Related papers: Boundary Integral Method for Stationary States of …
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…
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…
The plane-wave decomposition method (PWDM), a widely used means of numerically finding eigenstates of the Helmholtz equation in billiard systems is described as a variant of the mathematically well-established boundary integral method…
A numerically efficient Fredholm formulation of the billiard problem is presented. The standard solution in the framework of the boundary integral method in terms of a search for roots of a secular determinant is reviewed first. We next…
We study the behaviour of the normal derivative of eigenfunctions of the Helmholtz equation inside billiards with Dirichlet boundary condition. These boundary functions are of particular importance because they uniquely determine the…
Determining the flow of rays or particles driven by a force or velocity field is fundamental to modelling many physical processes, including weather forecasting and the simulation of molecular dynamics. High frequency wave energy…
Quantum chaos manifests itself also in algorithmical complexity of methods, including the numerical ones, in solving the Schr\"odinger equation. In this contribution we address the problem of calculating the eigenenergies and the…
We derive semiclassical contributions of periodic orbits from a boundary integral equation for three-dimensional billiard systems. We use an iterative method that keeps track of the composition of the stability matrix and the Maslov index…
We propose a robust and efficient algorithm for computing bound states of infinite tight-binding systems that are made up of a finite scattering region connected to semi-infinite leads. Our method uses wave matching in close analogy to the…
In this paper we have tested several general numerical methods in solving the quantum billiards, such as the boundary integral method (BIM) and the plane wave decomposition method (PWDM). We performed extensive numerical investigations of…
In this paper, we consider the boundary integral equation (BIE) method for solving the exterior Neumann boundary value problems of elastic and thermoelastic waves in three dimensions based on the Fredholm integral equations of the first…
We present the expanded boundary integral method for solving the planar Helmholtz problem, which combines the ideas of the boundary integral method and the scaling method and is applicable to arbitrary shapes. We apply the method to a…
The path integral approach to quantum mechanics requires a substantial generalisation to describe the dynamics of systems confined to bounded domains. Non-local boundary conditions can be introduced in Feynman's approach by means of…
We present a comprehensive review of the nodal domains and lines of quantum billiards, emphasizing a quantitative comparison of theoretical findings to experiments. The nodal statistics are shown to distinguish not only between regular and…
The exact and semiclassical quantum mechanics of the elliptic billiard is investigated. The classical system is integrable and exhibits a separatrix, dividing the phasespace into regions of oscillatory and rotational motion. The classical…
The semiclassical theory for billiards with mixed boundary conditions is developed and explicit expressions for the smooth and the oscillatory parts of the spectral density are derived. The parametric dependence of the spectrum on the…
In the present paper we derive the Wigner current of the particle in a multidimensional billiard -- the compact region of space in which the particle moves freely. The calculation is based on proposed by us previously method of imposing…
This is the first survey of highly excited eigenstates of a chaotic 3D billiard. We introduce a strongly chaotic 3D billiard with a smooth boundary and we manage to calculate accurate eigenstates with sequential number (of a 48-fold…
We examine the quantum mechanical eigensolutions of the two-dimensional infinite well or quantum billiard system consisting of a circular boundary with an infinite barrier or baffle along a radius. Because of the change in boundary…
We consider a billiard model of a self-bound, interacting three-body system in two spatial dimensions. Numerical studies show that the classical dynamics is chaotic. The corresponding quantum system displays spectral fluctuations that…