Geodesic
The high-temperature relaxation function of a spin system with a quadratic contribution of fluctuations to the resonance frequency
Teoretičeskaâ i matematičeskaâ fizika, Tome 121 (1999) no. 2, pp. 316-328 
O. A. Indyukov; M. A. Popov. The high-temperature relaxation function of a spin system with a quadratic contribution of fluctuations to the resonance frequency. Teoretičeskaâ i matematičeskaâ fizika, Tome 121 (1999) no. 2, pp. 316-328. http://geodesic.mathdoc.fr/item/TMF_1999_121_2_a8/
@article{TMF_1999_121_2_a8,
     author = {O. A. Indyukov and M. A. Popov},
     title = {The high-temperature relaxation function of a spin system with a quadratic contribution of fluctuations to the resonance frequency},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {316--328},
     year = {1999},
     volume = {121},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1999_121_2_a8/}
}
TY  - JOUR
AU  - O. A. Indyukov
AU  - M. A. Popov
TI  - The high-temperature relaxation function of a spin system with a quadratic contribution of fluctuations to the resonance frequency
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1999
SP  - 316
EP  - 328
VL  - 121
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1999_121_2_a8/
LA  - ru
ID  - TMF_1999_121_2_a8
ER  - 
%0 Journal Article
%A O. A. Indyukov
%A M. A. Popov
%T The high-temperature relaxation function of a spin system with a quadratic contribution of fluctuations to the resonance frequency
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1999
%P 316-328
%V 121
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1999_121_2_a8/
%G ru
%F TMF_1999_121_2_a8

Voir la notice de l'article provenant de la source Math-Net.Ru

We investigate the high-temperature relaxation function of a spin system with quadratic coupling of the resonance frequency to the Gaussian random process. In the general case, this function is expressed as an integral of an infinite auxiliary series. For the $N$-exponential Gauss–Markov process, the problem is reduced to solving a system of $2N$ linear equations. For brevity, we analyze the effect of fluctuations on the form of the magnetic resonance line (the Fourier image of the relaxation function). For both the one- and multiexponential processes in a crystal with dynamics of a relaxation type in the continuous phase transition domain, we find a nonmonotonic dependence of the asymmetrical homogeneously widened resonance line on the rate of fluctuations.

[1] A. Abragam, Yadernyi magnetizm, IL, M., 1963

[2] P. W. Anderson, P. R. Weiss, Rev. Mod. Phys., 25 (1953), 269 | DOI

[3] P. W. Anderson, J. Phys. Soc. Japan, 9 (1954), 316 | DOI

[4] W. B. Mims, Phys. Rev., 168 (1968), 370 | DOI

[5] V. E, Zobov, A. A. Lundin, Pisma v ZhETF, 43 (1986), 418

[6] E. L. Nagaev, Magnetiki so slozhnymi obmennymi vzaimodeistviyami, Nauka, M., 1988

[7] U. Kheberlen, M. Mering, YaMR vysokogo razresheniya v tverdykh telakh, Mir, M., 1980; U. Haeberlen, High Resolution NMR in Solids: Selective Averaging, Academic Press, New York–San Francisco–London, 1976; M. Mehring, High Resolution in NMR Spectroscopy in Solids, Springer-Verlag, Berlin–Heidelberg–New York, 1976

[8] I. N. Kovalenko, N. Yu. Kuznetsov, V. M. Shurenkov, Sluchainye protsessy, Naukova Dumka, Kiev, 1983 | MR

[9] R. Kubo, M. Toda, N. Hashitsume, Statistical physics, V. II, Springer-Verlag, Berlin–Heidelberg, 1985 | MR

[10] V. A. Emelichev, O. I. Melnikov, V. I. Sarvanov, R. I. Tyshkevich, Lektsii po teorii grafov, Nauka, M., 1990 | MR | Zbl

[11] V. E. Zobov, M. A. Popov, TMF, 102 (1995), 305 | Zbl

[12] Dzh. Ulenbek, Dzh. Ford, Lektsii po statisticheskoi mekhanike, Mir, M., 1965

[13] J. Łuczka, J. Phys. A, 21 (1988), 3063 | DOI | MR

[14] L. D. Landau, E. M. Lifshits, Statisticheskaya fizika, Chast 1, Nauka, M., 1976 | MR

[15] V. L. Ginzburg, FTT, 2 (1960), 2031 | MR

[16] R. L. Amstrong, Progr. in NMR Spectroscopy, 21 (1989), 151 | DOI