相关论文: Duality between quantum and classical dynamics for…

We consider Hamiltonian systems which can be described both classically and quantum mechanically. Trace formulas establish links between the energy spectra of the quantum description and the spectrum of actions of periodic orbits in the…

A comparison of classical and quantum evolution usually involves a quasi-probability distribution as a quantum analogue of the classical phase space distribution. In an alternate approach that we adopt here, the classical density is…

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…

The classical Liouville density on the constant energy surface reveals a number of interesting features when the initial density has no directional preference. It has been shown (Physical Review Letters, 93 (2004) 204102) that the…

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 the present note, we uncover a remarkable connection between the length of periodic orbit of a classical particle enclosed in a class of 2-dimensional planar billiards and the energy of a quantum particle confined to move in an identical…

N-disk microwave billiards, which are representative of open quantum systems, are studied experimentally. The transmission spectrum yields the quantum resonances which are consistent with semiclassical calculations. The spectral…

The geometry of a billiard boundary fundamentally governs its dynamics, ranging from integrable to mixed and fully chaotic regimes. Bean- and peanut-shaped billiards have varying curvature with both focusing and defocusing walls without a…

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…

We report on the experimental investigation of the properties of the eigenvalues and wavefunctions and the fluctuation properties of the scattering matrix of closed and open billiards, respectively, of which the classical dynamics undergoes…

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 the fact that the energy eigenstates of the equilateral triangle infinite well (or billiard) are available in closed form, we examine the connections between the energy eigenvalue spectrum and the classical closed paths in this…

We present a comprehensive review of the nodal domains and lines of quantum billiards, emphasizing a quantitative comparison of theoretical findings to experiments. The nodal statistics are shown to distinguish not only between regular and…

The exact and semiclassical quantum mechanics of the elliptic billiard is investigated. The classical system is integrable and exhibits a separatrix, dividing the phasespace into regions of oscillatory and rotational motion. The classical…

We perform numerical studies of the wave packet propagation through open quantum billiards whose classical counterparts exhibit regular and chaotic dynamics. We show that for t less or similar to tau (tau being the Heisenberg time), the…

A quantum wave function with localization on classical periodic orbits in a mesoscopic elliptic billiard has been achieved by appropriately superposing nearly degenerate eigenstates expressed as products of Mathieu functions. We analyze and…

The classical mechanics, exact quantum mechanics and semiclassical quantum mechanics of the billiard in the triaxial ellipsoid is investigated. The system is separable in ellipsoidal coordinates. A smooth description of the motion is given…

The structure of the semiclassical trace formula can be used to construct a quasi-classical evolution operator whose spectrum has a one-to-one correspondence with the semiclassical quantum spectrum. We illustrate this for marginally…

We analyse the transport phenomena of 2D quantum billiards with convex boundary of different shape. The quantum mechanical analysis is performed by means of the poles of the S-matrix while the classical analysis is based on the motion of a…

We study diffractive effects in two dimensional polygonal billiards. We derive an analytical trace formula accounting for the role of non-classical diffractive orbits in the quantum spectrum. As an illustration the method is applied to a…