On Pitaevskii’s Branch near the Two-Roton Threshold at Finite Temperatures

Abstract

PITAEVSKII[1] predicted in 1959 that the phonon-roton curve will terminate tangentially to the edge of the two-roton continuum at certain momentum Q_c In the neutron experiments, however, this asymptotic branch by PITAEVSKII has not been observed up to the end point Q_c The peak position is found to be at rather higher energy than twice the roton energy at large momentum transfer. This report shows that, at finite temperatures, due to the finite linewidth of rotons PITAEVSKII’s branch ceases to exist at a temperature dependent momentum Q_c(T) which is smaller than PITAEVSKII’s Q_c thereby explaining the above discrepancy. A brief report has been given by NAGAI [2]. ZAWADOWSKI et al.[3] have also shown numerically that the finite linewidth of rotons shifts PITAEVSKII’s branch to higher energy.