The law of large numbers for quantum stochastic filtering and control of many-particle systems

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The law of large numbers for quantum stochastic filtering and control of many-particle systems. / Kolokoltsov, V. N.

в: Theoretical and Mathematical Physics(Russian Federation), Том 208, № 1, 07.2021, стр. 937-957.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Author

Kolokoltsov, V. N. / The law of large numbers for quantum stochastic filtering and control of many-particle systems. в: Theoretical and Mathematical Physics(Russian Federation). 2021 ; Том 208, № 1. стр. 937-957.

BibTeX

@article{312980afab8f41bbbbf2ae2a330430b2,

title = "The law of large numbers for quantum stochastic filtering and control of many-particle systems",

abstract = "Abstract: There is an extensive literature on the dynamic law of large numbers for systems of quantum particles, that is, on the derivation of an equation describing the limiting individual behavior of particles in a large ensemble of identical interacting particles. The resulting equations are generally referred to as nonlinear Schr{\"o}dinger equations or Hartree equations, or Gross–Pitaevskii equations. In this paper, we extend some of these convergence results to a stochastic framework. Specifically, we work with the Belavkin stochastic filtering of many-particle quantum systems. The resulting limiting equation is an equation of a new type, which can be regarded as a complex-valued infinite-dimensional nonlinear diffusion of McKean–Vlasov type. This result is the key ingredient for the theory of quantum mean-field games developed by the author in a previous paper.",

keywords = "Belavkin equation, homodyne detection, infinite-dimensional McKean–Vlasov diffusion on manifold, nonlinear stochastic Schr{\"o}dinger equation, quantum control, quantum dynamic law of large numbers, quantum filtering, quantum interacting particles, quantum mean-field games, GAMES, EQUATIONS, nonlinear stochastic Schrodinger equation, infinite-dimensional McKean-Vlasov diffusion on manifold, EVOLUTION",

author = "Kolokoltsov, {V. N.}",

note = "Publisher Copyright: {\textcopyright} 2021, Pleiades Publishing, Ltd.",

year = "2021",

month = jul,

doi = "10.1134/S0040577921070084",

language = "English",

volume = "208",

pages = "937--957",

journal = "Theoretical and Mathematical Physics (Russian Federation)",

issn = "0040-5779",

publisher = "Springer Nature",

number = "1",

}

RIS

TY - JOUR

T1 - The law of large numbers for quantum stochastic filtering and control of many-particle systems

AU - Kolokoltsov, V. N.

PY - 2021/7

Y1 - 2021/7

N2 - Abstract: There is an extensive literature on the dynamic law of large numbers for systems of quantum particles, that is, on the derivation of an equation describing the limiting individual behavior of particles in a large ensemble of identical interacting particles. The resulting equations are generally referred to as nonlinear Schrödinger equations or Hartree equations, or Gross–Pitaevskii equations. In this paper, we extend some of these convergence results to a stochastic framework. Specifically, we work with the Belavkin stochastic filtering of many-particle quantum systems. The resulting limiting equation is an equation of a new type, which can be regarded as a complex-valued infinite-dimensional nonlinear diffusion of McKean–Vlasov type. This result is the key ingredient for the theory of quantum mean-field games developed by the author in a previous paper.

AB - Abstract: There is an extensive literature on the dynamic law of large numbers for systems of quantum particles, that is, on the derivation of an equation describing the limiting individual behavior of particles in a large ensemble of identical interacting particles. The resulting equations are generally referred to as nonlinear Schrödinger equations or Hartree equations, or Gross–Pitaevskii equations. In this paper, we extend some of these convergence results to a stochastic framework. Specifically, we work with the Belavkin stochastic filtering of many-particle quantum systems. The resulting limiting equation is an equation of a new type, which can be regarded as a complex-valued infinite-dimensional nonlinear diffusion of McKean–Vlasov type. This result is the key ingredient for the theory of quantum mean-field games developed by the author in a previous paper.

KW - Belavkin equation

KW - homodyne detection

KW - infinite-dimensional McKean–Vlasov diffusion on manifold

KW - nonlinear stochastic Schrödinger equation

KW - quantum control

KW - quantum dynamic law of large numbers

KW - quantum filtering

KW - quantum interacting particles

KW - quantum mean-field games

KW - GAMES

KW - EQUATIONS

KW - nonlinear stochastic Schrodinger equation

KW - infinite-dimensional McKean-Vlasov diffusion on manifold

KW - EVOLUTION

UR - http://www.scopus.com/inward/record.url?scp=85110542298&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/5258e46a-346b-3073-bb48-b7c0d08147c2/

U2 - 10.1134/S0040577921070084

DO - 10.1134/S0040577921070084

M3 - Article

AN - SCOPUS:85110542298

VL - 208

SP - 937

EP - 957

JO - Theoretical and Mathematical Physics (Russian Federation)

JF - Theoretical and Mathematical Physics (Russian Federation)

SN - 0040-5779

IS - 1

ER -

ID: 86493168