Quantum Stochastic Lie–Trotter Product Formula II
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Publication:5243290
DOI10.1093/IMRN/RNX306zbMATH Open1430.81044arXiv1707.05669OpenAlexW2962887315MaRDI QIDQ5243290
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Publication date: 18 November 2019
Published in: (Search for Journal in Brave)
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 genarators, 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.
Full work available at URL: https://arxiv.org/abs/1707.05669
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