Results 141 to 150 of about 72,880 (178)

A spectral approach to quantum stochastic integrals

Reports on Mathematical Physics, 1989
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Berezanskij, Yu. M., Zhernakov, N. V., Us, G. F.   +2 more
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Quantum Stochastic Integrals

1984
There have been many attempts to set up quantum analogues of the theory of stochastic processes and stochastic differential equations. I should mention the many papers of M. Lax [1] on “quantum noise”, and those of Senitzky [2]; these were inspired by the problem of describing a laser, and by quantum electronics.
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Causal structure of quantum stochastic integrators

Theoretical and Mathematical Physics, 1997
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Anticipating quantum stochastic integrals

Infinite Dimensional Analysis, Quantum Probability and Related Topics
Based on the quantum white noise theory, we formulate new types of anticipating quantum stochastic integrals by combining the Hitsuda–Skorokhod quantum stochastic integrals and the interactions between the integrands and the integrators. For our purpose, we prove various versions of analytic characterization theorems of symbols of white noise ...
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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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On Solutions of Quantum Stochastic Integral Equations

1986
Throughout the discussion, we employ the notation and concepts already introduced in [1]. Thus, we also adopt here the partial *-algebraic setting of that paper.
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Quantum Stochastic Processes and Quantum non-Markovian Phenomena

PRX Quantum, 2021
Simon Milz, Kavan Modi
exaly