The boundary integral method for magnetic billiards

The boundary integral method for magnetic billiards

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...

Boundary integral method applied in chaotic quantum billiards

The boundary integral method (BIM) is a formulation of Helmholtz equation in the form of an integral equation suitable for numerical discretization to solve the quantum billiard. This paper is an extensive numerical survey of BIM in a variety of quantum billiards, integrable (circle, rectangle), KAM systems (Robnik billiard) and fully chaotic (ergodic, such as stadium, Sinai billiard and cardio...

A boundary integral formalism for stochastic ray tracing in billiards.

Determining the flow of rays or non-interacting particles driven by a force or velocity field is fundamental to modelling many physical processes. These include particle flows arising in fluid mechanics and ray flows arising in the geometrical optics limit of linear wave equations. In many practical applications, the driving field is not known exactly and the dynamics are determined only up to ...

Boundary-integral method for poloidal axisymmetric AC magnetic fields

This paper presents a boundary-integral equation (BIE) method for the calculation of poloidal axisymmetric magnetic fields applicable in a wide range of ac frequencies. The method is based on the vector potential formulation and it uses the Green’s functions of Laplace and Helmholtz equations for the exterior and interior of conductors, respectively. The work is particularly focused on a calcul...

The Boundary Integral Equation Method