English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We give a detailed derivation of the second-order (local) hydrodynamics forBoltzmann equation with an external force by using the renormalization groupmethod. In this method, we solve the Boltzmann equation faithfully to extractthe hydrodynamics without recourse to any ansatz. Our method leads tomicroscopic expressions of not only all the transport coefficients that are ofthe same form as those in Chapman-Enskog method but also those of the viscousrelaxation times $\tau_i$ that admit physically natural interpretations. As anexample, we apply our microscopic expressions to calculate the transportcoefficients and the relaxation times of the cold fermionic atoms in aquantitative way, where the transition probability in the collision term isgiven explicitly in terms of the $s$-wave scattering length $a_s$. We therebydiscuss the quantum statistical effects, temperature dependence, andscattering-length dependence of the first-order transport coefficients and theviscous relaxation times: It is shown that as the temperature is lowered, thetransport coefficients and the relaxation times increase rapidly because Pauliprinciple acts effectively. On the other hand, as $a_s$ is increased, thesequantities decrease and become vanishingly small at unitarity because of thestrong coupling. The numerical calculation shows that the relation$\tau_\pi=\eta/P$, which is derived in the relaxation-time approximation andused in most of literature without almost any foundation, turns out to besatisfied quite well, while the similar relation for the relaxation time$\tau_J$ of the heat conductivity is satisfied only approximately with aconsiderable error.

Second-order hydrodynamics for fermionic cold atoms: Detailed analysis of transport coefficients and relaxation times