1,155 research outputs found

### 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.

- âŠ