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Fractional diffusion equations for open quantum system

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Abstract

To describe non-local interactions of quantum systems with environment we consider a fractional generalization of the quantum Markovian equation. Quantum analogs of fractional Laplacian operator for coordinate and momentum spaces are suggested. In phase-space form of quantum mechanics we obtain fractional equations for Wigner distribution function, where fractional Laplacian operators of the Grünvald–Letnikov type are used.

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Acknowledgements

The author expresses his gratitude to the guest editors Professor Juan J. Trujillo, Professor Dumitru Baleanu, Professor Donal O’Regan for kind invitation to contribute to a special issue titled “Nonlinear Fractional Differential equations and their applications”, in the journal Nonlinear Dynamics, which celebrates Professor Ravi P. Agarwal’s 65th birthday.

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  1. Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, 119991, Russia

    Vasily E. Tarasov

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  1. Vasily E. Tarasov
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Correspondence to Vasily E. Tarasov.

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Tarasov, V.E. Fractional diffusion equations for open quantum system. Nonlinear Dyn 71, 663–670 (2013). https://doi.org/10.1007/s11071-012-0498-8

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  • DOI: https://doi.org/10.1007/s11071-012-0498-8

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