Repeated Interaction Quantum Systems: van Hove Limits and Asymptotic States

Details Repeated Interaction Quantum Systems: van Hove Limits and Asymptotic States Repeated Interaction Quantum Systems: van Hove Limits and Asymptotic States

2008-04-10

arxiv.org/abs/0804.1783v2

Physics

Mathematical Physics

Final version accepted in J. Stat. Phys., some proofs corrected. 18 pages, no figures

Scientific paper

10.1007/s10955-008-9605-0

We establish the existence of two weak coupling regime effective dynamics for an open quantum system of repeated interactions (vanishing strength and individual interaction duration, respectively). This generalizes known results in that the von Neumann algebras describing the system and the chain element may not be of finite type. Then (but now assuming that the small system is of finite type), we prove that both effective dynamics capture the long-term behaviour of the system: existence of a unique asymptotic state for them implies the same property for the respective exact dynamics--provided that the perturbation parameter is sufficiently small. The zero-th order term in a power series expansion in the perturbation parameter of such an asymptotic state is given by the asymptotic state of the effective dynamics. We conclude by working out the case in which the small system and the chain element are spins.

Affiliated with

Also associated with

No associations

Rating

Repeated Interaction Quantum Systems: van Hove Limits and Asymptotic States does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Repeated Interaction Quantum Systems: van Hove Limits and Asymptotic States, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Repeated Interaction Quantum Systems: van Hove Limits and Asymptotic States will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-356614