Diagonalization of system plus environment Hamiltonians

TL;DR

This paper introduces a novel method using continuous unitary transformations to diagonalize system-environment Hamiltonians, effectively decoupling the system from its environment and enabling analysis of dissipative quantum systems, especially at low temperatures.

Contribution

The paper presents a new diagonalization technique for system plus environment Hamiltonians using infinitesimal unitary transformations, improving analysis of dissipative quantum systems.

Findings

Successfully diagonalized the super-Ohmic spin-boson model

Demonstrated decay of system observables into different structures

Method is particularly effective at low temperatures

Abstract

A new approach to dissipative quantum systems modelled by a system plus environment Hamiltonian is presented. Using a continuous sequence of infinitesimal unitary transformations the small quantum system is decoupled from its thermodynamically large environment. Dissipation enters through the observation that system observables generically decay completely into a different structure when the Hamiltonian is transformed into diagonal form. The method is particularly suited for studying low-temperature properties. This is demonstrated explicitly for the super-Ohmic spin-boson model.