Geodesic
Self-consistent description of spatial structures in one-dimensional quantum systems at finite temperatures
Teoretičeskaâ i matematičeskaâ fizika, Tome 75 (1988) no. 2, pp. 267-274

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A self-consistent system of maps for the analysis of spatial structures and their spectrum of small vibrations in a quantum chain of atoms in an external field at finite temperatures is derived. A numerical analysis of random structures and their stability is made. The local nature of the appearance of low-frequency vibrations is demonstrated. 
@article{TMF_1988_75_2_a10,
     author = {V. V. Beloshapkin and G. P. Berman and A. G. Tret'yakov},
     title = {Self-consistent description of spatial structures in one-dimensional quantum systems at finite temperatures},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {267--274},
     publisher = {mathdoc},
     volume = {75},
     number = {2},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1988_75_2_a10/}
}
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V. V. Beloshapkin; G. P. Berman; A. G. Tret'yakov. Self-consistent description of spatial structures in one-dimensional quantum systems at finite temperatures. Teoretičeskaâ i matematičeskaâ fizika, Tome 75 (1988) no. 2, pp. 267-274. http://geodesic.mathdoc.fr/item/TMF_1988_75_2_a10/