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    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

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Quantum stochastic Lie-Trotter product formula II

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>1/06/2019
<mark>Journal</mark>International Mathematics Research Notices
Issue number12
Volume2019
Number of pages39
Pages (from-to)3901–3939
Publication StatusPublished
Early online date25/01/18
<mark>Original language</mark>English

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.

Bibliographic 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