Related papers: Boundary Integral Method for Stationary States of …
We introduce a method for effectively identifying bound states in the continuum (BICs) - notably without computing the imaginary part of the eigenvalues - thereby simplifying the modeling and potentially reducing computation time. In real,…
The paper establishes the property of splittability of billiard boundary sequences in n dimensional cube into subsequences of fractional parts. This reveals a new property of integrable and weak perturbated Hamilton systems: under a simple…
Systems of three and four quantum particles in the boundary-condition model are considered. The Faddeev-Yakubovsky approach is applied to construct the Fredholm-type integral equations for these systems in framework of the Potential theory.…
For two dimensional Schroedinger Hamiltonians we formulate boundary conditions that split the Hilbert space according to the chirality of the eigenstates on the boundary. With magnetic fields, and in particular, for Quantum Hall Systems,…
This paper provides a rigorous analysis of boundary element methods for the magnetic field integral equation on Lipschitz polyhedra. The magnetic field integral equation is widely used in practical applications to model electromagnetic…
The properties of energy levels in a family of classically pseudointegrable systems, the barrier billiards, are investigated. An extensive numerical study of nearest-neighbor spacing distributions, next-to-nearest spacing distributions,…
This paper presents a re-formulation of the boundary integral method (BIM) for the Debye-Huckel model of molecular and colloidal electrostatics that removes the mathematical singularities that have been accepted as an intrinsic part of the…
Eigenfunctions of integrable planar billiards are studied - in particular, the number of nodal domains, $\nu$, of the eigenfunctions are considered. The billiards for which the time-independent Schr\"odinger equation (Helmholtz equation) is…
The relative motion of three impenetrable particles on a ring, in our case two identical fermions and one impurity, is isomorphic to a triangular quantum billiard. Depending on the ratio $\kappa$ of the impurity and fermion masses, the…
We present a computational scheme based on classical molecular dynamics to study chaotic billiards in static external magnetic fields. The method allows to treat arbitrary geometries and several interacting particles. We test the scheme for…
The purpose of this talk is to sketch some recent progress which has been made in calculating non-perturbatively the reflection factors for the sinh-Gordon model restricted to a half-line by integrable boundary conditions. The essential…
The quantum dynamics of a chaotic billiard with moving boundary is considered in this work. We found a shape parameter Hamiltonian expansion which enables us to obtain the spectrum of the deformed billiard for deformations so large as the…
We show that wave functions in planar rational polygonal billiards (all angles rationally related to Pi) can be expanded in a basis of quasi-stationary and spatially regular states. Unlike the energy eigenstates, these states are directly…
We obtain a semiclassical expression for the projector onto eigenfunctions by means of the Fredholm theory. We express the projector in the coherent state basis, thus obtaining the semiclassical Husimi representation of the stadium…
We study two-dimensional classically integrable field theory with independent boundary condition on each end, and obtain three possible generating functions for integrals of motion when this model is an ultralocal one. Classically…
We study the ground state energy of integrable $1+1$ quantum field theories with boundaries (the genuine Casimir effect). In the scalar case, this is done by introducing a new, ``R-channel TBA'', where the boundary is represented by a…
In this series of lectures we present the universal method based on the use of the functional integrals to derive the bound state equations for different two-body systems in elementary particle physics as well as in condensed matter theory:…
We present a boundary integral formulation of the Helmholtz equation with visco-thermal boundary conditions, in two dimensions. Such boundary conditions allow for the accurate simulation of viscous and thermal losses in the vicinity of the…
A new algorithm for determining the eigenstates of n-dimensional billiards is presented. It is based on the application of the Cauchy theorem for the determination of the null space of the boundary overlap matrix. The method is free from…
This paper presents a novel and efficient approach for the computation of energy eigenvalues in quantum semiconductor heterostructures. Accurate determination of the electronic states in these heterostructures is crucial for understanding…