Belavkin, V. P.
(1988)
*Multiquantum systems and point processes I. Generating functionals and nonlinear semigroups.*
(Preprint)

Text
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## Abstract

An algebraic approach to representation theory and the description of multicomponent quantum systems is considered. A generating multiquantum state functional and nonlinear completely positive map are introduced and a dilation theorem giving a nonlinear extension of GNS and Stinenspring theorem is proved. A number particle operator-valued weight and an empirical weight operator generating a macroscopic inductive algebra are defined, and asymptotic commutativity of this algebra is proved. A canonical multiquantum stochastic process called quasi-Poissonian is constructed and the general structure of the generator for infinite divisible multi-quantum states as well as multiquantum semigroups is found. An existence theorem extending the Lindblad theorem to unbounded generators as well as nonlinear generators is proven. The class of quasifree quantum point stochastic processes is introduced to describe Markovian dynamics of non-interacting quantum particles and corresponding birth, branching and current nonlinear semigroups and their generators are studied.

Item Type: | Article |
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Divisions: | School of Theoretical Physics > Preprints |

Date Deposited: | 19 Jun 2018 14:17 |

Last Modified: | 20 Dec 2022 14:43 |

URI: | https://dair.dias.ie/id/eprint/799 |

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