Quantum stochastic convolution cocycles I
J. Martin Lindsay, Adam G. Skalski (2005)
Annales de l'I.H.P. Probabilités et statistiques
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J. Martin Lindsay, Adam G. Skalski (2005)
Annales de l'I.H.P. Probabilités et statistiques
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Alexander Chebotarev, Dmitry Victorov (1998)
Banach Center Publications
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By using F. A. Berezin's canonical transformation method [5], we derive a nonadapted quantum stochastic differential equation (QSDE) as an equation for the strong limit of the family of unitary groups satisfying the Schrödinger equation with singularly degenerating Hamiltonians in Fock space. Stochastic differentials of QSDE generate a nonadapted associative Ito multiplication table, and the coefficients of these differentials satisfy the formal unitarity conditions of the Hudson-Parthasarathy...
Majewski, Adam W., Zegarlinski, Boguslaw (1995)
Mathematical Physics Electronic Journal [electronic only]
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Luigi. Accardi, M. Schürmann (1988)
Mathematische Zeitschrift
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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...
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.
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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Nicolas Privault (1998)
Banach Center Publications
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The aim of this paper is the study of a non-commutative decomposition of the conservation process in quantum stochastic calculus. The probabilistic interpretation of this decomposition uses time changes, in contrast to the spatial shifts used in the interpretation of the creation and annihilation operators on Fock space.