Related papers: Interfering resonances in a quantum billiard
The resonant state expansion, a rigorous perturbation theory, recently developed in electrodynamics, is applied to non-relativistic quantum mechanical systems in one dimension. The method is used here for finding the resonant states in…
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 have observed proximity resonances in a two dimensional system consisting of dielectric scatterers in a parallel plate waveguide. A numerical solution to the scattering problem supports the analysis of the experimental data.
This article presents a new method to calculate eigenvalues of right triangle billiards. Its efficiency is comparable to the boundary integral method and more recently developed variants. Its simplicity and explicitness however allow new…
A trial wave function is proposed for studying the instability of the two-dimensional Hubbard model with respect to d-wave superconductivity. Double occupancy is reduced in a similar way as in previous variational studies, but in addition…
For two-dimensional quantum billiards we derive the partial Weyl law, i.e. the average density of states, for a subset of eigenstates concentrating on an invariant region $\Gamma$ of phase space. The leading term is proportional to the area…
Recent work has explored binary waveguide arrays in the long-wavelength, near-continuum limit, here we examine the opposite limit, namely the vicinity of the so-called anti-continuum limit. We provide a systematic discussion of states…
We investigate a class of mechanical billiards, where a particle moves in a planar region under the influence of an n-centre potential and reflects elastically on a straight wall. Motivated by Boltzmann's original billiard model we explore…
Billiards tables - a minimal model for particles moving in a confined region - are known to present classical (and quantum) different features according to their shape, ranging from strongly chaotic to integrable dynamics. Here we consider…
We show that two-dimensional billiard systems are Turing complete, in the sense that the halting of any Turing machine with a given input is equivalent to a certain bounded trajectory in this system entering a specified open set. Billiards…
We study the convergence towards the equilibrium for a dissipative and stochastic time-dependent oval billiard. The dynamics of the system is described by using a generic four dimensional nonlinear map for the variables: the angular…
In this paper we consider embedded eigenvalues of a Schroedinger Hamiltonian in a waveguide induced by a symmetric perturbation. It is shown that these eigenvalues become unstable and turn into resonances after twisting of the waveguide.…
The present work consists of a numerical study of the dynamics of irrational polygonal billiards. Our contribution reinforces the hypothesis that these systems could be Strongly Mixing, although never demonstrably chaotic, and discuss the…
We study scattering from potentials that rise monotonically on one side; this is generally avoided. We report that resonant states are absent in such potentials when they are smooth and single-piece having less than three real turning…
Billiard models of single particles moving freely in two-dimensional regions enclosed by hard walls, have long provided ideal toy models for the investigation of dynamical systems and chaos. Recently, billiards with (semi-)permeable walls…
This paper explores the number of parallelograms that appear in a billiard path that enters one corner of a rectangle and leaves a second corner of a rectangle as a function of the normalized dimensions of the rectangle.
The notions of reflection from outside, reflection from inside and signature of a billiard trajectory within a quadric are introduced. Cayley-type conditions for periodical trajectories for the billiard in the region bounded by $k$ quadrics…
We study chaotic properties of eigenstates depending on the degree of complexity in boundaries of a 2D periodic billiard. Main attention is paid to the situation when the motion of a classical particle is strongly chaotic. Our approach…
The classical inner and outer billiards can be formulated in variational terms, with length and area as the respective generating functions. The other two combinations, ``inner with area'' and ``outer with length,'' are more recently…
We present experimental studies of the geometry-specific quantum scattering in microwave billiards of a given shape. We perform full quantum mechanical scattering calculations and find an excellent agreement with the experimental results.…