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

S.E. Kuratov^†^a, D.S. Shidlovski^a, b, S.I. Blinnikov^a, b, S.Yu. Igashov^a
^aDukhov Research Institute of Automatics, ul. Sushchevskaya 22, Moscow, 119017, Russian Federation
^bNational Research Center "Kurchatov Institute", Alikhanov Institute of Theoretical and Experimental Physics, ul. B. Cheremushkinskaya 25, Moscow, 117218, Russian Federation

A new nontrivial manifestation of quantum effects in a spherical mesoscopic system of degenerate electrons (with N_e ≲ 10⁹ electrons) is demonstrated. Analysis shows that the electron distribution function has a large spatial scale, of the order of the system size, which is much greater than the other spatial scale, the Fermi length of the electron. This result is obtained following four different strategies: an analytic method of semiclassical Green's functions, direct numerical summation of the exact solutions for electron wave functions in an infinite potential well, numerical construction of the exact Green's function using two linearly independent solutions, and the density functional method. The results obtained with these methods are in good qualitative and quantitative agreement with each other. We relate the nature of this phenomenon to quantum shell effects in a spherical mesoscopic system.

Keywords: electron distribution in a spherical potential, Green's function, density-functional theory, jellium model
PACS: 31.15.E−, 71.10.Ca, 71.15.Mb, 73.20.−r (all)
DOI: 10.3367/UFNe.2020.08.038817
URL: https://ufn.ru/en/articles/2021/8/e/
Web of Science

000711503200009
Scopus

2-s2.0-85119689311
ADS NASA

2021PhyU...64..836K
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. 64 836–851 (2021)

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Received: 8th, July 2020, accepted: 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 191 882–898 (2021); DOI: 10.3367/UFNr.2020.08.038817

References (37) Cited by (2) Similar articles (14) ↓

G.V. Shpatakovskaya “Semiclassical method of analysis and estimation of the orbital binding energies in many-electron atoms and ions” Phys. Usp. 62 186–197 (2019)
V.M. Rozenbaum, I.V. Shapochkina, L.I. Trakhtenberg “Quantum particle in a V-shaped well of arbitrary asymmetry. Brownian motors” Phys. Usp. 67 1046–1055 (2024)
Z.G. Bazhanova, V.V. Roizen, A.R. Oganov “High-pressure behavior of the Fe—S system and composition of the Earth's inner core” Phys. Usp. 60 1025–1032 (2017)
E.G. Maksimov, O.V. Dolgov “A note on the possible mechanisms of high-temperature superconductivity” Phys. Usp. 50 933–937 (2007)
S.I. Blinnikov, L.B. Okun, M.I. Vysotskii “Critical velocities c/sqrt{3} and c/sqrt{2} in the general theory of relativity” Phys. Usp. 46 1099–1103 (2003)
V.M. Rozenbaum, I.V. Shapochkina, L.I. Trakhtenberg “Green's function method in the theory of Brownian motors” Phys. Usp. 62 496–509 (2019)
P.A. Krachkov, A.I. Mil’shtein “An operator derivation of the quasiclassical Green's function” Phys. Usp. 61 896–899 (2018)
V.F. Gantmakher “Chemical localization” Phys. Usp. 45 1165–1174 (2002)
V.I. Ritus “Generalization of the k coefficient method in relativity to an arbitrary angle between the velocity of an observer (source) and the direction of the light ray from (to) a faraway source (observer) at rest” Phys. Usp. 63 601–610 (2020)
A.A. Rukhadze, V.P. Silin “From Lord Rayleigh to Professor A.A. Vlasov (from 1906 to 1945)” Phys. Usp. 62 691–698 (2019)
B.A. Klumov “On melting criteria for complex plasma” Phys. Usp. 53 1053–1065 (2010)
V.L. Kraĭnov, L.P. Presnyakov “Phase functions for potential scattering in optics” Phys. Usp. 36 (7) 621–627 (1993)
V.P. Bykov, V.I. Tatarskii “Perturbation theory for resolvents as applied to problems in radiation theory” Sov. Phys. Usp. 34 (2) 167–184 (1991)
S.I. Chermyanin “Predictions of the general theory of relativity are free from ambiguity” Sov. Phys. Usp. 33 (5) 385–387 (1990)

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