{"title":"沿变形黎曼流形的量子运动中的维格纳时延和哈特曼效应","authors":"Benjamin Schwager, Lars Meschede, Jamal Berakdar","doi":"10.1139/cjp-2023-0303","DOIUrl":null,"url":null,"abstract":"Elastic scattering of a wave can be quantified by a shift in the phase with respect to the incoming wave phase. A qualitative measure of the time during which the effect occurs is given by the Wigner time delay. The tunneling time in turn is known to saturate with increasing tunneling barrier width (Hartman effect). Here, we analyze the elastic quantum mechanical scattering in a deformed one-dimensional Riemannian manifold, particularly with respect to theWigner time delay and conclude on the Hartman effect. It is shown that scattering due to local curvature variations imply imperfect conduction behavior indicating resonance states and leads to a Wigner time delay which, at low energies, is in variance with the classical time delay that is inferred from the arc length. At moderate and high energies, however, classical and quantum time delays coincide.","PeriodicalId":9413,"journal":{"name":"Canadian Journal of Physics","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Wigner time delay and Hartman effect in quantum motion along deformed Riemannian manifolds\",\"authors\":\"Benjamin Schwager, Lars Meschede, Jamal Berakdar\",\"doi\":\"10.1139/cjp-2023-0303\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Elastic scattering of a wave can be quantified by a shift in the phase with respect to the incoming wave phase. A qualitative measure of the time during which the effect occurs is given by the Wigner time delay. The tunneling time in turn is known to saturate with increasing tunneling barrier width (Hartman effect). Here, we analyze the elastic quantum mechanical scattering in a deformed one-dimensional Riemannian manifold, particularly with respect to theWigner time delay and conclude on the Hartman effect. It is shown that scattering due to local curvature variations imply imperfect conduction behavior indicating resonance states and leads to a Wigner time delay which, at low energies, is in variance with the classical time delay that is inferred from the arc length. At moderate and high energies, however, classical and quantum time delays coincide.\",\"PeriodicalId\":9413,\"journal\":{\"name\":\"Canadian Journal of Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2024-02-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Canadian Journal of Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1139/cjp-2023-0303\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Canadian Journal of Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1139/cjp-2023-0303","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
Wigner time delay and Hartman effect in quantum motion along deformed Riemannian manifolds
Elastic scattering of a wave can be quantified by a shift in the phase with respect to the incoming wave phase. A qualitative measure of the time during which the effect occurs is given by the Wigner time delay. The tunneling time in turn is known to saturate with increasing tunneling barrier width (Hartman effect). Here, we analyze the elastic quantum mechanical scattering in a deformed one-dimensional Riemannian manifold, particularly with respect to theWigner time delay and conclude on the Hartman effect. It is shown that scattering due to local curvature variations imply imperfect conduction behavior indicating resonance states and leads to a Wigner time delay which, at low energies, is in variance with the classical time delay that is inferred from the arc length. At moderate and high energies, however, classical and quantum time delays coincide.
期刊介绍:
The Canadian Journal of Physics publishes research articles, rapid communications, and review articles that report significant advances in research in physics, including atomic and molecular physics; condensed matter; elementary particles and fields; nuclear physics; gases, fluid dynamics, and plasmas; electromagnetism and optics; mathematical physics; interdisciplinary, classical, and applied physics; relativity and cosmology; physics education research; statistical mechanics and thermodynamics; quantum physics and quantum computing; gravitation and string theory; biophysics; aeronomy and space physics; and astrophysics.