Home > Research > Publications & Outputs > Quantum stochastic Lie-Trotter product formula II

Electronic data

  • UploadedToPure2017.11.16FinalVersion.QSLieTrotterProductFormulaII

    Rights statement: This is a pre-copy-editing, author-produced PDF of an article accepted for publication in International Mathematics Research Notices following peer review. The definitive publisher-authenticated version J Martin Lindsay; Quantum Stochastic Lie–Trotter Product Formula II, International Mathematics Research Notices, , rnx306, https://doi.org/10.1093/imrn/rnx306 is available online at: https://academic.oup.com/imrn/article/2019/12/3901/4812375

    Accepted author manuscript, 476 KB, PDF document

    Available under license: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License

Links

Text available via DOI:

View graph of relations

Quantum stochastic Lie-Trotter product formula II

Research output: Contribution to journalJournal article

Published

Standard

Quantum stochastic Lie-Trotter product formula II. / Lindsay, J. Martin.

In: International Mathematics Research Notices, Vol. 2019, No. 12, 01.06.2019, p. 3901–3939.

Research output: Contribution to journalJournal article

Harvard

Lindsay, JM 2019, 'Quantum stochastic Lie-Trotter product formula II', International Mathematics Research Notices, vol. 2019, no. 12, pp. 3901–3939. https://doi.org/10.1093/imrn/rnx306

APA

Lindsay, J. M. (2019). Quantum stochastic Lie-Trotter product formula II. International Mathematics Research Notices, 2019(12), 3901–3939. https://doi.org/10.1093/imrn/rnx306

Vancouver

Lindsay JM. Quantum stochastic Lie-Trotter product formula II. International Mathematics Research Notices. 2019 Jun 1;2019(12):3901–3939. https://doi.org/10.1093/imrn/rnx306

Author

Lindsay, J. Martin. / Quantum stochastic Lie-Trotter product formula II. In: International Mathematics Research Notices. 2019 ; Vol. 2019, No. 12. pp. 3901–3939.

Bibtex

@article{687f93691c5d4a8b85ff885544bd9b42,
title = "Quantum stochastic Lie-Trotter product formula II",
abstract = "A natural counterpart to the Lie-Trotter product formula for norm-continuous one-parameter semigroups is proved, for the class of quasicontractive quantum stochastic operator cocycles whose expectation semigroup is norm continuous.Compared to previous such results, the assumption of a strong form of independence of the constituent cocycles is overcome. The analysis is facilitated by the development of some quantum Ito algebra. It is also shown how the maximal Gaussian component of a quantum stochastic generator may be extracted - leading to a canonical decomposition of such generators, and the connection to perturbation theory is described. Finally, the quantum Ito algebra is extended to quadratic form generators, and a conjecture is formulated for the extension of the product formula to holomorphic quantum stochastic cocycles.",
keywords = "Lie-Trotter product formula, quantum stochastic cocycle, one-parameter semigroup, series product, concatenation product, quantum Ito algebra, quantum stochastic analysis",
author = "Lindsay, {J. Martin}",
note = "This is a pre-copy-editing, author-produced PDF of an article accepted for publication in International Mathematics Research Notices following peer review. The definitive publisher-authenticated version J Martin Lindsay; Quantum Stochastic Lie–Trotter Product Formula II, International Mathematics Research Notices, , rnx306, https://doi.org/10.1093/imrn/rnx306 is available online at: https://academic.oup.com/imrn/article/2019/12/3901/4812375",
year = "2019",
month = jun
day = "1",
doi = "10.1093/imrn/rnx306",
language = "English",
volume = "2019",
pages = "3901–3939",
journal = "International Mathematics Research Notices",
issn = "1073-7928",
publisher = "Oxford University Press",
number = "12",

}

RIS

TY - JOUR

T1 - Quantum stochastic Lie-Trotter product formula II

AU - Lindsay, J. Martin

N1 - This is a pre-copy-editing, author-produced PDF of an article accepted for publication in International Mathematics Research Notices following peer review. The definitive publisher-authenticated version J Martin Lindsay; Quantum Stochastic Lie–Trotter Product Formula II, International Mathematics Research Notices, , rnx306, https://doi.org/10.1093/imrn/rnx306 is available online at: https://academic.oup.com/imrn/article/2019/12/3901/4812375

PY - 2019/6/1

Y1 - 2019/6/1

N2 - A natural counterpart to the Lie-Trotter product formula for norm-continuous one-parameter semigroups is proved, for the class of quasicontractive quantum stochastic operator cocycles whose expectation semigroup is norm continuous.Compared to previous such results, the assumption of a strong form of independence of the constituent cocycles is overcome. The analysis is facilitated by the development of some quantum Ito algebra. It is also shown how the maximal Gaussian component of a quantum stochastic generator may be extracted - leading to a canonical decomposition of such generators, and the connection to perturbation theory is described. Finally, the quantum Ito algebra is extended to quadratic form generators, and a conjecture is formulated for the extension of the product formula to holomorphic quantum stochastic cocycles.

AB - A natural counterpart to the Lie-Trotter product formula for norm-continuous one-parameter semigroups is proved, for the class of quasicontractive quantum stochastic operator cocycles whose expectation semigroup is norm continuous.Compared to previous such results, the assumption of a strong form of independence of the constituent cocycles is overcome. The analysis is facilitated by the development of some quantum Ito algebra. It is also shown how the maximal Gaussian component of a quantum stochastic generator may be extracted - leading to a canonical decomposition of such generators, and the connection to perturbation theory is described. Finally, the quantum Ito algebra is extended to quadratic form generators, and a conjecture is formulated for the extension of the product formula to holomorphic quantum stochastic cocycles.

KW - Lie-Trotter product formula

KW - quantum stochastic cocycle

KW - one-parameter semigroup

KW - series product

KW - concatenation product

KW - quantum Ito algebra

KW - quantum stochastic analysis

U2 - 10.1093/imrn/rnx306

DO - 10.1093/imrn/rnx306

M3 - Journal article

VL - 2019

SP - 3901

EP - 3939

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

IS - 12

ER -