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Publication details

Document type
Journal articles

Document subtype
Full paper

Title
Chaos, ergodicity, and equilibria in a quantum Kac model

Participants in the publication
Eric A. Carlen (Author)
RUTGERS UNIVERSITY
Maria C. Carvalho (Author)
Dep. Matemática
CMAF - Centro de Matemática e Aplicações Fundamentais 
Michael P. Loss (Author)

Scope
International

Refereeing
Yes

Summary
We introduce quantum versions of the Kac Master Equation and the Kac Boltzmann Equation. We study the steady states of each of these equations, and prove a propagation of chaos theorem that relates them. The Quantum Kac Master Equation (QKME) describes a quantum Markov semigroup \n, while the Kac Boltzmann Equation describes a non-linear evolution of density matrices on the single particle state space. All of the steady states of the N particle quantum system described by the QKME are separable, and thus the evolution described by the QKME is entanglement breaking. The results set the stage for a quantitative study of approach to equilibrium in quantum kinetic theory, and a quantitative study of the rate of destruction of entanglement in a class of quantum Markov semigroups describing binary interactions.

Date of Publication
2019-12

Where published
Advances in Mathematics

Publication Identifiers
ISSN - 0001-8708

Publisher
Elsevier BV

Volume
358

Number of pages
50
Starting page
106827

Document Identifiers
DOI - https://doi.org/10.1016/j.aim.2019.106827
URL - http://dx.doi.org/10.1016/j.aim.2019.106827

Keywords
Quantum Master Equation Completely Positive Equilibrium


Export

APA
Eric A. Carlen, Maria C. Carvalho, Michael P. Loss, (2019). Chaos, ergodicity, and equilibria in a quantum Kac model. Advances in Mathematics, 358, ISSN 0001-8708. eISSN . http://dx.doi.org/10.1016/j.aim.2019.106827

IEEE
Eric A. Carlen, Maria C. Carvalho, Michael P. Loss, "Chaos, ergodicity, and equilibria in a quantum Kac model" in Advances in Mathematics, vol. 358, 2019. 10.1016/j.aim.2019.106827

BIBTEX
@article{45061, author = {Eric A. Carlen and Maria C. Carvalho and Michael P. Loss}, title = {Chaos, ergodicity, and equilibria in a quantum Kac model}, journal = {Advances in Mathematics}, year = 2019, volume = 358 }