Results 251 to 260 of about 3,832 (288)

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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Symmetrized double quantum stochastic product integrals

Journal of Mathematical Physics, 2000
A theory is developed of product integrals of the form ∏a<s<b ∏c<t<d(1+g[h] (ds,dt)). Here [a,b[ and [c,d[ are disjoint finite subintervals of R+, and g[h] is a formal power series in the indeterminate h whose constant term is zero and whose coefficients are elements of L⊗L, where ℒ is the space of basic differentials of a ...
Hudson, R. L., Pulmannová, S.
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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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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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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 Behaviour of the Magnetisation in a Classically Integrable Quantum System

Europhysics Letters (EPL), 1991
We present a two-dimensional model of noninteracting electrons in an external magnetic field. This model is of common use in the study of the Hall effect. In the classical limit the system is integrable. Nevertheless at the quantum level, the magnetisation as a function of the number of electrons exhibits a chaotic behaviour.
K. REZAKHANLOU, H. KUNZ, CRISANTI, Andrea   +2 more
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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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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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