8,228 research outputs found
Periodic Chaotic Billiards: Quantum-Classical Correspondence in Energy Space
We investigate the properties of eigenstates and local density of states
(LDOS) for a periodic 2D rippled billiard, focusing on their quantum-classical
correspondence in energy representation. To construct the classical
counterparts of LDOS and the structure of eigenstates (SES), the effects of the
boundary are first incorporated (via a canonical transformation) into an
effective potential, rendering the one-particle motion in the 2D rippled
billiard equivalent to that of two-interacting particles in 1D geometry. We
show that classical counterparts of SES and LDOS in the case of strong chaotic
motion reveal quite a good correspondence with the quantum quantities. We also
show that the main features of the SES and LDOS can be explained in terms of
the underlying classical dynamics, in particular of certain periodic orbits. On
the other hand, statistical properties of eigenstates and LDOS turn out to be
different from those prescribed by random matrix theory. We discuss the quantum
effects responsible for the non-ergodic character of the eigenstates and
individual LDOS that seem to be generic for this type of billiards with a large
number of transverse channels.Comment: 13 pages, 18 figure
Chaotic Waveguide-Based Resonators for Microlasers
We propose the construction of highly directional emission microlasers using
two-dimensional high-index semiconductor waveguides as {\it open} resonators.
The prototype waveguide is formed by two collinear leads connected to a cavity
of certain shape. The proposed lasing mechanism requires that the shape of the
cavity yield mixed chaotic ray dynamics so as to have the appropiate (phase
space) resonance islands. These islands allow, via Heisenberg's uncertainty
principle, the appearance of quasi bound states (QBS) which, in turn,
propitiate the lasing mechanism. The energy values of the QBS are found through
the solution of the Helmholtz equation. We use classical ray dynamics to
predict the direction and intensity of the lasing produced by such open
resonators for typical values of the index of refraction.Comment: 5 pages, 5 figure
A semiquantal approach to finite systems of interacting particles
A novel approach is suggested for the statistical description of quantum
systems of interacting particles. The key point of this approach is that a
typical eigenstate in the energy representation (shape of eigenstates, SE) has
a well defined classical analog which can be easily obtained from the classical
equations of motion. Therefore, the occupation numbers for single-particle
states can be represented as a convolution of the classical SE with the quantum
occupation number operator for non-interacting particles. The latter takes into
account the wavefunctions symmetry and depends on the unperturbed energy
spectrum only. As a result, the distribution of occupation numbers can be
numerically found for a very large number of interacting particles. Using the
model of interacting spins we demonstrate that this approach gives a correct
description of even in a deep quantum region with few single-particle
orbitals.Comment: 4 pages, 2 figure
Influence of a dynamical gluon mass in the and forward scattering
We compute the tree level cross section for gluon-gluon elastic scattering
taking into account a dynamical gluon mass, and show that this mass scale is a
natural regulator for this subprocess cross section. Using an eikonal approach
in order to examine the relationship between this gluon-gluon scattering and
the elastic and channels, we found that the dynamical gluon
mass is of the same order of magnitude as the {\it ad hoc} infrared mass scale
underlying eikonalized QCD-inspired models. We argue that this
correspondence is not an accidental result, and that this dynamical scale
indeed represents the onset of non-perturbative contributions to the elastic
hadron-hadron scattering. We apply the eikonal model with a dynamical infrared
mass scale to obtain predictions for ,
, slope , and differential elastic
scattering cross section at Tevatron and CERN-LHC
energies.Comment: 20 pages, 5 figures; misprints corrected and comments added. To
appear in Phys. Rev.
Classical versus Quantum Structure of the Scattering Probability Matrix. Chaotic wave-guides
The purely classical counterpart of the Scattering Probability Matrix (SPM)
of the quantum scattering matrix is defined for 2D
quantum waveguides for an arbitrary number of propagating modes . We compare
the quantum and classical structures of for a waveguide
with generic Hamiltonian chaos. It is shown that even for a moderate number of
channels, knowledge of the classical structure of the SPM allows us to predict
the global structure of the quantum one and, hence, understand important
quantum transport properties of waveguides in terms of purely classical
dynamics. It is also shown that the SPM, being an intensity measure, can give
additional dynamical information to that obtained by the Poincar\`{e} maps.Comment: 9 pages, 9 figure
Basin structure in the two-dimensional dissipative circle map
Fractal basin structure in the two-dimensional dissipative circle map is
examined in detail. Numerically obtained basin appears to be riddling in the
parameter region where two periodic orbits co-exist near a boundary crisis, but
it is shown to consist of layers of thin bands.Comment: published in J. Phys. Soc. Jpn., 72, 1943-1947 (2003
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