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Monotone quantum stochastic processes and covariant dynamical hemigroups |
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| Authors: | Jaeseong Heo Viacheslav P Belavkin |
| Institution: | a Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Republic of Korea b Mathematics Department, University of Nottingham, University Park, Nottingham NG72RD, UK c Department of Mathematics, Research Institute of Mathematical Finance, Chungbuk National University, Cheongju 361-763, Republic of Korea |
| Abstract: | Based on the Hilbert C?-module structure we study non-stationary monotone quantum stochastic processes and general Markov processes constructed from quantum dynamical hemigroups indexed by a totally ordered set. We prove that the quantum stochastic monotone process implementing the weakly covariant process described by a covariant quantum dynamical hemigroup with respect to a symmetry semigroup is again covariant in the strong sense. |
| Keywords: | Hilbert _method=retrieve& _eid=1-s2 0-S002212361100293X& _mathId=si2 gif& _pii=S002212361100293X& _issn=00221236& _acct=C000054348& _version=1& _userid=3837164& md5=83a4a60154513fc53a8fe9b6fa2a9295')" style="cursor:pointer C?-module" target="_blank">" alt="Click to view the MathML source" title="Click to view the MathML source">C?-module Positive definite function Quantum stochastic process (Covariant) quantum dynamical hemigroup |
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