Dissipative generation of pure steady states and a gambler's ruin problem

Popkov, Vladislav (author), Essink, Simon (author), Kollath, Corinna (author), Presilla, Carlo (author)

We consider an open quantum system, with dissipation applied only to a part of its degrees of freedom, evolving via a quantum Markov dynamics. We demonstrate that, in the Zeno regime of large dissipation, the relaxation of the quantum system towards a pure quantum state is linked to the evolution of a classical Markov process towards a single absorbing state. The rates of the associated classical Markov process are determined by the original quantum dynamics. Extension of this correspondence to absorbing states with internal structure allows us to establish a general criterion for having a Zeno-limit nonequilibrium stationary state of arbitrary finite rank. An application of this criterion is illustrated in the case of an open XXZ spin-1/2 chain dissipatively coupled at its edges to baths with fixed and different polarizations. For this system, we find exact nonequilibrium steady-state solutions of ranks 1 and 2.

• Language: English
• Keywords: quantum mechanics, open quantum systems, Markov processes
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Author Accepted Manuscript
• Year: 2020
• Number of pages: Str. 032205-1-032205-7
• Numbering: Vol. 102, iss. 3
• PID: 20.500.12556/RUL-124029
• UDC: 530.145
• ISSN on article: 2469-9926
• DOI: 10.1103/PhysRevA.102.032205
• COBISS.SI-ID: 43012099
• Publication date in RUL: 21.12.2020

Record is a part of a journal

• Title: Physical review. A
• Publisher: American Physical Society
• ISSN: 2469-9926
• COBISS.SI-ID: 2996836

Secondary language

• Language: Slovenian
• Keywords: kvantna mehanika, odprti kvantni sistemi, markovski procesi

Projects

• Funder: EC - European Commission
• Funding programme: H2020
• Project number: 694544
• Name: Open Many-body Non-Equilibrium Systems
• Acronym: OMNES