On Howland time-independent formulation of CP-divisible quantum evolutions

Krzysztof Szczygielski , Robert Alicki


We extend Howland time-independent formalism to the case of completely positive and trace preserving dynamics of finite-dimensional open quantum systems governed by periodic, time-dependent Lindbladian in Weak Coupling Limit, expanding our result from previous papers. We propose the Bochner space of periodic, square integrable matrix-valued functions, as well as its tensor product representation, as the generalized space of states within the time-independent formalism. We examine some densely defined operators on this space, together with their Fourier-like expansions and address some problems related to their convergence by employing general results on Banach space-valued Fourier series, such as the generalized Carleson–Hunt theorem. We formulate Markovian dynamics in the generalized space of states by constructing appropriate time-independent Lindbladian in standard (Lindblad–Gorini–Kossakowski–Sudarshan) form, as well as one-parameter semigroup of bounded evolution maps. We show their similarity with Markovian generators and dynamical maps defined on matrix space, i.e. the generator still possesses a standard form (extended by closed perturbation) and the resulting semigroup is also completely positive, trace preserving and a contraction.
Publication typeIn press (online first, early view)
Author Krzysztof Szczygielski (FMPI/ITPA)
Krzysztof Szczygielski,,
- Institute of Theoretical Physics and Astrophysics
, Robert Alicki (ICTQT)
Robert Alicki,,
- International Centre for Theory of Quantum Technologies
Journal seriesReviews in Mathematical Physics, ISSN 0129-055X, e-ISSN 1793-6659, (N/A 100 pkt)
Issue year2019
Noonline first
Publication size in sheets0.30
Article number2050021
Keywords in Polishkwantowe układy otwarte, dynamika CP-podzielna, formalizm Floqueta, przestrzenie Bochnera
Keywords in Englishopen quantum systems, CP-divisible dynamics, Floquet formalism, Bochner spaces
ASJC Classification2610 Mathematical Physics; 3109 Statistical and Nonlinear Physics
Languageen angielski
Score (nominal)100
Score sourcejournalList
ScoreMinisterial score = 100.0, 07-03-2020, ArticleFromJournal
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2016 = 1.432; WoS Impact Factor: 2018 = 1.092 (2) - 2018=1.327 (5)
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