Cocycles of CCR flows

DOI10.1090/memo/0709zbMath0976.46050OpenAlexW2000780223MaRDI QIDQ2704685

B. V. Rajarama Bhat

Publication date: 17 December 2001

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/memo/0709

zbMATH Keywords

factorizationcocyclesquantum stochastic calculuscompletely positive maps\(E_0\)-semigroupsquantum dynamical semigroupsHeisenberg motion groupquantum Itô formulaminimal dilationsCCR flowsabstract Feynman-Kac perturbationsHudson-Parthasarathy cocyclessecond quantized shift operators on the Boson Fock space

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55) Quantum stochastic calculus (81S25) Research exposition (monographs, survey articles) pertaining to functional analysis (46-02)

Related Items (17)

Type I product systems of Hilbert modules ⋮ QUANTUM MARKOV SEMIGROUPS: PRODUCT SYSTEMS AND SUBORDINATION ⋮ Non-commutative Markov chains and multi-analytic operators ⋮ Invariants for normal completely positive maps on the hyperfinite \(II_1\) factor ⋮ Dark energy states from quantization of boson fields in a universe with unstable modes ⋮ Invariants for \(E_{0}\)-semigroups on II\(_{1}\) factors ⋮ E\(_{0}\)-semigroups of type II\(_{0}\) and \(q\)-purity: boundary weight maps of range rank one and two ⋮ Arveson's characterisation of CCR flows: the multiparameter case ⋮ Constructing proper Markov semigroups for Arveson systems ⋮ Weak Markov processes as linear systems ⋮ Interacting Fock spaces and subproduct systems ⋮ Minimal isometric dilations of operator cocycles ⋮ Local unitary cocycles of \(E_0\)-semigroups ⋮ Quasifree stochastic cocycles and quantum random walks ⋮ Spatial Markov semigroups admit Hudson-Parthasarathy dilations ⋮ Markovian cocycles on operator algebras adapted to a Fock filtration ⋮ Cocycles for one-parameter flows of \(\mathfrak B(\mathfrak h)\)

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