Generic occurrence of rings in rotating systems

In rotating scattering systems, the generic saddle-center scenario leads to stable islands in phase space. Non-interacting particles whose initial conditions are defined in such islands will be trapped and form rotating rings. This result is generic and also holds for systems quite different from planetary rings.Comment: 10 pages, 5 ps figures; uses elsart.sty and epsfig.sty Accepted in Phys. Lett.

Phase-Space Volume of Regions of Trapped Motion: Multiple Ring Components and Arcs

The phase--space volume of regions of regular or trapped motion, for bounded or scattering systems with two degrees of freedom respectively, displays universal properties. In particular, sudden reductions in the phase-space volume or gaps are observed at specific values of the parameter which tunes the dynamics; these locations are approximated by the stability resonances. The latter are defined by a resonant condition on the stability exponents of a central linearly stable periodic orbit. We show that, for more than two degrees of freedom, these resonances can be excited opening up gaps, which effectively separate and reduce the regions of trapped motion in phase space. Using the scattering approach to narrow rings and a billiard system as example, we demonstrate that this mechanism yields rings with two or more components. Arcs are also obtained, specifically when an additional (mean-motion) resonance condition is met. We obtain a complete representation of the phase-space volume occupied by the regions of trapped motion.Comment: 19 pages, 17 figure

Thermalized non-equilibrated matter and high temperature superconducting state in quantum many-body systems

A characteristic feature of thermalized non-equilibrated matter is that, in spite of energy relaxation--equilibration, a phase memory of the way the many-body system was excited remains. As an example, we analyze data on a strong forward peaking of thermal proton yield in the Bi($\gamma$,p) photonuclear reaction. New analysis shows that the phase relaxation in highly-excited heavy nuclei can be 8 orders of magnitude or even much longer than the energy relaxation. We argue that thermalized non-equilibrated matter resembles a high temperature superconducting state in quantum many-body systems. We briefly present results on the time-dependent correlation function of the many-particle density fluctuations for such a superconducting state. It should be of interest to experimentally search for manifestations of thermalized non-equilibrated matter in many-body mesoscopic systems and nanostructures.Comment: 12 pages, 1 eps figure. To be published in Radiation Effects and Defects in Solid

Quantum-classical transition for an analog of double-slit experiment in complex collisions: Dynamical decoherence in quantum many-body systems

We study coherent superpositions of clockwise and anti-clockwise rotating intermediate complexes with overlapping resonances formed in bimolecular chemical reactions. Disintegration of such complexes represents an analog of famous double-slit experiment. The time for disappearance of the interference fringes is estimated from heuristic arguments related to fingerprints of chaotic dynamics of a classical counterpart of the coherently rotating complex. Validity of this estimate is confirmed numerically for the H+D$_2$ chemical reaction. Thus we demonstrate the quantum--classical transition in temporal behavior of highly excited quantum many-body systems in the absence of external noise and coupling to an environment.Comment: 5 pages, 2 ps color figures. Accepted for publication in Phys. Rev.

Non-Ergodic Behaviour of the k-Body Embedded Gaussian Random Ensembles for Bosons

We investigate the shape of the spectrum and the spectral fluctuations of the $k$-body Embedded Gaussian Ensemble for Bosons in the dense limit, where the number of Bosons $m \to \infty$ while both $k$, the rank of the interaction, and $l$, the number of single-particle states, are kept fixed. We show that the relative fluctuations of the low spectral moments do not vanish in this limit, proving that the ensemble is non-ergodic. Numerical simulations yield spectra which display a strong tendency towards picket-fence type. The wave functions also deviate from canonical random-matrix behaviourComment: 7 pages, 5 figures, uses epl.cls (included

Wigner--Dyson statistics for a class of integrable models

We construct an ensemble of second--quantized Hamiltonians with two bosonic degrees of freedom, whose members display with probability one GOE or GUE statistics. Nevertheless, these Hamiltonians have a second integral of motion, namely the boson number, and thus are integrable. To construct this ensemble we use some ``reverse engineering'' starting from the fact that $n$--bosons in a two--level system with random interactions have an integrable classical limit by the old Heisenberg association of boson operators to actions and angles. By choosing an $n$--body random interaction and degenerate levels we end up with GOE or GUE Hamiltonians. Ergodicity of these ensembles completes the example.Comment: 3 pages, 1 figur

Spectral statistics of the k-body random-interaction model

We reconsider the question of the spectral statistics of the k-body random-interaction model, investigated recently by Benet, Rupp, and Weidenmueller, who concluded that the spectral statistics are Poissonian. The binary-correlation method that these authors used involves formal manipulations of divergent series. We argue that Borel summation does not suffice to define these divergent series without further (arbitrary) regularization, and that this constitutes a significant gap in the demonstration of Poissonian statistics. Our conclusion is that the spectral statistics of the k-body random-interaction model remains an open question.Comment: 17 pages, no figure

Fluctuations of wave functions about their classical average

Quantum-classical correspondence for the average shape of eigenfunctions and the local spectral density of states are well-known facts. In this paper, the fluctuations that quantum mechanical wave functions present around the classical value are discussed. A simple random matrix model leads to a Gaussian distribution of the amplitudes. We compare this prediction with numerical calculations in chaotic models of coupled quartic oscillators. The expectation is broadly confirmed, but deviations due to scars are observed.Comment: 9 pages, 6 figures. Sent to J. Phys.