M. B. Semenov, V. D. Krevchik, P. V. Krevchik, I. M. Semenov, D. A. Saburova, T. P. Yurtaeva, A. E. Zhurina, D. A. Mukhaev, A. I. Sal’nikova, I. S. Antonov, A. V. Druzhinina, A. A. Mashkarina, I. A. Rubtsov
{"title":"An Analytical Model of 2D Dissipative Tunnel Bifurcations for Planar Structures with Gold Nanoparticles in an External Electric Field","authors":"M. B. Semenov, V. D. Krevchik, P. V. Krevchik, I. M. Semenov, D. A. Saburova, T. P. Yurtaeva, A. E. Zhurina, D. A. Mukhaev, A. I. Sal’nikova, I. S. Antonov, A. V. Druzhinina, A. A. Mashkarina, I. A. Rubtsov","doi":"10.1134/s1063785023700050","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The modern physics of condensed matter, chemistry, and biology deal with quite a large number of systems that are modeled by 1D and 2D oscillatory double-well potentials of variable topology, the parameters of which can change in an external electric field. In solving quantum problems, an exact analytical solution of the Schrödinger equation can only be obtained for a limited number of models (a well with infinite walls, a quantum oscillator, a hydrogen atom, a cubic parabola potential, a double-well oscillator, and some others). When studying a double-well oscillator potential, which simulates the low-temperature chemical kinetics, tunneling transport in structures with quantum dots (QDs) and quantum molecules and another analytical solution to the Schrödinger equation can only be found under the zero temperature condition and the assumption of the absent interaction of tunneling particles with a medium‒thermostat matrix. If these parameters are taken into account, the Schrödinger equation cannot be solved analytically within the conventional quantum-mechanical approach. In the semiclassical approximation (when the de Broglie wavelength of a tunneling particle is significantly shorter than the subbarrier length), using the instanton method, one can analytically determine the tunneling probability. This was first done by the pioneers of the science of quantum tunneling with dissipation: Acad. of the Russian Academy of Sciences A.I. Larkin, Prof. Yu.N. Ovchinnikov (Landau Institute for Theoretical Physics, Russian Academy of Sciences), and winner of the Nobel Prize in Physics (2003) Prof. A.J. Leggett et al. when modeling Josephson contacts with a cubic parabola potential [1, 2, 11]. A.A. Ovchinnikov, Yu.I. Dakhnovsky, and M.B. Semenov [11] were the first to obtain an analytical solution for a 1D double-well oscillatory potential within this theory when modeling low-temperature chemical reactions as tunnel systems with dissipation.</p>","PeriodicalId":784,"journal":{"name":"Technical Physics Letters","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Technical Physics Letters","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1134/s1063785023700050","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"PHYSICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
The modern physics of condensed matter, chemistry, and biology deal with quite a large number of systems that are modeled by 1D and 2D oscillatory double-well potentials of variable topology, the parameters of which can change in an external electric field. In solving quantum problems, an exact analytical solution of the Schrödinger equation can only be obtained for a limited number of models (a well with infinite walls, a quantum oscillator, a hydrogen atom, a cubic parabola potential, a double-well oscillator, and some others). When studying a double-well oscillator potential, which simulates the low-temperature chemical kinetics, tunneling transport in structures with quantum dots (QDs) and quantum molecules and another analytical solution to the Schrödinger equation can only be found under the zero temperature condition and the assumption of the absent interaction of tunneling particles with a medium‒thermostat matrix. If these parameters are taken into account, the Schrödinger equation cannot be solved analytically within the conventional quantum-mechanical approach. In the semiclassical approximation (when the de Broglie wavelength of a tunneling particle is significantly shorter than the subbarrier length), using the instanton method, one can analytically determine the tunneling probability. This was first done by the pioneers of the science of quantum tunneling with dissipation: Acad. of the Russian Academy of Sciences A.I. Larkin, Prof. Yu.N. Ovchinnikov (Landau Institute for Theoretical Physics, Russian Academy of Sciences), and winner of the Nobel Prize in Physics (2003) Prof. A.J. Leggett et al. when modeling Josephson contacts with a cubic parabola potential [1, 2, 11]. A.A. Ovchinnikov, Yu.I. Dakhnovsky, and M.B. Semenov [11] were the first to obtain an analytical solution for a 1D double-well oscillatory potential within this theory when modeling low-temperature chemical reactions as tunnel systems with dissipation.
期刊介绍：
Technical Physics Letters is a companion journal to Technical Physics and offers rapid publication of developments in theoretical and experimental physics with potential technological applications. Recent emphasis has included many papers on gas lasers and on lasing in semiconductors, as well as many reports on high Tc superconductivity. The excellent coverage of plasma physics seen in the parent journal, Technical Physics, is also present here with quick communication of developments in theoretical and experimental work in all fields with probable technical applications. Topics covered are basic and applied physics; plasma physics; solid state physics; physical electronics; accelerators; microwave electron devices; holography.
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