Quantum stochastic differential equations driven by free noises and dilations of markovian semigroups
Maria Elvira Mancino (1994)
Rendiconti del Seminario Matematico della Università di Padova
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Maria Elvira Mancino (1994)
Rendiconti del Seminario Matematico della Università di Padova
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J. Martin Lindsay, Adam G. Skalski (2006)
Banach Center Publications
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We summarise recent results concerning quantum stochastic convolution cocycles in two contexts-purely algebraic and C*-algebraic. In each case the class of cocycles arising as the solution of a quantum stochastic differential equation is characterised and the form taken by the stochastic generator of a *-homomorphic cocycle is described. Throughout the paper a common viewpoint on the algebraic and C*-algebraic situations is emphasised; the final section treats the unifying example of...
Luigi. Accardi, M. Schürmann (1988)
Mathematische Zeitschrift
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Majewski, Adam W., Zegarlinski, Boguslaw (1995)
Mathematical Physics Electronic Journal [electronic only]
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(1998)
Banach Center Publications
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John Gough (2006)
Banach Center Publications
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We present quantum stochastic calculus in terms of diagrams taking weights in the algebra of observables of some quantum system. In particular, we note the absence of non-time-consecutive Goldstone diagrams. We review recent results in Markovian limits in these terms.
Amosov, G.G. (2003)
International Journal of Mathematics and Mathematical Sciences
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Viacheslav Belavkin, Matthew Brown (2011)
Banach Center Publications
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In this paper we first introduce the Fock-Guichardet formalism for the quantum stochastic (QS) integration, then the four fundamental processes of the dynamics are introduced in the canonical basis as the operator-valued measures, on a space-time σ-field , of the QS integration. Then rigorous analysis of the QS integrals is carried out, and continuity of the QS derivative D is proved. Finally, Q-adapted dynamics is discussed, including Bosonic (Q = I), Fermionic (Q = -I), and monotone...
Michael Schürmann (1991)
Séminaire de probabilités de Strasbourg
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Jürgen Hellmich, Claus Köstler, Burkhard Kümmerer (1998)
Banach Center Publications
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From the operator algebraic approach to stationary (quantum) Markov processes there has emerged an axiomatic definition of quantum white noise. The role of Brownian motion is played by an additive cocycle with respect to its time evolution. In this report we describe some recent work, showing that this general structure already allows a rich theory of stochastic integration and stochastic differential equations. In particular, if a quantum Markov process is represented by a unitary cocycle,...
J. T. Lewis, L. C. Thomas (1975)
Annales de l'I.H.P. Physique théorique
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