Results 191 to 200 of about 971 (209)

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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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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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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A new form and a ⋆-algebraic structure of quantum stochastic integrals in Fock space

Rendiconti del Seminario Matematico e Fisico di Milano, 1988
Summary: An algebraic definition of the basic quantum process for the noncommutative stochastic calculus is given in terms of the Fock representation of a Lie *-algebra of matrices in a pseudo-Euclidean space. An operator definition of the quantum stochastic integral is given and its continuity is proved in a projective limit uniform operator topology.
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Infinite dimensional integrals and partial differential equations for stochastic and quantum phenomena

Journal of Geometric Mechanics, 2019
Sonia Mazzucchi, Albeverio Sérgio, Mazzucchi Sonia   +2 more
exaly  

INDEPENDENCE FOR QUANTUM STOCHASTIC INTEGRATORS

1991
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ALGEBRAIC STOCHASTIC DIFFERENTIAL EQUATIONS AND A FUBINI THEOREM FOR SYMMETRISED DOUBLE QUANTUM STOCHASTIC PRODUCT INTEGRALS

2001
R L Hudson
exaly  

A new form and a ⋆-algebraic structure of quantum stochastic integrals in Fock space

Milan Journal of Mathematics, 2008
V P Belavkin
exaly