Findings

Accurately describes non-equilibrium correlation functions

Applies to exactly solvable and non-trivial dissipative models

Demonstrates effectiveness across all time scales

Abstract

We discuss a new analytical approach to real-time evolution in quantum many-body systems. Our approach extends the framework of continuous unitary transformations such that it amounts to a novel solution method for the Heisenberg equations of motion for an operator. It is our purpose to illustrate the accuracy of this approach by studying dissipative quantum systems on all time scales. In particular, we obtain results for non-equilibrium correlation functions for general initial conditions. We illustrate our ideas for the exactly solvable dissipative oscillator, and, as a non-trivial model, for the dissipative two-state system.