Results 201 to 210 of about 1,022 (229)

Quantum stochastic integral representations of Fock space operators

Stochastics, 2009
An (unbounded) operator Ξ on Boson Fock space over L 2(R +) is called regular if it is an admissible white noise operator such that the conditional expectations give rise to a regular quantum martingale. We prove that an admissible white noise operator is regular if and only if it admits a quantum stochastic integral representation.
Un Cig Ji, Nobuaki Obata
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Quasi-free quantum stochastic integrals in the plane

Reports on Mathematical Physics, 2002
In the classical theory of stochastic integration, Wong and Zakai followed by Cairoli and Walsh, developed a calculus for two-parameter martingales in the seventies. Here, the authors provide quantum analogues of that kind of integrals and calculus, involving two-parameter processes like quasi-free boson or fermion creation and annihilation.
Spring, W. J., Wilde, I. F.
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Algebraic theory of product integrals in quantum stochastic calculus

Journal of Mathematical Physics, 2000
Motivated by the search for solutions of the quantum Yang–Baxter equation, an algebraic theory of quantum stochastic product integrals is developed. The product integrators are formal power series in an indeterminate h whose coefficients are elements of the Lie algebra ℒ labelling the usual integrators of a many-dimensional quantum stochastic calculus.
Hudson, R. L., Pulmannová, S.
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Stochastic Integration and Quantum Ito’s Formula

1992
In Section 21 we have already seen how the classical stochastic processes with independent increments can be realised as suitable linear combinations of the creation, conservation and annihilation operators in the boson Fock space Γs (ℋ) over a Hilbert space ℋ. This includes, in particular, the Brownian motion and Poisson process.
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The stochastic action integral interpretation of the quantum-mechanical transformation function

Lettere Al Nuovo Cimento Series 2, 1980
F~,Y~MAN (i) originally noted the interesting result that, for quadratic actions, an average over all paths between fixed endpoints of the transition led to a separation of the quantum-mechanical transformation function into two factors. One factor depends upon the time interval of transition and the fixed endpoints, while the other factor is dependent
SANTAMATO, ENRICO, B. H. LAVENDA
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Stochastic path integrals and open quantum systems

Physical Review A, 1996
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Quantum martingales and stochastic integrals

1988
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QUASI-FREE FERMION PLANAR QUANTUM STOCHASTIC INTEGRALS

Quantum Probability and Infinite-Dimensional Analysis, 2003
W. J. SPRING, I. F. WILDE
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INDEPENDENCE FOR QUANTUM STOCHASTIC INTEGRATORS

1991
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Quasi-free quantum stochastic integrals for the CAR and CCR

, 1983
Christopher B. Barnett, R. F. Streater, Ivan F. Wilde   +2 more
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