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Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 158, Number 2, Pages 214–233
DOI: https://doi.org/10.4213/tmf6310
(Mi tmf6310)
 

This article is cited in 23 scientific papers (total in 23 papers)

Fractional generalization of the quantum Markovian master equation

V. E. Tarasov

Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University
References:
Abstract: We propose a generalization of the quantum Markovian equation for observables. In this generalized equation, we use superoperators that are fractional powers of completely dissipative superoperators. We prove that the suggested superoperators are infinitesimal generators of completely positive semigroups and describe the properties of this semigroup. We solve the proposed fractional quantum Markovian equation for the harmonic oscillator with linear friction. A fractional power of the Markovian superoperator can be considered a parameter describing a measure of "screening" of the environment of the quantum system: the environmental influence on the system is absent for α=0, the environment completely influences the system for α=1, and we have a powerlike environmental influence for 0<α<1.
Keywords: fractional power of an operator, non-Hamiltonian quantum system, quantum Markovian equation, completely positive semigroup.
Received: 27.03.2008
Revised: 23.06.2008
English version:
Theoretical and Mathematical Physics, 2009, Volume 158, Issue 2, Pages 179–195
DOI: https://doi.org/10.1007/s11232-009-0015-5
Bibliographic databases:
Language: Russian
Citation: V. E. Tarasov, “Fractional generalization of the quantum Markovian master equation”, TMF, 158:2 (2009), 214–233; Theoret. and Math. Phys., 158:2 (2009), 179–195
Citation in format AMSBIB
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Linking options:
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  • https://doi.org/10.4213/tmf6310
  • https://www.mathnet.ru/eng/tmf/v158/i2/p214
  • This publication is cited in the following 23 articles:
    1. Andy Manapany, Sébastien Fumeron, Malte Henkel, “Fractional diffusion equations interpolate between damping and waves”, J. Phys. A: Math. Theor., 57:35 (2024), 355202  crossref
    2. Diethelm K., Kiryakova V., Luchko Yu., Machado J.A.T., Tarasov V.E., “Trends, Directions For Further Research, and Some Open Problems of Fractional Calculus”, Nonlinear Dyn., 107:4 (2022), 3245–3270  crossref  isi
    3. Tarasov V.E., “General Non-Markovian Quantum Dynamics”, Entropy, 23:8 (2021), 1006  crossref  mathscinet  isi
    4. Tarasov V.E., “Non-Markovian Dynamics of Open Quantum System With Memory”, Ann. Phys., 434 (2021), 168667  crossref  mathscinet  isi
    5. Tarasov V.E., “Lattice Fractional Quantum Field Theory: Exact Differences Approach”, Mod. Phys. Lett. A, 36:14 (2021), 2140001  crossref  mathscinet  isi
    6. Beybalaev V.D. Abduragimov I E. Yakubov A.Z. Meilanov R.R. Aliverdiev A.A., “Numerical Research of Non-Isothermal Filtration Process in Fractal Medium With Non-Locality in Time”, Therm. Sci., 25:1, B (2021), 465–475  crossref  isi
    7. Tarasov V.E., “Quantum Maps With Memory From Generalized Lindblad Equation”, Entropy, 23:5 (2021), 544  crossref  mathscinet  isi
    8. El-Nabulsi R.A., “On Generalized Fractional Spin, Fractional Angular Momentum, Fractional Momentum Operators in Quantum Mechanics”, Few-Body Syst., 61:3 (2020), 25  crossref  isi
    9. Wang J., Zhang L., Mao J., Zhou J., Xu D., “Fractional Order Equivalent Circuit Model and Soc Estimation of Supercapacitors For Use in Hess”, IEEE Access, 7 (2019), 52565–52572  crossref  isi
    10. Ozturk O., Yilmazer R., “An Application of the Sonine-Letnikov Fractional Derivative For the Radial Schrodinger Equation”, Fractal Pract., 3:2 (2019), 16  crossref  mathscinet  isi
    11. Tarasov V.E., Tarasova V.V., “Time-Dependent Fractional Dynamics With Memory in Quantum and Economic Physics”, Ann. Phys., 383 (2017), 579–599  crossref  mathscinet  zmath  isi  scopus  scopus
    12. Kostrobij P. Markovych B. Viznovych O. Tokarchuk M., “Generalized diffusion equation with fractional derivatives within Renyi statistics”, J. Math. Phys., 57:9 (2016), 093301  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    13. Tarasov V.E., “Fractional Quantum Field Theory: From Lattice To Continuum”, Adv. High. Energy Phys., 2014, 957863  crossref  mathscinet  isi  scopus  scopus
    14. Calik A.E., Ertik H., Oder B., Sirin H., “A Fractional Calculus Approach to Investigate the Alpha Decay Processes”, Int. J. Mod. Phys. E-Nucl. Phys., 22:7 (2013), 1350049  crossref  adsnasa  isi  scopus  scopus
    15. Tarasov V.E., “Review of Some Promising Fractional Physical Models”, Int. J. Mod. Phys. B, 27:9 (2013), 1330005  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    16. Tarasov V.E., “Fractional Diffusion Equations for Open Quantum System”, Nonlinear Dyn., 71:4, SI (2013), 663–670  crossref  mathscinet  isi  scopus  scopus
    17. Mongiovi M.S., Zingales M., “A Non-Local Model of Thermal Energy Transport: the Fractional Temperature Equation”, Int. J. Heat Mass Transf., 67 (2013), 593–601  crossref  isi  elib  scopus  scopus
    18. Tarasov V.E., “Quantum Dissipation From Power-Law Memory”, Ann. Phys., 327:6 (2012), 1719–1729  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    19. Tarasov V.E., “The Fractional Oscillator as an Open System”, Cent. Eur. J. Phys., 10:2 (2012), 382–389  crossref  mathscinet  isi  elib  scopus  scopus
    20. Sirin H., Buyukkilic F., Ertik H., Demirhan D., “The effect of time fractality on the transition coefficients: Historical Stern-Gerlach experiment revisited”, Chaos Solitons & Fractals, 44:1–3 (2011), 43–47  crossref  zmath  adsnasa  isi  scopus  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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