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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">mrisel</journal-id><journal-title-group><journal-title xml:lang="en">Magnetic Resonance in Solids</journal-title><trans-title-group xml:lang="ru"><trans-title>Magnetic Resonance in Solids</trans-title></trans-title-group></journal-title-group><issn pub-type="epub">2072-5981</issn><publisher><publisher-name>Kazan Federal University</publisher-name></publisher></journal-meta><article-meta><article-id custom-type="elpub" pub-id-type="custom">mrisel-102</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>Статьи</subject></subj-group></article-categories><title-group><article-title>Random walks in disordered lattice, CTRW, memory and dipole transport</article-title><trans-title-group xml:lang="ru"><trans-title></trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Dzheparov</surname><given-names>F. S.</given-names></name></name-alternatives><bio xml:lang="en"><p>ITEP, Moscow 117258; Moscow 115409</p></bio><email xlink:type="simple">dzheparov@itep.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff xml:lang="en" id="aff-1"><institution>National Research Center "Kurchatov Institute", ITEP; National Research Nuclear University "MEPhI"</institution><country>Russian Federation</country></aff><pub-date pub-type="collection"><year>2017</year></pub-date><pub-date pub-type="epub"><day>14</day><month>11</month><year>2017</year></pub-date><volume>19</volume><issue>2</issue><elocation-id>17201 (11 pp.)</elocation-id><permissions><copyright-statement>Copyright &amp;#x00A9; Dzheparov F.S., 2024</copyright-statement><copyright-year>2024</copyright-year><copyright-holder xml:lang="ru">Dzheparov F.S.</copyright-holder><copyright-holder xml:lang="en">Dzheparov F.S.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://www.mrsej.ru/jour/article/view/102">https://www.mrsej.ru/jour/article/view/102</self-uri><abstract><p>Application of CTRW (continuous time random walks) to dipole hopping transport is reviewed. Conditions of applicability of basic kinetic equations to spin systems are indicated. Correct versions of derivation of the CTRW-equations are presented. Existence of different forms of memory kernels is demonstrated. Correction of Scher-Lax memory kernel within geometrical memory approach is fulfilled in accordance with leading terms of concentration expansion. Approximate solution for autocorrelation function is considered. Modern state of numerical simulation and experimental measurements of autocorrelation function in nuclear polarization delocalization are described. It is shown, that application of the CTRW was more successful in description of dipole transport than for hopping conductivity.</p></abstract><kwd-group xml:lang="en"><kwd>random walks</kwd><kwd>random media</kwd><kwd>disordered lattice</kwd><kwd>survival probability</kwd><kwd>dipole transport</kwd><kwd>hopping transport</kwd><kwd>master equation</kwd><kwd>memory kernel</kwd><kwd>projection operator</kwd><kwd>spin diffusion</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Dzheparov F.S., Lundin A.A. Sov. Phys. JETP 48, 514 (1978)</mixed-citation><mixed-citation xml:lang="en">Dzheparov F.S., Lundin A.A. Sov. Phys. JETP 48, 514 (1978)</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Scher H., Lax M. Phys. Rev. B 7, 4491, 4502 (1973)</mixed-citation><mixed-citation xml:lang="en">Scher H., Lax M. Phys. Rev. B 7, 4491, 4502 (1973)</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Gochanour C.R., Andersen H.C., Fayer M.D. J. Chem. Phys. 70, 4254 (1979)</mixed-citation><mixed-citation xml:lang="en">Gochanour C.R., Andersen H.C., Fayer M.D. J. Chem. Phys. 70, 4254 (1979)</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Abov Yu.G., Gulko A.D., Dzheparov F.S., Stepanov S.V., Trostin S.S. Phys. Part. Nucl. 26, 692 (1995)</mixed-citation><mixed-citation xml:lang="en">Abov Yu.G., Gulko A.D., Dzheparov F.S., Stepanov S.V., Trostin S.S. Phys. Part. Nucl. 26, 692 (1995)</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Abragam A. Principles of Nuclear Magnetism, Oxford University Press, Oxford (1961)</mixed-citation><mixed-citation xml:lang="en">Abragam A. Principles of Nuclear Magnetism, Oxford University Press, Oxford (1961)</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Abragam A., Goldman M. Nuclear Magnetism: Order and Disorder, Clarendon Press, Oxford (1982)</mixed-citation><mixed-citation xml:lang="en">Abragam A., Goldman M. Nuclear Magnetism: Order and Disorder, Clarendon Press, Oxford (1982)</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Salikhov K.M., Semenov A.G., Tsvetkov Yu.D. Elektronnoe spinovoe echo i yego primeneniya, Nauka, Novosibirsk (1976) (in Russian)</mixed-citation><mixed-citation xml:lang="en">Salikhov K.M., Semenov A.G., Tsvetkov Yu.D. Elektronnoe spinovoe echo i yego primeneniya, Nauka, Novosibirsk (1976) (in Russian)</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Atsarkin V.A., Dzheparov F.S. Z. Phys. Chem. 231, 545 (2017)</mixed-citation><mixed-citation xml:lang="en">Atsarkin V.A., Dzheparov F.S. Z. Phys. Chem. 231, 545 (2017)</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Montroll E.W., Weiss G.H. J. Math. Phys. 6, 167 (1965)</mixed-citation><mixed-citation xml:lang="en">Montroll E.W., Weiss G.H. J. Math. Phys. 6, 167 (1965)</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Ashurov M.Kh., Basiev T.T., Burshtein A.I., Voron'ko Yu.K., Osiko V.V.. JETP Lett. 40, 841 (1984)</mixed-citation><mixed-citation xml:lang="en">Ashurov M.Kh., Basiev T.T., Burshtein A.I., Voron'ko Yu.K., Osiko V.V.. JETP Lett. 40, 841 (1984)</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Gapontsev V.P., Dzheparov F.S., Platonov N.S., Shestopal V.E. JETP Lett. 41, 561 (1985)</mixed-citation><mixed-citation xml:lang="en">Gapontsev V.P., Dzheparov F.S., Platonov N.S., Shestopal V.E. JETP Lett. 41, 561 (1985)</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Dzheparov F., Gul'ko A., Heitjans P., L'vov D., Schirmer A., Shestopal V., Stepanov S., Trostin S. Physica B 297, 288 (2001)</mixed-citation><mixed-citation xml:lang="en">Dzheparov F., Gul'ko A., Heitjans P., L'vov D., Schirmer A., Shestopal V., Stepanov S., Trostin S. Physica B 297, 288 (2001)</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Hughes B.D. Random Walks and Random Environment, Clarendorn Press, Oxford (1995)</mixed-citation><mixed-citation xml:lang="en">Hughes B.D. Random Walks and Random Environment, Clarendorn Press, Oxford (1995)</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Kutner R., Masoliver J. Eur. Phys. J. B 90, 50 (2017)</mixed-citation><mixed-citation xml:lang="en">Kutner R., Masoliver J. Eur. Phys. J. B 90, 50 (2017)</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Dzheparov F.S. Radiospektroskopiya (Perm) 13, 135 (1980) (in Russian)</mixed-citation><mixed-citation xml:lang="en">Dzheparov F.S. Radiospektroskopiya (Perm) 13, 135 (1980) (in Russian)</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Dzheparov F.S. Sov. Phys. JETP 72, 546 (1991)</mixed-citation><mixed-citation xml:lang="en">Dzheparov F.S. Sov. Phys. JETP 72, 546 (1991)</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Butcher P.N. J. Phys. C 7, 879 (1974)</mixed-citation><mixed-citation xml:lang="en">Butcher P.N. J. Phys. C 7, 879 (1974)</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Vugmeister B.E. Phys. Stat. Sol. (b) 76, 161 (1976)</mixed-citation><mixed-citation xml:lang="en">Vugmeister B.E. Phys. Stat. Sol. (b) 76, 161 (1976)</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Haan S.W., Zwanzig R. J. Chem. Phys. 68, 1879 (1978)</mixed-citation><mixed-citation xml:lang="en">Haan S.W., Zwanzig R. J. Chem. Phys. 68, 1879 (1978)</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Klafter J., Silbey R. Phys. Rev. Lett. 44, 55 (1980)</mixed-citation><mixed-citation xml:lang="en">Klafter J., Silbey R. Phys. Rev. Lett. 44, 55 (1980)</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Dzheparov F.S., Smelov V.S., Shestopal V.E. JETP Lett. 32, 47 (1980)</mixed-citation><mixed-citation xml:lang="en">Dzheparov F.S., Smelov V.S., Shestopal V.E. JETP Lett. 32, 47 (1980)</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Bodunov E.N., Malyshev V.A. Sov. Phys. Solid State 26, 1804 (1984)</mixed-citation><mixed-citation xml:lang="en">Bodunov E.N., Malyshev V.A. Sov. Phys. Solid State 26, 1804 (1984)</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Dzheparov F.S., Shestopal V.E. Theor. Math. Phys. 94, 345 (1993)</mixed-citation><mixed-citation xml:lang="en">Dzheparov F.S., Shestopal V.E. Theor. Math. Phys. 94, 345 (1993)</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Huber D.L., Hamilton D.S., Barnett B. Phys. Rev. В 16, 4642 (1977)</mixed-citation><mixed-citation xml:lang="en">Huber D.L., Hamilton D.S., Barnett B. Phys. Rev. В 16, 4642 (1977)</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Dzheparov F.S., Lvov D.V., Shestopal V.E. J. Supercond. Novel Magn. 20, 175 (2007)</mixed-citation><mixed-citation xml:lang="en">Dzheparov F.S., Lvov D.V., Shestopal V.E. J. Supercond. Novel Magn. 20, 175 (2007)</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Dzheparov F.S. JETP Lett. 82, 521 (2005)</mixed-citation><mixed-citation xml:lang="en">Dzheparov F.S. JETP Lett. 82, 521 (2005)</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Dzheparov F.S., Gulko A.D., Ermakov O.N., Lyubarev A.A., Stepanov S.V., Trostin S.S. Appl. Magn. Reson. 35, 411 (2009)</mixed-citation><mixed-citation xml:lang="en">Dzheparov F.S., Gulko A.D., Ermakov O.N., Lyubarev A.A., Stepanov S.V., Trostin S.S. Appl. Magn. Reson. 35, 411 (2009)</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Abov Yu.G., Gulko A.D., Dzheparov F.S., Ermakov O.N., Lvov D.V., Lyubarev A.A. Phys. At. Nucl. 77, 682 (2014)</mixed-citation><mixed-citation xml:lang="en">Abov Yu.G., Gulko A.D., Dzheparov F.S., Ermakov O.N., Lvov D.V., Lyubarev A.A. Phys. At. Nucl. 77, 682 (2014)</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Godzik K., Jortner J. J. Chem. Phys. 72, 4471 (1980)</mixed-citation><mixed-citation xml:lang="en">Godzik K., Jortner J. J. Chem. Phys. 72, 4471 (1980)</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">Franchi D.S., Loring R.F., Mukamel S. J. Chem. Phys. 86, 6419 (1987)</mixed-citation><mixed-citation xml:lang="en">Franchi D.S., Loring R.F., Mukamel S. J. Chem. Phys. 86, 6419 (1987)</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">Zvyagin I.P. Transport Phenomena in Disordered Semiconductors, MSU Publ., Moscow (1984) (in Russian)</mixed-citation><mixed-citation xml:lang="en">Zvyagin I.P. Transport Phenomena in Disordered Semiconductors, MSU Publ., Moscow (1984) (in Russian)</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
