Analytic continuation average spectrum method for transport in quantum liquids

Abstract

Recently, we have applied the analytic continuation averaged spectrum method (ASM) to calculate collective density fluctuations in quantum liquid [27]. Unlike the maximum entropy (MaxEnt) method, the ASM approach is capable of revealing resolved modes in the dynamic structure factor in agreement with experiments. In this work we further develop the ASM to study single-particle dynamics in quantum liquids with dynamical susceptibilities that are characterized by a smooth spectrum. Surprisingly, we find that for the power spectrum of the velocity autocorrelation function there are pronounced differences in comparison with the MaxEnt approach, even for this simple case of smooth unimodal dynamic response. We show that for liquid para-hydrogen the ASM is closer to the centroid molecular dynamics (CMD) result while for normal liquid helium it agrees better with the quantum mode coupling theory (QMCT) and with the MaxEnt approach.