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Low temperature equilibrium correlation functions in dissipative quantum systems
Author(s) -
Kehrein Stefan K.,
Mielke Andreas
Publication year - 1997
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19975090203
Subject(s) - dissipative system , physics , hamiltonian (control theory) , unitary state , infinitesimal , quantum , observable , boson , dissipation , dissipative operator , quantum system , quantum mechanics , statistical physics , mathematics , mathematical analysis , mathematical optimization , political science , law
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.