Time inversion in dynamical systems
2004 (English)In: Annals of Physics, ISSN 0003-4916, E-ISSN 1096-035X, Vol. 310, no 1, 106-126 p.Article in journal (Refereed) Published
We consider the case of a dynamical system when the time evolution is generated by a non-hermitian superoperator on the states of the system. Assuming the left and right eigenvectors of this to provide complete basis sets, we propose a generalized scalar product which can be used to construct a monotonically changing functional of the state, a generalized entropy. Combining the time-dependent state with its time-reversed counterpart we can define the operation of time inversion even in this case of irreversible evolution. We require that both the forward and reversed time evolution can be obtained from a generalized action principle, and this demand serves to define the form of the time-reversed state uniquely. The work thus generalizes the quantum treatment from the unitary case to the irreversible one. We present a discussion of the approach and derive some of the direct consequences of our results.
Place, publisher, year, edition, pages
2004. Vol. 310, no 1, 106-126 p.
open quantum systems, irreversible evolution, time inversion, time-reversed state, generalized entropy
IdentifiersURN: urn:nbn:se:kth:diva-45360DOI: 10.1016/j.aop.2003.09.001ISI: 000189100500004ScopusID: 2-s2.0-1442280667OAI: oai:DiVA.org:kth-45360DiVA: diva2:452840
QC 201110312011-10-312011-10-282011-10-31Bibliographically approved