The heat kernel for two Aharonov-Bohm solenoids in a uniform magnetic field

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• 作者：Pavel &Scaron ; ťoví ; ček ^{stovicek@kmlinux.fjfi.cvut.cz}
• 关键词：Aharonov&ndash ; Bohm solenoid ; Uniform magnetic field ; Heat kernel ; Landau level
• 刊名：Annals of Physics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：376
• 期：Complete
• 页码：254-282
• 全文大小：1518 K
• 卷排序：376

文摘

A non-relativistic quantum model is considered with a point particle carrying a charge ee and moving in the plane pierced by two infinitesimally thin Aharonov–Bohm solenoids and subjected to a perpendicular uniform magnetic field of magnitude BB. Relying on a technique originally due to Schulman, Laidlaw and DeWitt which is applicable to Schrödinger operators on multiply connected configuration manifolds a formula is derived for the corresponding heat kernel. As an application of the heat kernel formula, approximate asymptotic expressions are derived for the lowest eigenvalue lying above the first Landau level and for the corresponding eigenfunction while assuming that |eB|R2/(ħc)|eB|R2/(ħc) is large, where RR is the distance between the two solenoids.