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A Homomorphism Theorem and a Trotter Product Formula for Quantum Stochastic Flows with Unbounded Coefficients

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Abstract

We give a new method for proving the homomorphic property of a quantum stochastic flow satisfying a quantum stochastic differential equation with unbounded coefficients, under some further hypotheses. As an application, we prove a Trotter product formula for quantum stochastic flows and obtain quantum stochastic dilations of a class of quantum dynamical semigroups generalizing results of Goswami et al. (Inst H Poincare Probab Stat 41:505–522, 2005).

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Authors and Affiliations

  1. Institute of Mathematics of Polish Academy of Sciences, ul. Śniadeckich 8, P.O. Box 21, 00-956, Warszawa, Poland

    Biswarup Das

  2. Indian Statistical Institute, Kolkata, India

    Debashish Goswami

  3. J.N. Centre for Advanced Scientific Research, Indian Institute of Science, Bangalore, India

    Kalyan B. Sinha

Authors
  1. Biswarup Das
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  2. Debashish Goswami
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  3. Kalyan B. Sinha
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Correspondence to Debashish Goswami.

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Communicated by A. Connes

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Das, B., Goswami, D. & Sinha, K.B. A Homomorphism Theorem and a Trotter Product Formula for Quantum Stochastic Flows with Unbounded Coefficients. Commun. Math. Phys. 330, 435–467 (2014). https://doi.org/10.1007/s00220-014-1993-1

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  • DOI: https://doi.org/10.1007/s00220-014-1993-1

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