221 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
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
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 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
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
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
Levy distribution in many-particle quantum systems
Levy distribution, previously used to describe complex behavior of classical
systems, is shown to characterize that of quantum many-body systems. Using two
complimentary approaches, the canonical and grand-canonical formalisms, we
discovered that the momentum profile of a Tonks-Girardeau gas, -- a
one-dimensional gas of impenetrable (hard-core) bosons, harmonically
confined on a lattice at finite temperatures, obeys Levy distribution. Finally,
we extend our analysis to different confinement setups and demonstrate that the
tunable Levy distribution properly reproduces momentum profiles in
experimentally accessible regions. Our finding allows for calibration of
complex many-body quantum states by using a unique scaling exponent.Comment: 7 pages, 6 figures, results are generalized, new examples are adde
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
Deriving Boltzmann Equations from Kadanoff-Baym Equations in Curved Space-Time
To calculate the baryon asymmetry in the baryogenesis via leptogenesis
scenario one usually uses Boltzmann equations with transition amplitudes
computed in vacuum. However, the hot and dense medium and, potentially, the
expansion of the universe can affect the collision terms and hence the
generated asymmetry. In this paper we derive the Boltzmann equation in the
curved space-time from (first-principle) Kadanoff-Baym equations. As one
expects from general considerations, the derived equations are covariant
generalizations of the corresponding equations in Minkowski space-time. We find
that, after the necessary approximations have been performed, only the
left-hand side of the Boltzmann equation depends on the space-time metric. The
amplitudes in the collision term on the right--hand side are independent of the
metric, which justifies earlier calculations where this has been assumed
implicitly. At tree level, the matrix elements coincide with those computed in
vacuum. However, the loop contributions involve additional integrals over the
the distribution function.Comment: 14 pages, 5 figures, extended discussion of the constraint equations
and the solution for the spectral functio
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