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arXiv:math/0512290

On Stochastic Generators of Positive Definite Exponents

V. P. Belavkin

Published Dec 13, 2005• 1 citation
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Abstract

A characterisation of quantum stochastic positive definite (PD) exponent is given in terms of the conditional positive definiteness (CPD) of their form-generator. The pseudo-Hilbert dilation of the stochastic form-generator and the pre-Hilbert dilation of the corresponding dissipator is found. The structure of quasi-Poisson stochastic generators giving rise to a quantum stochastic birth processes is studied.

DOI
10.48550/arxiv.math/0512290

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This is a continuation of the study of the theory of quantum stochastic dilation of completely positive semigroups on a von Neumann or C∗C^*C∗ algebra, here with unbounded generators. The additional assumption of symmetry with respect to a semifinite trace allows the use of the Hilbert space techniques, while the covariance gives rise to better handle on domains. An Evans-Hudson flow is obtained, dilating the given semigroup.