The boundary integral method for magnetic billiards

Abstract

We introduce a boundary integral method for two-dimensional quantum billiards subjected to a constant magnetic field. It allows to calculate spectra and wave functions, in particular at strong fields and semiclassical values of the magnetic length. The method is presented for interior and exterior problems with general boundary conditions. We explain why the magnetic analogues of the field-free single and double layer equations exhibit an infinity of spurious solutions and how these can be eliminated at the expense of dealing with (hyper-)singular operators. The high efficiency of the method is demonstrated by numerical calculations in the extreme semiclassical regime.

28 pages, 12 figures

References in corpus (2)

• Periodic Orbit Theory of the circular billiard in homogeneous magnetic fields
• Semi-classical spectrum of integrable systems in a magnetic field

Cited by in corpus (5)

• Consolidating boundary methods for finding the eigenstates of billiards
• Magnetic edge states of impenetrable stripe
• Resonant alteration of propagation in guiding structures with complex Robin parameter and its magnetic-field-induced restoration
• Guiding structures with multiply connected cross-sections: evolution of propagation in external fields at complex Robin parameters
• Spectral cross correlations of magnetic edge states