Quantum Markov processes: From attractor structure to explicit forms of asymptotic states

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F18%3A00325008" target="_blank" >RIV/68407700:21340/18:00325008 - isvavai.cz</a>

Result on the web

<a href="https://link.springer.com/article/10.1140%2Fepjp%2Fi2018-12109-8" target="_blank" >https://link.springer.com/article/10.1140%2Fepjp%2Fi2018-12109-8</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1140/epjp/i2018-12109-8" target="_blank" >10.1140/epjp/i2018-12109-8</a>

Result language

angličtina

Original language name

Quantum Markov processes: From attractor structure to explicit forms of asymptotic states

Original language description

Markov processes play an important role in physics and in particular in the theory of open systems. In this paper we study the asymptotic evolution of trace-nonincreasing homogeneous quantum Markov processes (both types, discrete quantum Markov chains and continuous quantum Markov dynamical semigroups) equipped with a subinvariant faithful state in the Schrödinger and the Heisenberg picture. We derive a fundamental theorem specifying the structure of the asymptotics and uncover a rich set of transformations between attractors of quantum Markov processes in both pictures. Moreover, we generalize the structure theorem derived earlier for quantum Markov chains to quantum Markov dynamical semigroups showing how the internal structure of generators of quantum Markov processes determines attractors in both pictures. Based on these results we provide two characterizations of all asymptotic and stationary states, both strongly reminding in form the well-known Gibbs states of statistical mechanics. We prove that the dynamics within the asymptotic space is of unitary type, i.e. quantum Markov processes preserve a certain scalar product of operators from the asymptotic space, but there is no corresponding unitary evolution on the original Hilbert space of pure states. Finally simple examples illustrating the derived theory are given.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10300 - Physical sciences

Project

<a href="/en/project/GA16-09824S" target="_blank" >GA16-09824S: Equilibrium formation in quantum networks</a><br>

Continuities

S - Specificky vyzkum na vysokych skolach

Publication year

2018

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

EUROPEAN PHYSICAL JOURNAL PLUS

ISSN

2190-5444

e-ISSN

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Volume of the periodical

133

Issue of the periodical within the volume

310

Country of publishing house

DE - GERMANY

Number of pages

17

Pages from-to

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UT code for WoS article

000440760100002

EID of the result in the Scopus database

2-s2.0-85052108746