Quantum Tunneling Effect on the Transverse Motion Energy Spectrum for the Channeling Positrons in the Silicon Crystal

V. V. Syshchenko; Сыщенко В. В.; A. I. Tarnovsky; Тарновский А. И.; V. I. Dronik; Дроник В. И.; A. Yu. Isupov; Исупов А. Ю.

doi:10.31857/S1028096023060158

Quantum Tunneling Effect on the Transverse Motion Energy Spectrum for the Channeling Positrons in the Silicon Crystal

Authors: Syshchenko V.V.¹, Tarnovsky A.I.², Dronik V.I.¹, Isupov A.Y.²
Affiliations:
1. Belgorod State University
2. Laboratory of High Energy Physics, Joint Institute for Nuclear Research
Issue: No 6 (2023)
Pages: 88-93
Section: Articles
URL: https://bakhtiniada.ru/1028-0960/article/view/137773
DOI: https://doi.org/10.31857/S1028096023060158
EDN: https://elibrary.ru/DKNZVA
ID: 137773

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Abstract
About the authors
References
Supplementary files
Statistics

Abstract

The charged particles motion in the crystal could be either regular or chaotic. In the quantum picture the chaos manifests itself in the statistical properties of the energy levels set. The systems with regular motion domains in the phase space separated by the chaotic one are of a particular interest. The possibility to tunnel between dynamically isolated domains of the phase space influences essentially on the energy levels statistics. This effect account leads to Podolskiy–Narimanov distribution function. The tunneling matrix elements for the transversal motion of 20 and 40 GeV positrons axially channeled in [100] direction of Si crystal are estimated in the present paper. The parameter of the Podolskiy–Narimanov distribution is derived from this estimation. It is demonstrated that this distribution successfully describes the level spacing statistics for the energy levels set of the positron transversal motion.

Keywords

regular dynamics, chaotic dynamics, quantum chaos, channeling, semiclassical approximation, level spacing statistics, Berry–Robnik distribution, dynamical tunneling, chaos-assisted tunneling, Podolskiy–Narimanov distribution.

References

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