A. I. Burshtein, A. A. Zharikov, S. I. Temkin, “Non-Markov theory of sudden modulation”, TMF, 66:2 (1986), 253–263; Theoret. and Math. Phys., 66:2 (1986), 166

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Teoreticheskaya i Matematicheskaya Fizika, 1986, Volume 66, Number 2, Pages 253–263 (Mi tmf4621)

This article is cited in 18 scientific papers (total in 18 papers)

Non-Markov theory of sudden modulation

A. I. Burshtein, A. A. Zharikov, S. I. Temkin

Full-text PDF (1109 kB) Citations (18)

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Abstract: Kinetic equations are obtained for the averaged evolution operator of a quantum system whose Hamiltonian depends on a parameter that varies randomly in the time. It is assumed that the fluctuations of the parameter occur instantaneously, i.e., during the time of a “jump” that is appreciably shorter than the mean interval between jumps, when the parameter keeps a constant value. For an arbitrary distribution with respect to the times between jumps, the “noise” effect that modulates parametrically the system is not a Markov process. Nevertheless, one can find for the response of the system closed integrodifferential equations that contain as a special case the well-known results of the theory of sudden modulation for a homogeneous (Poisson) sequence of jumps in time. As an application, the reasons for oscillating behavior of the correlation functions of the dynamical variables in a dense medium are investigated.

Received: 19.12.1984

English version:
Theoretical and Mathematical Physics, 1986, Volume 66, Issue 2, Pages 166–173
DOI: https://doi.org/10.1007/BF01017769

Bibliographic databases:

Language: Russian

Citation: A. I. Burshtein, A. A. Zharikov, S. I. Temkin, “Non-Markov theory of sudden modulation”, TMF, 66:2 (1986), 253–263; Theoret. and Math. Phys., 66:2 (1986), 166–173

Citation in format AMSBIB

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\jour Theoret. and Math. Phys.

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\crossref{https://doi.org/10.1007/BF01017769}

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https://www.mathnet.ru/eng/tmf4621

https://www.mathnet.ru/eng/tmf/v66/i2/p253

This publication is cited in the following 18 articles:

Martin Falcke, Victor Nicolai Friedhoff, “The stretch to stray on time: Resonant length of random walks in a transient”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 28:5 (2018)
Helena Stage, Sergei Fedotov, “Non-linear continuous time random walk models”, Eur. Phys. J. B, 90:11 (2017)
V. P. Shkilev, “Boundary conditions for the subdiffusion equation”, J. Exp. Theor. Phys., 116:4 (2013), 703
Igor Goychuk, “Fractional-time random walk subdiffusion and anomalous transport with finite mean residence times: Faster, not slower”, Phys. Rev. E, 86:2 (2012)
E. Heinsalu, M. Patriarca, I. Goychuk, P. Hänggi, “Fractional Fokker-Planck subdiffusion in alternating force fields”, Phys. Rev. E, 79:4 (2009)
I.M. Sokolov, J. Klafter, “Continuous-time random walks in an oscillating field: Field-induced dispersion and the death of linear response”, Chaos, Solitons & Fractals, 34:1 (2007), 81
I. M. Sokolov, M. G. W. Schmidt, F. Sagués, “Reaction-subdiffusion equations”, Phys. Rev. E, 73:3 (2006)
Igor Goychuk, Peter Hänggi, “Quantum two-state dynamics driven by stationary non-Markovian discrete noise: Exact results”, Chemical Physics, 324:1 (2006), 160
I. M. Sokolov, J. Klafter, “Field-Induced Dispersion in Subdiffusion”, Phys. Rev. Lett., 97:14 (2006)
I. Goychuk, E. Heinsalu, M. Patriarca, G. Schmid, P. Hänggi, “Current and universal scaling in anomalous transport”, Phys. Rev. E, 73:2 (2006)
I. M. Sokolov, “Linear response to perturbation of nonexponential renewal process: A generalized master equation approach”, Phys. Rev. E, 73:6 (2006)
Igor Goychuk, Peter Hänggi, Jose L. Vega, Salvador Miret-Artés, “Non-Markovian stochastic resonance: Three-state model of ion channel gating”, Phys. Rev. E, 71:6 (2005)
A V Chechkin, R Gorenflo, I M Sokolov, “Fractional diffusion in inhomogeneous media”, J. Phys. A: Math. Gen., 38:42 (2005), L679
Igor Goychuk, “Rate processes with non-Markovian dynamical disorder”, The Journal of Chemical Physics, 122:16 (2005)
Igor Goychuk, Peter Hänggi, “Quantum dynamics in strong fluctuating fields”, Advances in Physics, 54:6-7 (2005), 525
Igor Goychuk, Peter Hänggi, “Fractional diffusion modeling of ion channel gating”, Phys. Rev. E, 70:5 (2004)
Igor Goychuk, “Quantum dynamics with non-Markovian fluctuating parameters”, Phys. Rev. E, 70:1 (2004)
A. A. Zharikov, S. I. Temkin, A. I. Burshtein, “Relaxation of the dynamic system induced by the parametric modulation of its hamiltonian by the functional of the Markov process”, Radiophys Quantum Electron, 33:6 (1990), 488

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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