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Mat. Zametki, 2017, Volume 102, Issue 6, Pages 908–916 (Mi mz11613)  

This article is cited in 7 scientific papers (total in 7 papers)

Quadratic Fermionic Dynamics with Dissipation

A. E. Teretenkov

Lomonosov Moscow State University

Abstract: Gaussian solutions of the Cauchy problem for the GKS-L equation (in the Schrödinger picture) with quadratic fermionic generators are obtained. These Gaussian solutions are represented both as exponentials of quadratic forms in fermionic creation-annihilation operators and by their normal symbols. The coefficients of these forms are represented as algebraic functions of matrices.

Keywords: the Gorini–Kossakowski–Sudarshan equation, the Lindblad equation, quantum dissipation, Gaussian states, completely positive quantum dynamics.

DOI: https://doi.org/10.4213/mzm11613

Full text: PDF file (488 kB)
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English version:
Mathematical Notes, 2017, 102:6, 846–854

Bibliographic databases:

UDC: 517
Received: 29.03.2017

Citation: A. E. Teretenkov, “Quadratic Fermionic Dynamics with Dissipation”, Mat. Zametki, 102:6 (2017), 908–916; Math. Notes, 102:6 (2017), 846–854

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. I. Trubilko, A. M. Basharov, “Kinetic equation for the density matrix of atoms in the field of a broadband one-photon packet taking into account the non-Wiener dynamics”, J. Exp. Theor. Phys., 126:5 (2018), 604–619  crossref  crossref  isi  elib  elib  scopus
    2. A. E. Teretenkov, “Dynamics of Moments for Quadratic GKSL Generators”, Math. Notes, 106:1 (2019), 151–155  mathnet  crossref  crossref  mathscinet  isi  elib
    3. A. E. Teretenkov, “Pseudomode Approach and Vibronic Non-Markovian Phenomena in Light-Harvesting Complexes”, Proc. Steklov Inst. Math., 306 (2019), 242–256  mathnet  crossref  crossref  mathscinet  isi  elib
    4. A. E. Teretenkov, “Irreversible quantum evolution with quadratic generator: review”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 22:4 (2019), 1930001  crossref  mathscinet  zmath  isi
    5. A. E. Teretenkov, “Dynamics of Moments of Arbitrary Order for Stochastic Poisson Compressions”, Math. Notes, 107:4 (2020), 695–698  mathnet  crossref  crossref  mathscinet  isi  elib
    6. Yu. A. Nosal, A. E. Teretenkov, “Exact Dynamics of Moments and Correlation Functions for GKSL Fermionic Equations of Poisson Type”, Math. Notes, 108:6 (2020), 911–915  mathnet  crossref  crossref  mathscinet  isi  elib
    7. A. E. Teretenkov, “An Example of Explicit Generators of Local and Nonlocal Quantum Master Equations”, Proc. Steklov Inst. Math., 313 (2021), 236–245  mathnet  crossref  crossref  isi  elib
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