Low temperature equilibrium correlation functions in dissipative quantum systems

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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.

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