Semiclassical Quantization by Pade Approximant to Periodic Orbit Sums

Periodic orbit quantization requires an analytic continuation of non-convergent semiclassical trace formulae. We propose a method for semiclassical quantization based upon the Pade approximant to the periodic orbit sums. The Pade approximant allows the re-summation of the typically exponentially divergent periodic orbit terms. The technique does not depend on the existence of a symbolic dynamics and can be applied to both bound and open systems. Numerical results are presented for two different systems with chaotic and regular classical dynamics, viz. the three-disk scattering system and the circle billiard.Comment: 7 pages, 3 figures, submitted to Europhys. Let

Echoes in classical dynamical systems

Echoes arise when external manipulations to a system induce a reversal of its time evolution that leads to a more or less perfect recovery of the initial state. We discuss the accuracy with which a cloud of trajectories returns to the initial state in classical dynamical systems that are exposed to additive noise and small differences in the equations of motion for forward and backward evolution. The cases of integrable and chaotic motion and small or large noise are studied in some detail and many different dynamical laws are identified. Experimental tests in 2-d flows that show chaotic advection are proposed.Comment: to be published in J. Phys.

Wave function correlations on the ballistic scale: Exploring quantum chaos by quantum disorder

We study the statistics of wave functions in a ballistic chaotic system. The statistical ensemble is generated by adding weak smooth disorder. The conjecture of Gaussian fluctuations of wave functions put forward by Berry and generalized by Hortikar and Srednicki is proven to hold on sufficiently short distances, while it is found to be strongly violated on larger scales. This also resolves the conflict between the above conjecture and the wave function normalization. The method is further used to study ballistic correlations of wave functions in a random magnetic field.Comment: 4 page

Semiclassical cross section correlations

We calculate within a semiclassical approximation the autocorrelation function of cross sections. The starting point is the semiclassical expression for the diagonal matrix elements of an operator. For general operators with a smooth classical limit the autocorrelation function of such matrix elements has two contributions with relative weights determined by classical dynamics. We show how the random matrix result can be obtained if the operator approaches a projector onto a single initial state. The expressions are verified in calculations for the kicked rotor.Comment: 6 pages, 2 figure

Small Disks and Semiclassical Resonances

We study the effect on quantum spectra of the existence of small circular disks in a billiard system. In the limit where the disk radii vanish there is no effect, however this limit is approached very slowly so that even very small radii have comparatively large effects. We include diffractive orbits which scatter off the small disks in the periodic orbit expansion. This situation is formally similar to edge diffraction except that the disk radii introduce a length scale in the problem such that for wave lengths smaller than the order of the disk radius we recover the usual semi-classical approximation; however, for wave lengths larger than the order of the disk radius there is a qualitatively different behaviour. We test the theory by successfully estimating the positions of scattering resonances in geometries consisting of three and four small disks.Comment: Final published version - some changes in the discussion and the labels on one figure are correcte

Sampling of an STT event over the Eastern Mediterranean region by lidar and electrochemical sonde

International audienceA two-wavelength ultraviolet (289?316nm) ozone Differential Absorption Lidar (DIAL) system is used to perform ozone measurements in the free troposphere in the Eastern Mediterranean (Northern Greece). The ozone DIAL profiles obtained during a Stratosphere-to-Troposphere Transport (STT) event are compared to that acquired by an electrochemical ozonesonde, in the altitude range between 2 and 10 km. The measurement accuracy of these two instruments is also discussed. The mean difference between the ozone profiles obtained by the two techniques is of the order of 1.11 ppbv (1.86%), while the corresponding standard deviation is 4.69 ppbv (8.16%). A case study of an STT event which occurred on 29 November 2000 is presented and analyzed, using ozone lidar, satellite and meteorological data, as well as air mass back-trajectory analysis. During this STT event ozone mixing ratios of 55?65 ppbv were observed between 5 and 7 km height above sea level (a.s.l.). Stratospheric air was mixed with tropospheric air masses, leading to potential vorticity (PV) losses due to diabatic processes. The ozone DIAL system can be used for following STT events and small-scale mixing phenomena in the free troposphere, and for providing sequences of vertical ozone profiles in the free troposphere. Keywords. Atmospheric composition and structure (Evolution of the atmosphere; Instruments and techniques) ? Meteorology and atmospheric dynamics (Middle atmosphere dynamics; Turbulence

Energy diffusion in strongly driven quantum chaotic systems

The energy evolution of a quantum chaotic system under the perturbation that harmonically depends on time is studied for the case of large perturbation, in which the rate of transition calculated from the Fermi golden rule exceeds the frequency of perturbation. It is shown that the energy evolution retains its diffusive character, with the diffusion coefficient that is asymptotically proportional to the magnitude of perturbation and to the square root of the density of states. The results are supported by numerical calculation. They imply the absence of the quantum-classical correspondence for the energy diffusion and the energy absorption in the classical limit $\hbar \to 0$.Comment: 12 pages, 3 figures, RevTe

Second moment of the Husimi distribution as a measure of complexity of quantum states

We propose the second moment of the Husimi distribution as a measure of complexity of quantum states. The inverse of this quantity represents the effective volume in phase space occupied by the Husimi distribution, and has a good correspondence with chaoticity of classical system. Its properties are similar to the classical entropy proposed by Wehrl, but it is much easier to calculate numerically. We calculate this quantity in the quartic oscillator model, and show that it works well as a measure of chaoticity of quantum states.Comment: 25 pages, 10 figures. to appear in PR

Symmetry Decomposition of Chaotic Dynamics

Discrete symmetries of dynamical flows give rise to relations between periodic orbits, reduce the dynamics to a fundamental domain, and lead to factorizations of zeta functions. These factorizations in turn reduce the labor and improve the convergence of cycle expansions for classical and quantum spectra associated with the flow. In this paper the general formalism is developed, with the $N$-disk pinball model used as a concrete example and a series of physically interesting cases worked out in detail.Comment: CYCLER Paper 93mar01

Signatures of Classical Periodic Orbits on a Smooth Quantum System

Gutzwiller's trace formula and Bogomolny's formula are applied to a non--specific, non--scalable Hamiltonian system, a two--dimensional anharmonic oscillator. These semiclassical theories reproduce well the exact quantal results over a large spatial and energy range.Comment: 12 pages, uuencoded postscript file (1526 kb