This article is cited in 2 scientific papers (total in 2 papers)
Cauchy problem for stochastic Liouville equation with randomly variable Hamiltonian of perturbations in the form of a bounded operator
Yu. N. Barabanenkov
A class of stochastic problems is considered, in which the perturbation hamiltoniarn of dynamic system depends on a random function of time and coordinates (“the potential”). It is assumed that the perturbation hamiltonian is a bounded operator for sufficiently regular realisations of the potential. The condition for the random potential to belong to the measurable real Hilbert space with finite measure as well as the property of potential correlations weakening is formulated in terms of cumulant functions. For the class of problems under consideration, the solution of the stochastic Liouville–Neumann equation is constructed and limiting theorem about the validity of basic kinetic equation is proved, which includes the approximation of weak interaction with external system and the approximation of small density.
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Theoretical and Mathematical Physics, 1980, 42:1, 66–73
Yu. N. Barabanenkov, “Cauchy problem for stochastic Liouville equation with randomly variable Hamiltonian of perturbations in the form of a bounded operator”, TMF, 42:1 (1980), 101–111; Theoret. and Math. Phys., 42:1 (1980), 66–73
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\paper Cauchy problem for stochastic Liouville equation with randomly variable Hamiltonian of~perturbations in~the form of~a~bounded operator
\jour Theoret. and Math. Phys.
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This publication is cited in the following articles:
Yu. N. Barabanenkov, “Asymptotic method in the theory of the passage of fast charged particles through matter”, Theoret. and Math. Phys., 47:2 (1981), 442–449
R. V. Bobrik, “Hierarchies of moment equations for the solution of the Schrödinger equation with random potential and their closure”, Theoret. and Math. Phys., 68:2 (1986), 841–847
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