Square billiard with a magnetic flux

Abstract

Eigenstates and energy levels of a square quantum billiard in a magnetic field, or with an Aharonov-Bohm flux line, are found in quasiclassical approximation, that is, for high enough energy. Explicit formulas for the energy levels and wavefunctions are found. A number of interesting states are shown, together with their wavefunctions. Some states are diamagnetic, others paramagnetic, still others both dia- and paramagnetic. Some states are strongly localized. Related systems and possible experiments are briefly mentioned.

15 pages, 14 eps figures; added the following comment about the availability of figures: the higher quality figures are available in postscript from the authors at [email protected]

References in corpus (4)

• Recent Developments in the Theory of Scarring
• Magnetic Force Exerted by the Aharonov-Bohm Line (II)
• Distribution of Husimi Zeroes in Polygonal Billiards
• Semiclassical Treatment of Diffraction in Billiard Systems with a Flux Line

Cited by in corpus (6)

• Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities
• Imaginary time propagation code for large-scale two-dimensional eigenvalue problems in magnetic fields
• Billiards in magnetic fields: A molecular dynamics approach
• Relaxation properties in classical diamagnetism
• Diamagnetic persistent currents for electrons in ballistic billiards subject to a point flux
• Persistent currents in diffusive metallic cavities: Large values and anomalous scaling with disorder