Propagation of sound and second sound using heat pulses

Abstract

We present a detailed account of the transition from second sound to ballistic phonon flow in liquid He II as a function of temperature (0.1-1 K), pressure (up to the solidification point), and propagation length (\ensuremath{\sim} 0.23-7.0 cm). Below 10 bar and 0.5 K, the phonon-phonon scattering time ${\ensuremath{\tau}}_{\mathrm{pp}}$ has the form ${\ensuremath{\tau}}_{\mathrm{pp}}\ensuremath{\sim}(7\ifmmode\pm\else\textpm\fi{}3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}{(\frac{T}{\ensuremath{\Theta}})}^{\ensuremath{-}3}$ sec, where $\ensuremath{\Theta}$ is the low-temperature Debye temperature. Above 10 bar, $\ensuremath{\nu}{\ensuremath{\tau}}_{\mathrm{pp}}>2$ cm for $T\ensuremath{\lesssim}0.7$ K, where $\ensuremath{\nu}$ is the sound velocity. The strong pressure dependence of ${\ensuremath{\tau}}_{\mathrm{pp}}$ is qualitatively consistent with the theoretical model of J\"ackle and Kehr. The phonon-roton scattering time ${\ensuremath{\tau}}_{\mathrm{pr}}$ is found to be nearly pressure independent and has a value \ensuremath{\sim} ${10}^{\ensuremath{-}6}$ sec at \ensuremath{\sim} 0.75 K in agreement with the calculations of Khalatnikov and Chernikova. Evidence for separate roton second sound (at high pressures) and phonon second sound at SVP is presented. An elementary excitation picture of second sound in the entire gas of excitations in He II is presented and the close analogy with phonon second sound in solids (bismuth) and in a gas of particles (${\mathrm{He}}^{4}$) is experimentally illustrated. Estimates for the number of collisions required for the formation of the collective mode from the single-particle-like excitations are given.