期刊
REVIEWS IN MATHEMATICAL PHYSICS
卷 32, 期 7, 页码 -出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0129055X2050021X
关键词
Open quantum systems; CP-divisible dynamics; Floquet formalism; Bochner spaces
资金
- National Science Centre, Poland [2016/23/D/ST1/02043]
- ICTQT through the International Research Agendas Programme (IRAP) of the Foundation for Polish Science (FNP)
- European Union (EU)
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.
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