Relaxation rates of the linearized Uehling-Uhlenbeck equation for bosons

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Gust, Erich
Reichl, L. E.

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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.



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Gust, Erich, and L. E. Reichl. "Relaxation rates of the linearized Uehling-Uhlenbeck equation for bosons." Physical Review E 81, no. 6 (2010): 061202.