On the temperature behavior of second sound and Poiseuille flow

Abstract

The linearized Peierls equation for the phonon density N(kλ, rt) is solved by replacing the collision operator in the subspace orthogonal to the collision invariants by k-dependent relaxation rates. For the normal process relaxation time the behavior τN(kλ)∝| k|−p for small k is assumed. Taking into account this k-dependence of τN explicitly and avoiding an expansion with respect to ΩτN(kλ) before performing the necessary integration over k yields new, non-analytic, terms in the hydrodynamic equations describing second sound and Poiseuille flow. It is shown that this may lead to a temperature dependence of second sound damping and thermal conductivity in the Poiseuille flow region differing from the usual theoretical predictions and in better agreement with experiments. © 1975, Springer-Verlag. All rights reserved.