 99431 Pavel Exner, Vladimir A. Geyler
 Berry phase in magnetic systems with point perturbations
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Nov 13, 99

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Abstract. We study a twodimensional charged particle interacting with a
magnetic field, in general nonhomogeneous, 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 zerorange one. We also discuss the
behavior of the lowest Landau level in this setting obtaining an
explicit example of the WilczekZee phase for an infinitely
degenerated eigenvalue.
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