Quantum stochastic processes arising from the strong resolvent limits of the Schrödinger evolution in Fock space

Alexander Chebotarev; Dmitry Victorov

Banach Center Publications (1998)

  • Volume: 43, Issue: 1, page 119-133
  • ISSN: 0137-6934

Abstract

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By using F. A. Berezin's canonical transformation method [5], we derive a nonadapted quantum stochastic differential equation (QSDE) as an equation for the strong limit of the family of unitary groups satisfying the Schrödinger equation with singularly degenerating Hamiltonians in Fock space. Stochastic differentials of QSDE generate a nonadapted associative Ito multiplication table, and the coefficients of these differentials satisfy the formal unitarity conditions of the Hudson-Parthasarathy type [10].

How to cite

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Chebotarev, Alexander, and Victorov, Dmitry. "Quantum stochastic processes arising from the strong resolvent limits of the Schrödinger evolution in Fock space." Banach Center Publications 43.1 (1998): 119-133. <http://eudml.org/doc/208831>.

@article{Chebotarev1998,
abstract = {By using F. A. Berezin's canonical transformation method [5], we derive a nonadapted quantum stochastic differential equation (QSDE) as an equation for the strong limit of the family of unitary groups satisfying the Schrödinger equation with singularly degenerating Hamiltonians in Fock space. Stochastic differentials of QSDE generate a nonadapted associative Ito multiplication table, and the coefficients of these differentials satisfy the formal unitarity conditions of the Hudson-Parthasarathy type [10].},
author = {Chebotarev, Alexander, Victorov, Dmitry},
journal = {Banach Center Publications},
keywords = {stochastic processes; Fock space; Schrödinger’s equation; non-adapted quantum stochastic differential equation; strongly degenerating Hamiltonians; differentials},
language = {eng},
number = {1},
pages = {119-133},
title = {Quantum stochastic processes arising from the strong resolvent limits of the Schrödinger evolution in Fock space},
url = {http://eudml.org/doc/208831},
volume = {43},
year = {1998},
}

TY - JOUR
AU - Chebotarev, Alexander
AU - Victorov, Dmitry
TI - Quantum stochastic processes arising from the strong resolvent limits of the Schrödinger evolution in Fock space
JO - Banach Center Publications
PY - 1998
VL - 43
IS - 1
SP - 119
EP - 133
AB - By using F. A. Berezin's canonical transformation method [5], we derive a nonadapted quantum stochastic differential equation (QSDE) as an equation for the strong limit of the family of unitary groups satisfying the Schrödinger equation with singularly degenerating Hamiltonians in Fock space. Stochastic differentials of QSDE generate a nonadapted associative Ito multiplication table, and the coefficients of these differentials satisfy the formal unitarity conditions of the Hudson-Parthasarathy type [10].
LA - eng
KW - stochastic processes; Fock space; Schrödinger’s equation; non-adapted quantum stochastic differential equation; strongly degenerating Hamiltonians; differentials
UR - http://eudml.org/doc/208831
ER -

References

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  10. [10] R. L. Hudson and K. R. Parthasarathy, Quantum Ito's formula and stochastic evolutions, Commun. Math. Phys., Vol. 93, N3, 1984, 301-323. Zbl0546.60058
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  13. [13] P. A. Meyer, Quantum probability for probabilists, Lecture Notes in Math., vol. 1338, 1993. Zbl0773.60098
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