Pavel Exner, Vladimir A. Geyler
Berry phase for a potential well transported in a homogeneous
magnetic field
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ABSTRACT. 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
$2\pi\,{\rm sgn}\,e$ 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.