Geodesic
Semiclassical asymptotic behavior of the~lower spectral bands of the~Schr\"odinger operator with a~trigonal-symmetric periodic potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 202 (2020) no. 2, pp. 264-277

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We study the semiclassical approximation of the lower bands of the Schrödinger operator with a periodic two-dimensional potential with a trigonal symmetry and consider the cases where the potential has one or two wells in the elementary cell. We obtain the exponentially small asymptotic behavior of the band width and find the dispersion relations. We investigate the form of the Bloch functions. Solving this problem is the first step in studying the more complicated (and more physically interesting) problem of tunnel effects in rotating dimers.
Keywords: periodic Schrödinger operator, semiclassical asymptotic behavior, spectral band
Mots-clés : tunnel effect. 
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     author = {A. Yu. Anikin and M. A. Vavilova},
     title = {Semiclassical asymptotic behavior of the~lower spectral bands of {the~Schr\"odinger} operator with a~trigonal-symmetric periodic potential},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {264--277},
     publisher = {mathdoc},
     volume = {202},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2020_202_2_a5/}
}
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A. Yu. Anikin; M. A. Vavilova. Semiclassical asymptotic behavior of the~lower spectral bands of the~Schr\"odinger operator with a~trigonal-symmetric periodic potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 202 (2020) no. 2, pp. 264-277. http://geodesic.mathdoc.fr/item/TMF_2020_202_2_a5/