Geodesic
Random walks in disordered systems with long-range transitions. Asymptotically exactly solvable models
Teoretičeskaâ i matematičeskaâ fizika, Tome 94 (1993) no. 3, pp. 496-514 Cet article a éte moissonné depuis la source Math-Net.Ru

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Random-jump 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 ${\mathcal A}_{xy}={\mathcal A}_{yx}={\mathcal A}_{x-y,0}$, the transition rates are determined by multipole-type interactions and $\{\xi _x\}$ have several first negative moments (the random-jump-rate 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 long-time 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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     title = {Random walks in disordered systems with long-range transitions. {Asymptotically} exactly solvable models},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {496--514},
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F. S. Dzheparov; V. E. Shestopal. Random walks in disordered systems with long-range transitions. Asymptotically exactly solvable models. Teoretičeskaâ i matematičeskaâ fizika, Tome 94 (1993) no. 3, pp. 496-514. http://geodesic.mathdoc.fr/item/TMF_1993_94_3_a12/

[1] Zvyagin I. P., Kineticheskie yavleniya v neuporyadochennykh poluprovodnikakh, MGU, M., 1984

[2] Shklovskii B. I., Efros A. Ya., Elektronnye svoistva legirovannykh poluprovodnikov, Nauka, M., 1979

[3] Gochanour C. R., Fayer M. D., J. Phys. Chem., 85 (1989), 1981

[4] Ashurov M. Kh., Basiev T. T., Burshtein A. N. i dr., Pisma v ZhETF, 40 (1984), 98

[5] Gapontsev V. P., Dzheparov F. S., Platonov N. S., Shestopal V. E., Pisma v ZhETF, 41 (1985), 561

[6] Gomez-John L., Kasinski J., Muller R. J. D., Chem. Phys. Lettr., 125 (1986), 500 | DOI

[7] Hart D. E., Anfinrud P. A., Struve V. S., J. Chem. Phys., 86 (1987), 2689 | DOI

[8] Abov Yu. G. i dr., ZhETF, 99:3 (1991), 962; Изв. АН СССР, сер. физ., 52 (1988), 460

[9] Bodunov E. N., Izv. AN SSSR, ser. fiz., 42 (1978), 303 | MR

[10] Alexander S., Bernasconi J., Schneider W., Orbach R., Rev. Mod. Phys., 53 (1981), 175 | DOI | MR

[11] Zwanzig R., J. Stat. Phys., 28 (1982), 127 | DOI | MR

[12] Anshelevich V. V., Khanin K. M., Sinai Ja. G., Commun. Math. Phys., 85 (1982), 449 | DOI | MR | Zbl

[13] Sinai Ya. G., Teoriya veroyatn. i ee primen., 27 (1982), 247 | MR | Zbl

[14] Denteneer P. J. H., Ernst M. H., Phys. Rev. B, 29 (1984), 1755 | DOI

[15] Pronin K. A., TMF, 61:3 (1984), 442–452 | MR

[16] Kozlov S. M., UMN, 40 (1985), 61 | MR

[17] Kozlov S. M., Molchanov S. A., DAN SSSR, 278:3 (1984), 531 | MR | Zbl

[18] Harrison A. K., Zwanzig R., J. Stat. Phys., 42 (1986), 935 | DOI | MR

[19] Kundu K., Izzo D., Phillips P., J. Chem. Phys., 88 (1988), 2692 | DOI

[20] Letchikov A. V., DAN SSSR, 304 (1989), 25 | MR

[21] Sher H., Lax M., Phys. Rev., V7 (1973), 4491, 4502 | DOI | MR

[22] Dzheparov F. S., ZhETF, 99:3 (1991), 982; Радиоспектроскопия (Пермь), 1980, No 13, 135

[23] Loring R. F., Franchi D. S., Mukamel S., J. Chem. Phys., 86 (1987), 1323 | DOI

[24] Dzheparov F. S., Stepanov S. V., Shestopal V. E., Preprint ITEF No 133, ITEF, M., 1987

[25] Dzheparov F. S., Shestopal V. E., Sluchainye bluzhdaniya v neuporyadochennykh sistemakh s dalnodeistviem. Asimptoticheski tochno reshaemye modeli, preprint ITEF No 141, ITEF, M., 1991; Dzheparov F. S., Shestopal V. E., Random walks in disordered systems with long-range transitions. Asymptotically exactly soluble models, preprint ITEP No 11, ITEP, M., 1990

[26] Dzheparov F. S., Shestopal V. E., Izv. vuzov. Fizika, 30:6 (1987), 77

[27] Hernandez-Garcia E., Rodrigez M. A., Pesquera L. San-Miguel, Phys. Rev., B42:16 (1990), 10653 | DOI

[28] Bouchaud J.-Ph., Georges A., Phys. Rep., 185:4,5 (1990), 127 | DOI | MR

[29] Bricmont J., Kupiainen A., Phys. Rev. Lettr., 66:13 (1990), 1689 | DOI | MR

[30] Ziman I. M., Principles of the theory of solids, Cambridge, 1964 | MR

[31] Born M., Huang K., Dynamical theory of crystal lattice, Oxford, 1954 | MR

[32] Evgrafov M. A., Asimptoticheskie otsenki i tselye funktsii, Nauka, M., 1979 | MR | Zbl

[33] Fedoryuk M. F., Asimptotika: integraly i ryady, Nauka, M., 1987 | MR

[34] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, t. 2, Mir, M., 1984 | MR

[35] Shklovskii B. I., Fiz. tekhn. poluprov., 10 (1976), 1440

[36] Pollak M., Riess I., J. Phys., S9 (1976), 2339

[37] Bodunov E. N., Malyshev V. A., FTT, 2 (1982), 3654

[38] Movaghar B., Ries B., Grunewald M., Phys. Rev., V34 (1986), 5574 | DOI

[39] Esser B., J. Phys., S21 (1988), 911 | DOI | MR

[40] Zvyagin I. P., Phys. Stat. Sol. (b), 152 (1989), 231 | DOI