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 ($\hbar \longrightarrow 0$) 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, $\eta/ s$, for any fluid always exceeds $\hbar/(4 \pi k_B)$. 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 $\eta/s$, 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 $\gamma$ 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

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

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

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