Chapter

Long-time diffusion for a quantum particle

Wojciech De Roeck

in Quantum Theory from Small to Large Scales

Published in print May 2012 | ISBN: 9780199652495
Published online September 2012 | e-ISBN: 9780191741203 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199652495.003.0009

Series: Lecture Notes of the Les Houches Summer School

Long-time diffusion for a quantum particle

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This chapter reviews and summarizes some recent progress on the rigorous derivation of irreversible behaviour in simple models of open quantum systems, in particular spins and particles interacting with phonons or photons. In this derivation, ‘Markov’ approximations play a distinguished role. Such approximations can often be derived in a scaling limit where, depending on the model, space, time, and coupling strength are scaled so as to eliminate memory effects. Because of the scaling limit involved, the description one obtains is valid only for times that are not too long (compared to the coupling strength). To obtain information in the long-time limit, one therefore has to go beyond the Markov approximation.

Keywords: quantum field theory; Lindblad operators; Markov approximation; Van Hove scaling limit; open quantum systems

Chapter.  4810 words. 

Subjects: Atomic, Molecular, and Optical Physics

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