Low temperature equilibrium correlation functions in dissipative quantum systems

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.

38 pages, LaTeX2e, seven postscript figures included, figure 8 is available on request from one of the authors (A.M.). The revised version contains minor changes, it will appear in this form in Ann. Physik (Leipzig) 1996

References in corpus (4)

• On the spin--boson model with a sub--Ohmic bath
• Equilibrium dynamics of the dissipative two-state system
• Flow Equations for Electron-Phonon Interactions
• Theory of the Anderson impurity model: The Schrieffer--Wolff transformation re--examined

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