Related papers: Semiclassical wave functions in billiards built on…
Square billiards are quantum systems complying with the dynamical quantum-classical correspondence. Hence an initially localized wavefunction launched along a classical periodic orbit evolves along that orbit, the spreading of the quantum…
Integrability of a square billiard is spontaneously broken as it rotates about one of its corners. The system becomes quasi-integrable where the invariant tori are broken with respect to a certain parameter, $\lambda = 2E/\omega^{2}$ where…
We derive semiclassical approximations for wavefunctions, Green's functions and expectation values for classically chaotic quantum systems. Our method consists of applying singular and regular perturbations to quantum Hamiltonians. The…
We investigate the influence of spin-orbit interaction on ballistic transport through chaotic cavities by using semiclassical methods. Our approach is based on the Landauer formalism and the Fisher-Lee relations, appropriately generalized…
Numerical calculations studying bound eigenstates in chaotic regions of phase space, including those of the stadium billiard, are summarized. These calculations demonstrate that the scars of periodic orbit model is seriously flawed. An…
A semiclassical approximation for the matrix elements of a quantum chaotic propagator in the scar function basis has been derived. The obtained expression is solely expressed in terms of canonical invariant objects. For our purpose, we have…
An electron in quantum confinement takes on a discrete energy spectrum which is defined based on the solution to the Schrodinger Equation for a given potential. Well defined closed-form energy spectra are known for the particle in a box,…
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…
We derive many-body single- and multi-reference wave functions for quantum Monte Carlo of periodic systems with an anti-symmetric portion that explicitly integrates over the Brillouin zone of one-particle Bloch states. The wave functions…
We propose a semiclassical approach to calculate multiparticle cross sections in scalar theories, which have been strongly argued to have the exponential form $\exp(\lambda^{-1}F(\lambda n,\epsilon))$ in the regime $\lambda\to0$, $\lambda…
The energy spectrum and the eigenstates of a rectangular quantum dot containing soft potential walls in contact with a superconductor are calculated by solving the Bogoliubov-de Gennes (BdG) equation. We compare the quantum mechanical…
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…
Using semiclassical methods, it is possible to construct very accurate approximations in the short wavelength limit of quantum dynamics that rely exclusively on classical dynamical input. For systems whose classical realization is strongly…
We numerically investigate the stability of exceptional periodic classical trajectories in rather generic chaotic many-body systems and explore a possible connection between these trajectories and exceptional nonthermal quantum eigenstates…
We derive a four-component Vlasov equation for a system composed of spin-1/2 fermions (typically electrons). The orbital part of the motion is classical, whereas the spin degrees of freedom are treated in a completely quantum-mechanical…
In numerically solving the Helmholtz equation inside a connected plane domain with Dirichlet boundary conditions (the problem of the quantum billiard) one surprisingly faces enormous difficulties if the domain has a problematic geometry…
Semiclassical behavior of Stark resonances is studied. The complex distortion outside a cone is introduced to study resonances in any energy region for the Stark Hamiltonians with non-globally analytic potentials. The non-trapping resolvent…
We study a special kind of semiclassical limit of quantum dynamics on a circle and in a box (infinite potential well with hard walls) as the Planck constant tends to zero and time tends to infinity. The results give detailed information…
We study the effect on the density of states in mesoscopic ballistic billiards to which a superconducting lead is attached. The expression for the density of states is derived in the semiclassical S-matrix formalism shedding insight into…
We introduce the spherical wedge billiard, a dynamical system consisting of a particle moving along a geodesic on a closed non-Euclidean surface of a spherical wedge. We derive the analytic form of the corresponding Poincar\'e map and find…