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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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