Andreas Mielke
Institut for Theoretical Physics
Ruprecht-Karls University
Philosophenweg 19
D-69120 Heidelberg
Germany
Tel.: ++49 6221 549431 (Secretary)
Fax: ++49 6221 549331
e-mail: mielke@tphys.uni-heidelberg.de

### Andreas Mielke: Diagonalization of Dissipative Quantum Systems I: Exact solution of the Spin-Boson Model with an Ohmic bath at $\alpha =1/2$preprint, (2000) .

#### Abstract

This paper shows how flow equations can be used to diagonalize dissipative quantum systems. Applying a continuous unitary transformation to the spin-boson model, one obtains exact flow equations for the Hamiltonian and for an observable. They are solved exactly for the case of an Ohmic bath with a coupling $\alpha =1/2$. Using the explicite expression for the transformed observable one obtains dynamical correlation functions. This yields some new insight to the exactly solvable case $\alpha =1/2$. The main motivation of this work is to demonstrate, how the method of flow equations can be used to treat dissipative quantum systems in a new way. The approach can be used to construct controllable approximation schemes for other environments.

#### BibTeX-entry

@article{Mielke2000,
author="Andreas Mielke",
title="Diagonalization of Dissipative Quantum Systems I: Exact solution of the Spin-Boson Model with an Ohmic bath at $\alpha =1/2$",
journal="preprint",
year="2000"
}


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Last changes: 17.6.2018. mielke@tphys.uni-heidelberg.de