
This article is cited in 4 scientific papers (total in 4 papers)
Random walks in disordered systems with longrange transitions. Asymptotically exactly solvable models
F. S. Dzheparov^{}, V. E. Shestopal^{} ^{} Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
Abstract:
Randomjump models of transport in disordered system are studied.
They are described by the master equation
$\dot P={\mathcal A}\xi P$, where ${\mathcal A}$ is the generator of the spatially and
temporary uniform random walks process on a regular lattice, $\xi$ is the diagonal
operator, $\xi _{xy}=\xi _x \delta _{xy}$, where $\{\xi _x\}$ are independent
positive random variables with the same distribution. The case is elaborated
when ${\mathcal A}_{xy}={\mathcal A}_{yx}={\mathcal A}_{xy,0}$, the transition rates are determined by multipoletype interactions and $\{\xi _x\}$ have several first negative moments
(the randomjumprate model – with unbounded jumps). Methods of asymptotical
expansion of the propagator for small Laplace parameter values and for long times are developed. It is made also by means of functional integral representation. The influence of disorder and of interaction power on the longtime asymptotics is considered. A method of investigation for system with a forced drift along a certain direction is suggested. Some methods of reciprocal transformation of asymptotically–exactly solvable problems are
discussed and linkages with other known models are demonstrated. The $l_1$norm
of resolvent is obtained for any Markov process with a countable set of states
and $l_1$bounded generator.
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Theoretical and Mathematical Physics, 1993, 94:3, 345–357
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Received: 07.05.1992
Citation:
F. S. Dzheparov, V. E. Shestopal, “Random walks in disordered systems with longrange transitions. Asymptotically exactly solvable models”, TMF, 94:3 (1993), 496–514; Theoret. and Math. Phys., 94:3 (1993), 345–357
Citation in format AMSBIB
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\by F.~S.~Dzheparov, V.~E.~Shestopal
\paper Random walks in disordered systems with longrange transitions. Asymptotically exactly solvable models
\jour TMF
\yr 1993
\vol 94
\issue 3
\pages 496514
\mathnet{http://mi.mathnet.ru/tmf1439}
\mathscinet{http://www.ams.org/mathscinetgetitem?mr=1226226}
\transl
\jour Theoret. and Math. Phys.
\yr 1993
\vol 94
\issue 3
\pages 345357
\crossref{https://doi.org/10.1007/BF01017267}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1993MA71000013}
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http://mi.mathnet.ru/eng/tmf1439 http://mi.mathnet.ru/eng/tmf/v94/i3/p496
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This publication is cited in the following articles:

V. E. Shestopal, “Multiparameter models for random walks in disordered lattice systems”, Theoret. and Math. Phys., 119:2 (1999), 660–669

Dzheparov F., Gul'ko A., Heitjans P., L'vov D., Schirmer A., Shestopal V., Stepanov S., Trostin S., “Spin dynamics and betaNMR after polarized neutrons capture”, Physica B, 297:1–4 (2001), 288–292

F. S. Dzheparov, V. E. Shestopal, “Asymptotically Exactly Solvable Models of Processes in Stochastically Homogeneous Disordered Lattice Media”, Theoret. and Math. Phys., 135:1 (2003), 549–565

F. S. Dzheparov, “Delocalization of excitations in disordered media with dipole transfer”, JETP Letters, 82:8 (2005), 521–525

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