1,159 research outputs found
Scattering from Spatially Localized Chaotic and Disordered Systems
A version of scattering theory that was developed many years ago to treat
nuclear scattering processes, has provided a powerful tool to study
universality in scattering processes involving open quantum systems with
underlying classically chaotic dynamics. Recently, it has been used to make
random matrix theory predictions concerning the statistical properties of
scattering resonances in mesoscopic electron waveguides and electromagnetic
waveguides. We provide a simple derivation of this scattering theory and we
compare its predictions to those obtained from an exactly solvable scattering
model; and we use it to study the scattering of a particle wave from a random
potential. This method may prove useful in distinguishing the effects of chaos
from the effects of disorder in real scattering processes.Comment: 24 pages, 11 figures typos added. Published in 'Foundation of
physics' February issu
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Relaxation rates of the linearized Uehling-Uhlenbeck equation for bosons
We linearize the Uehling-Uhlenbeck equation for bosonic gases close to thermal equilibrium under the assumption of a contact interaction characterized by a scattering length a. We show that the spectrum of relaxation rates is similar to that of a classical hard-sphere gas. However, the relaxation rates show a significant dependence on the fugacity z of the gas, increasing by as much as 60% of their classical value for z approaching 1. The relaxation modes are also significantly altered at higher values of z. The relaxation rates and modes are determined by the eigenvalues and eigenvectors of a Fredholm integral operator of the second kind. We derive an analytical form for the kernel of this operator and present numerical results for the first few eigenvalues and eigenvectors.Robert A. Welch Foundation F-1051Physic
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Arnold diffusion in a driven optical lattice
The effect of time-periodic forces on matter has been a topic of growing interest since the advent of lasers. It is known that dynamical systems with 2.5 or more degrees of freedom are intrinsically unstable. As a consequence, time-periodic driven systems can experience large excursions in energy. We analyze the classical and quantum dynamics of rubidium atoms confined to a time-periodic optical lattice with 2.5 degrees of freedom. When the laser polarizations are orthogonal, the system consists of two 1.5 uncoupled dynamical systems. When laser polarizations are turned away from orthogonal, an Arnold web forms and the dynamics undergoes a fundamental change. For parallel polarizations, we find huge random excursions in the rubidium atom energies and significant entanglement of energies in the quantum dynamics.Robert A. Welch Foundation (USA) F-1051Physic
Coherent Control of Trapped Bosons
We investigate the quantum behavior of a mesoscopic two-boson system produced
by number-squeezing ultracold gases of alkali metal atoms. The quantum Poincare
maps of the wavefunctions are affected by chaos in those regions of the phase
space where the classical dynamics produces features that are comparable to
hbar. We also investigate the possibility for quantum control in the dynamics
of excitations in these systems. Controlled excitations are mediated by pulsed
signals that cause Stimulated Raman Adiabatic passage (STIRAP) from the ground
state to a state of higher energy. The dynamics of this transition is affected
by chaos caused by the pulses in certain regions of the phase space. A
transition to chaos can thus provide a method of controlling STIRAP.Comment: 17 figures, Appended a paragraph on section 1 and explained details
behind the hamiltonian on section
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