Vladimir A. Geyler | Searcharxiv

arXiv2000

Berry phase for a potential well transported in a homogeneous magnetic field

We consider a two-dimensional particle of charge $e$ interacting with a homogeneous magnetic field perpendicular to the plane and a potential well which is transported along a closed loop in the plane. We show that a bound state corresponding to a simple isolated eigenvalue acquires at that Berry's phase equal to $2π{\rm sgn} e$ times the number of flux quanta through the oriented area encircled by the loop. We also argue that this is a purely quantum effect since the corresponding Hannay angle is zero.

quant-ph↗

arXiv1999

Berry phase in magnetic systems with point perturbations

We study a two-dimensional charged particle interacting with a magnetic field, in general non-homogeneous, perpendicular to the plane, a confining potential, and a point interaction. If the latter moves adiabatically along a loop the state corresponding to an isolated eigenvalue acquires a Berry phase. We derive an expression for it and evaluate it in several examples such as a homogeneous field, a magnetic whisker, a particle confined at a ring or in quantum dots, a parabolic and a zero-range one. We also discuss the behavior of the lowest Landau level in this setting obtaining an explicit example of the Wilczek-Zee phase for an infinitely degenerated eigenvalue.

quant-ph↗