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TMF, 2009, Volume 158, Number 2, Pages 214–233 (Mi tmf6310)  

This article is cited in 13 scientific papers (total in 13 papers)

Fractional generalization of the quantum Markovian master equation

V. E. Tarasov

Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University

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 $\alpha=0$, the environment completely influences the system for $\alpha=1$, and we have a powerlike environmental influence for $0<\alpha<1$.

Keywords: fractional power of an operator, non-Hamiltonian quantum system, quantum Markovian equation, completely positive semigroup


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English version:
Theoretical and Mathematical Physics, 2009, 158:2, 179–195

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Received: 27.03.2008
Revised: 23.06.2008

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
\by V.~E.~Tarasov
\paper Fractional generalization of the~quantum Markovian master equation
\jour TMF
\yr 2009
\vol 158
\issue 2
\pages 214--233
\jour Theoret. and Math. Phys.
\yr 2009
\vol 158
\issue 2
\pages 179--195

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    This publication is cited in the following articles:
    1. Iomin, A, “Fractional-time quantum dynamics”, Physical Review E, 80:2 (2009), 022103  crossref  mathscinet  adsnasa  isi  elib  scopus  scopus
    2. 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
    3. Tarasov V.E., “Quantum Dissipation From Power-Law Memory”, Ann. Phys., 327:6 (2012), 1719–1729  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    4. 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
    5. 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
    6. 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
    7. Tarasov V.E., “Fractional Diffusion Equations for Open Quantum System”, Nonlinear Dyn., 71:4, SI (2013), 663–670  crossref  mathscinet  isi  scopus  scopus
    8. 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
    9. Tarasov V.E., “Fractional Quantum Field Theory: From Lattice To Continuum”, Adv. High. Energy Phys., 2014, 957863  crossref  mathscinet  isi  scopus  scopus
    10. 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
    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. 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
    13. Ozturk O., Yilmazer R., “An Application of the Sonine-Letnikov Fractional Derivative For the Radial Schrodinger Equation”, Fractal Pract., 3:2 (2019), 16  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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