Quantum stochastic Lie-Trotter product formula II

Lindsay, J. Martin (2019) Quantum stochastic Lie-Trotter product formula II. International Mathematics Research Notices, 2019 (12). 3901–3939. ISSN 1073-7928

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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.

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Journal Article
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International Mathematics Research Notices
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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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19 Dec 2017 09:06
Last Modified:
17 Sep 2023 02:10