Related papers: Boundary Integral Method for Stationary States of …
We present a scheme for controlling the state of a quantum system by modifying the boundary conditions. This constitutes an infinite-dimensional control problem. We provide conditions for the existence of solutions of the dynamics and prove…
The Cahn-Hilliard equation is a fundamental model for describing phase separation phenomena in binary mixtures. Traditional numerical methods, such as finite difference and finite element methods, often incur substantial computational cost,…
The eigenvalues of the Hyperspherical billiard are calculated in the semiclassical approximation. The eigenvalues where this approximation fails are identified and found to be related to caustics that approach the wall of the billiard. The…
We examine the quantum motion of two particles interacting through a contact force which are confined in a rectangular domain in two and three dimensions. When there is a difference in the mass scale of two particles, adiabatic separation…
We present a distinct mechanism for the formation of bound states in the continuum (BICs). In chiral quantum systems there appear zero-energy states in which the wave function has finite amplitude only in one of the subsystems defined by…
We study the quantum mechanics of a billiard (Robnik 1983) in the regime of mixed-type classical phase space (the shape parameter \lambda=0.15) at very high-lying eigenstates, starting at about 1.000.000th eigenstate and including the…
The boundary of the lemon billiards is defined by the intersection of two circles of equal unit radius with the distance $2B$ between their centers, as introduced by Heller and Tomsovic in Phys. Today {\bf 46} 38 (1993). This paper is a…
Quantization of a toy model of a pseudointegrable Hamiltonian impact system is introduced, including EBK quantization conditions, a verification of Weyl's law, the study of their wavefunctions and a study of their energy levels properties.…
We consider billiard ball motion in a convex domain on a constant curvature surface influenced by the constant magnetic field. We examine the existence of integral of motion which is polynomial in velocities. We prove that if such an…
A new method is proposed for determining the ground state wave function of a quantum many-body system on a quantum computer, without requiring an initial trial wave function that has good overlap with the true ground state. The technique of…
This dissertation presents and prove the viability of a non-standard method for controlling the state of a quantum system by modifying its boundary conditions instead of relying on the action of external fields. The standard approach to…
We propose time-domain boundary integral and coupled boundary integral and variational formulations for acoustic scattering by linearly elastic obstacles. Well posedness along with stability and error bounds with explicit time dependence…
Single and double-slit experiments are performed with two microwave billiards with the shapes of a rectangle, respectively, a quarter stadium. The classical dynamics of the former is regular, that of the latter is chaotic. Microwaves can…
Most problems in electrodynamics do not have an analytical solution so much effort has been put in the development of numerical schemes, such as the finite-difference method, volume element methods, boundary element methods, and related…
We study numerically quantum transport through a billiard with a classically mixed phase space. In particular, we calculate the conductance and Wigner delay time by employing a recursive Green's function method. We find sharp, isolated…
A new approach to solving two-point boundary value problems for a wave equation is developed. This new approach exploits the principle of stationary action to reformulate and solve such problems in the framework of optimal control. In…
We illustrate some of the techniques to identify chaos signatures at the quantum level using as a guiding examples some systems where a particle is constrained to move on a radial symmetric, but non planar, surface. In particular, two…
With a perturbation body technique intensity distributions of the electric field strength in a flat microwave billiard with a barrier inside up to mode numbers as large as about 700 were measured. A method for the reconstruction of the…
We propose a general method that allows to detect the existence of normalizable ground states in supersymmetric quantum mechanical systems with non-Fredholm spectrum. We apply our method to show the existence of bound states at threshold in…
The paper is devoted to the Hamiltonian treatment of classical and quantum properties of Liouville field theory on a timelike strip in 2d Minkowski space. We give a complete description of classical solutions regular in the interior of the…