Related papers: Semiclassical approximation for barrier billiards
We develop an Over Barrier Model for computing charge exchange between ions and one-active-electron atoms at low impact energies. The main feature of the model is the treatment of the barrier crossing process by the electron within a…
We present a comprehensive semiclassical investigation of the three-dimensional Sinai billiard, addressing a few outstanding problems in "quantum chaos". We were mainly concerned with the accuracy of the semiclassical trace formula in two…
We study the influence of a tunnel barrier on the quantum transport through a circular cavity. Our analysis in terms of classical trajectories shows that the semiclassical approaches developed for ballistic transport can be adapted to deal…
This work studies the semiclassical methods in multi-dimensional quantum systems bounded by finite potentials. By replacing the Maslov index by the scattering phase, the modified transfer operator method gives rather accurate corrections to…
Consider a family of smooth potentials $V_{\epsilon}$, which, in the limit $\epsilon\to0$, become a singular hard-wall potential of a multi-dimensional billiard. We define auxiliary billiard domains that asymptote, as $\epsilon\to0$ to the…
For a class of non-selfadjoint semiclassical operators in dimension one, we get a complete asymptotic description of all eigenvalues near a critical value of the leading symbol of the operator on the boundary of the pseudospectrum.
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…
We discuss consequences of a recent observation that the sequence of periodic orbits in a chaotic billiard behaves like a poissonian stochastic process on small scales. This enables the semiclassical form factor $K_{sc}(\tau)$ to agree with…
The semiclassical trace formula provides the basic construction from which one derives the semiclassical approximation for the spectrum of quantum systems which are chaotic in the classical limit. When the dimensionality of the system…
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…
In a recent letter [Phys. Rev. Lett. {\bf 100}, 164101 (2008)] and within the context of quantized chaotic billiards, random plane wave and semiclassical theoretical approaches were applied to an example of a relatively new class of…
We construct semi-infinite billiard domains which reverse the direction of most incoming particles. We prove that almost all particles will leave the open billiard domain after a finite number of reflections. Moreover, with high probability…
We study the aspects of quantum chaos in mushroom billiards introduced by Bunimovich. This family of billiards classically has the property of mixed phase space with precisely one entirely regular and one fully chaotic (ergodic) component,…
We discuss several problems in quasiclassical physics for which approximate solutions were recently obtained by a new method, and which can also be solved by novel versions of the Born-Oppenheimer approximation. These cases include the…
Quantum billiards provide an excellent forum for the analysis of quantum chaos. Toward this end, we consider quantum billiards with time-varying surfaces, which provide an important example of quantum chaos that does not require the…
Transmission through potential barriers is a fundamental problem in quantum mechanics. While semiclassical methods can approximate certain aspects of transmission, they fail to capture the intrinsically quantum interference associated with…
In order to verify Percival's conjecture [J. Phys. B 6,L229 (1973)] we study a planar billiard in its classical and quantum versions. We provide an evaluation of the nearest-neighbor level-spacing distribution for the Cassini oval billiard,…
We consider the problem of a semiclassical description of quantum chaotic transport, when a tunnel barrier is present in one of the leads. Using a semiclassical approach formulated in terms of a matrix model, we obtain transport moments as…
The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the…
The boundary integral method for calculating the stationary states of a quantum particle in nano-devices and quantum billiards is presented in detail at an elementary level. According to the method, wave functions inside the domain of the…