224 research outputs found
Vibrating quantum billiards on Riemannian manifolds
Quantum billiards provide an excellent forum for the analysis of quantum
chaos. Toward this end, we consider quantum billiards with time-varying
surfaces, which provide an important example of quantum chaos that does not
require the semiclassical () or high quantum-number
limits. We analyze vibrating quantum billiards using the framework of
Riemannian geometry. First, we derive a theorem detailing necessary conditions
for the existence of chaos in vibrating quantum billiards on Riemannian
manifolds. Numerical observations suggest that these conditions are also
sufficient. We prove the aforementioned theorem in full generality for one
degree-of-freedom boundary vibrations and briefly discuss a generalization to
billiards with two or more degrees-of-vibrations. The requisite conditions are
direct consequences of the separability of the Helmholtz equation in a given
orthogonal coordinate frame, and they arise from orthogonality relations
satisfied by solutions of the Helmholtz equation. We then state and prove a
second theorem that provides a general form for the coupled ordinary
differential equations that describe quantum billiards with one
degree-of-vibration boundaries. This set of equations may be used to illustrate
KAM theory and also provides a simple example of semiquantum chaos. Moreover,
vibrating quantum billiards may be used as models for quantum-well
nanostructures, so this study has both theoretical and practical applications.Comment: 23 pages, 6 figures, a few typos corrected. To appear in
International Journal of Bifurcation and Chaos (9/01
Is there a "most perfect fluid" consistent with quantum field theory?
It was recently conjectured that the ratio of the shear viscosity to entropy
density, , for any fluid always exceeds . This
conjecture was motivated by quantum field theoretic results obtained via the
AdS/CFT correspondence and from empirical data with real fluids. A theoretical
counterexample to this bound can be constructed from a nonrelativistic gas by
increasing the number of species in the fluid while keeping the dynamics
essentially independent of the species type. The question of whether the
underlying structure of relativistic quantum field theory generically inhibits
the realization of such a system and thereby preserves the possibility of a
universal bound is considered here. Using rather conservative assumptions, it
is shown here that a metastable gas of heavy mesons in a particular controlled
regime of QCD provides a realization of the counterexample and is consistent
with a well-defined underlying relativistic quantum field theory. Thus, quantum
field theory appears to impose no lower bound on , at least for
metastable fluids.Comment: 4 pages; typos corrected and references added in new versio
Decoherence Effects in Reactive Scattering
Decoherence effects on quantum and classical dynamics in reactive scattering
are examined using a Caldeira-Leggett type model. Through a study of dynamics
of the collinear H+H2 reaction and the transmission over simple one-dimensional
barrier potentials, we show that decoherence leads to improved agreement
between quantum and classical reaction and transmission probabilities,
primarily by increasing the energy dispersion in a well defined way. Increased
potential nonlinearity is seen to require larger decoherence in order to attain
comparable quantum-classical agreement.Comment: 25 pages, 6 figures, to be published in J. Chem. Phy
Bose-Einstein Condensate Driven by a Kicked Rotor in a Finite Box
We study the effect of different heating rates of a dilute Bose gas confined
in a quasi-1D finite, leaky box. An optical kicked-rotor is used to transfer
energy to the atoms while two repulsive optical beams are used to confine the
atoms. The average energy of the atoms is localized after a large number of
kicks and the system reaches a nonequilibrium steady state. A numerical
simulation of the experimental data suggests that the localization is due to
energetic atoms leaking over the barrier. Our data also indicates a correlation
between collisions and the destruction of the Bose-Einstein condensate
fraction.Comment: 7 pages, 8 figure
Time parameterization and stationary distributions in a relativistic gas
In this paper we consider the effect of different time parameterizations on
the stationary velocity distribution function for a relativistic gas. We
clarify the distinction between two such distributions, namely the J\"{u}ttner
and the modified J\"{u}ttner distributions. Using a recently proposed model of
a relativistic gas, we show that the obtained results for the proper-time
averaging does not lead to modified J\"{u}ttner distribution (as recently
conjectured), but introduces only a Lorentz factor to the well-known
J\"{u}ttner function which results from observer-time averaging. We obtain
results for rest frame as well as moving frame in order to support our claim.Comment: 5 pages, 2 figure
Quantum Mechanics without an Equation of Motion
We propose a formulation of quantum mechanics in three dimensions with
spherical symmetry for a finite level system whose dynamics is not governed by
a differential equation of motion. The wavefunction is written as an infinite
sum in a complete set of square integrable functions. Interaction in the theory
is introduced in function space by a real finite tridiagonal symmetric matrix.
Information about the structure and dynamics of the system is contained in the
scattering matrix, which is defined in the usual way.Comment: 7 pages, 2 figures, and 3 table
The Simple Non-degenerate Relativistic Gas: Statistical Properties and Brownian Motion
This paper shows a novel calculation of the mean square displacement of a
classical Brownian particle in a relativistic thermal bath. The result is
compared with the expressions obtained by other authors. Also, the
thermodynamic properties of a non-degenerate simple relativistic gas are
reviewed in terms of a treatment performed in velocity space.Comment: 6 pages, 2 figure
Quasi-classical Approach to Bose Condensation in a Finite Potential Well
We treat the problem of self-consistently interacting bosons in the presence
of a finite (but macroscopic) potential well within a quasi-classical
approximation for the normal component and the order parameter. We solve the
equilibrium problem and show, that actually condensation occurs in two steps.
One already at low densities with Bose condensation only in the well and
another one corresponding to the usual condensation in bulk. The peak and width
of the distribution of trapped particles in the well display a distinct
signature of the local condensation. A possible connection to recent
experiments with excitons is discussed
On freeze-out problem in hydro-kinetic approach to A+A collisions
A new method for evaluating spectra and correlations in the hydrodynamic
approach is proposed. It is based on an analysis of Boltzmann equations (BE) in
terms of probabilities for constituent particles to escape from the interacting
system. The conditions of applicability of Cooper-Frye freeze-out prescription
are considered within the method. The results are illustrated with a
non-relativistic exact solution of BE for expanding spherical fireball as well
as with approximate solutions for ellipsoidally expanding ones.Comment: 4 pages including 2 figures, RevTex, stylistic and clarifying
corrections are made, submitted to Phys. Rev. Let
The Nonlinear Permittivity Including Non-Abelian Self-interaction of Plasmons in Quark-Gluon Plasma
By decomposing the distribution functions and color field to regular and
fluctuation parts, the solution of the semi-classical kinetic equations of
quark-gluon plasma is analyzed. Through expanding the kinetic equations of the
fluctuation parts to third order, the nonlinear permittivity including the
self-interaction of gauge field is obtained and a rough numerical estimate is
given out for the important \vk =0 modes of the pure gluon plasma.Comment: 7 pages, shortened version accepted by Chin.Phys.Let
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