Related papers: Semiclassical quantization with short periodic orb…

The semiclassical description of billiard spectra is extended to include the diffractive contributions from orbits which are nearly tangent to a concave part of the boundary. The leading correction for an unstable isolated orbit is of the…

We present a new semiclassical technique which relies on replacing complicated classical manifold structure with simpler manifolds, which are then evaluated by the usual semiclassical rules. Under circumstances where the original manifold…

We analyze the semiclassical limit of spectral theory on manifolds whose metrics have jump-like discontinuities. Such systems are quite different from manifolds with smooth Riemannian metrics because the semiclassical limit does not relate…

We apply periodic orbit theory to a two-dimensional non-integrable billiard system whose boundary is varied smoothly from a circular to an equilateral triangular shape. Although the classical dynamics becomes chaotic with increasing…

For a class of non-selfadjoint semiclassical pseudodifferential operators with double characteristics, we study bounds for resolvents and estimates for low lying eigenvalues. Specifically, assuming that the quadratic approximations of 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 introduce a semiclassical quantization method which is based on a stroboscopic description of the classical and the quantum flows. We show that this approach emerges naturally when one is interested in extracting the energy spectrum…

While a wealth of results has been obtained for chaos in single-particle quantum systems, much less is known about chaos in quantum many-body systems. We contribute to recent efforts to make a semiclassical analysis of such systems…

Let M = R n or possibly a Riemannian, non compact manifold. We consider semi-excited resonances for a h-differential operator H(x, hD x ; h) on L 2 (M) induced by a non-degenerate periodic orbit $\gamma$ 0 of semi-hyperbolic type, which is…

In this text we study billiards on ovals and investigate some consequences of a rotational symmetry of the boundary on the dynamics. As it simplifies some calculations, the symmetry helps to obtain the results. We focus on periodic orbits…

We have developed a semiclassical theory of short periodic orbits to obtain all quantum information of a bounded chaotic Hamiltonian system. If T_1 is the period of the shortest periodic orbit, T_2 the period of the next one and so on, the…

A class of singular integral operators, encompassing two physically relevant cases arising in perturbative QCD and in classical fluid dynamics, is presented and analyzed. It is shown that three special values of the parameters allow for an…

We study billiards in plane domains, with a perpendicular magnetic field and a potential. We give some results on periodic orbits, KAM tori and adiabatic invariants. We also prove the existence of bound states in a related scattering…

An initial coherent state is propagated exactly by a kicked quantum Hamiltonian and its associated classical stroboscopic map. The classical trajectories within the initial state are regular for low kicking strengths, then bifurcate and…

In this letter we give a systematic derivation and justification of the semiclassical model for the slow degrees of freedom in adiabatic slow-fast systems first found by Littlejohn and Flynn [5]. The classical Hamiltonian obtains a…

Harmonic inversion is introduced as a powerful tool for both the analysis of quantum spectra and semiclassical periodic orbit quantization. The method allows to circumvent the uncertainty principle of the conventional Fourier transform and…

This paper studies a class of $1\frac12$-degree-of-freedom Hamiltonian systems with a slowly varying phase that unfolds a Hamiltonian pitchfork bifurcation. The main result of the paper is that there exists an order of…

We present a classical and quantum mechanical study of an Andreev billiard with a chaotic normal dot. We demonstrate that in general the classical dynamics of these normal-superconductor hybrid systems is mixed, thereby indicating the…

A tight binding representation of the kicked Harper model is used to obtain an integrable semiclassical Hamiltonian consisting of degenerate "quantized" orbits. New orbits appear when renormalized Harper parameters cross integer multiples…

We study the quantum-interference effect in the ballistic Aharonov-Bohm (AB) billiard. The wave-number averaged conductance and the correlation function of the non-averaged conductance are calculated by use of semiclassical theory. Chaotic…