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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 8, Pages 1383–1393 (Mi zvmmf10989)  

This article is cited in 1 scientific paper (total in 1 paper)

Dynamics of a set of quantum states generated by a nonlinear Liouville–von Neumann equation

A. D. Grekhnevaa, V. Zh. Sakbaevbcde

a Gromov Flight Research Institute, Zhukovskii, Moscow oblast, 140180 Russia
b Moscow Institute of Physics and Technology (National Research University), Dolgoprudnyi, Moscow oblast, 141701 Russia
c Steklov Mathematical Institute, Russian Academy of Sciences, 119991, Moscow, Russia
d Open Education Institute, Lobachevsky State University of Nizhny Novgorod (National Research University), Nizhny Novgorod, 603950 Russia
e Institute of Mathematics with Computing Center, Ufa Federal Research Center, Russian Academy of Sciences, Ufa, 450008 Bashkortostan, Russia

Abstract: A model describing the dynamics of a set of quantum states generated by a nonlinear Schrödinger equation is studied. The relationship between the blow-up of a solution with self-focusing and the transition from pure to mixed states of a quantum system was investigated in [1]. In this context, a natural question is concerned with the dynamics generated by the nonlinear Schrödinger equation in the set of mixed quantum states. The dynamics of mixed quantum states is described by the Liouville–von Neumann equation corresponding to the nonlinear Schrödinger equation. For the former equation, conditions for the global existence of a unique solution of the Cauchy problem and blow-up conditions are obtained.

Key words: nonlinear Schrödinger equation, quantum state, gradient catastrophe, regularization.

DOI: https://doi.org/10.31857/S0044466920080098


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:8, 1337–1347

Bibliographic databases:

UDC: 517.63
Received: 07.11.2019
Revised: 07.11.2019
Accepted:09.04.2020

Citation: A. D. Grekhneva, V. Zh. Sakbaev, “Dynamics of a set of quantum states generated by a nonlinear Liouville–von Neumann equation”, Zh. Vychisl. Mat. Mat. Fiz., 60:8 (2020), 1383–1393; Comput. Math. Math. Phys., 60:8 (2020), 1337–1347

Citation in format AMSBIB
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\paper Dynamics of a set of quantum states generated by a nonlinear Liouville--von Neumann equation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2020
\vol 60
\issue 8
\pages 1383--1393
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\transl
\jour Comput. Math. Math. Phys.
\yr 2020
\vol 60
\issue 8
\pages 1337--1347
\crossref{https://doi.org/10.1134/S0965542520080096}
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    This publication is cited in the following articles:
    1. L. S. Efremova, E. N. Makhrova, “Odnomernye dinamicheskie sistemy”, UMN, 76:5(461) (2021), 81–146  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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