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Title: Lower bounds to the spectral gap of Davies generators

We construct lower bounds to the spectral gap of a family of Lindblad generators known as Davies maps. These maps describe the thermalization of quantum systems weakly coupled to a heat bath. The steady state of these systems is given by the Gibbs distribution with respect to the system Hamiltonian. The bounds can be evaluated explicitly, when the eigenbasis and the spectrum of the Hamiltonian is known. A crucial assumption is that the spectrum of the Hamiltonian is non-degenerate. Furthermore, we provide a counterexample to the conjecture, that the convergence rate is always determined by the gap of the associated Pauli master equation. We conclude that the full dynamics of the Lindblad generator has to be considered. Finally, we present several physical example systems for which the bound to the spectral gap is evaluated.
Authors:
 [1]
  1. Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
Publication Date:
OSTI Identifier:
22250736
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 54; Journal Issue: 12; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONVERGENCE; EQUATIONS; HAMILTONIANS; HEAT; MAPS; SPECTRA; STEADY-STATE CONDITIONS; THERMALIZATION