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Two scales of quantum effects in a mesoscopic system of degenerate electrons

 a,  a, b,  c, a, b, d,  a
a Dukhov Research Institute of Automatics, ul. Sushchevskaya 22, Moscow, 119017, Russian Federation
b National Research Center "Kurchatov Institute", Alikhanov Institute of Theoretical and Experimental Physics, ul. B. Cheremushkinskaya 25, Moscow, 117218, Russian Federation
c Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russian Federation
d Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwanoha 5-1-5, Kashiwa, 277-8568, Japan

A new non-trivial manifestation of quantum effects in a spherical mesoscopic system of degenerate electrons ($ N_e \lesssim 10^9 $) is demonstrated. As a result of the analysis, it was shown that the electron distribution function has a large spatial scale, which is of the order of the size of the system and significantly larger than the other spatial scale - the Fermi length of the electron $ \sim h / p_{\rm F} $. This result was obtained using four different methodological approaches: the analytical method - the method of quasiclassical Green functions, direct numerical summation of exact solutions for electronic wave functions in an infinite potential well, the numerical method for constructing the exact Green function using two linearly independent solutions, and the density functional method. The results obtained using these methods are in good qualitative and quantitative agreement among themselves. The authors attribute the nature of the effect to the manifestation of quantum shell effects in a spherical mesoscopic system.

DOI: 10.3367/UFNe.2020.08.038817
Citation: Kuratov S E, Shidlovski D S, Blinnikov S I, Igashov S Yu "Two scales of quantum effects in a mesoscopic system of degenerate electrons" Phys. Usp., accepted

Received: 8th, July 2020, 11th, August 2020

Оригинал: Куратов С Е, Шидловский Д С, Блинников С И, Игашов С Ю «Два масштаба квантовых эффектов в мезоскопической системе вырожденных электронов» УФН, принята к публикации; DOI: 10.3367/UFNr.2020.08.038817

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