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Motivated by recent experiments in Phys. Rev. Lett. 121, 145301 (2018), westudy sound propagation in a two-dimensional (2D) Bose gas across thesuperfluid-thermal transition using classical field dynamics. Below thetransition temperature we find a Bogoliubov and a non-Bogoliubov mode, above itwe find the normal sound mode and the diffusive mode, as we determine from thedynamical structure factor. Our simulations of the experimental procedure agreewith the measured velocities, and show that below the transition temperaturethe measurements detect the Bogoliubov mode. Above the transition, they eitherdetect the normal sound mode for low densities or weak interactions, or thediffusive mode for high densities or strong interactions. As a key observation,we discuss the weak coupling regime in which the non-Bogoliubov mode has ahigher velocity than the Bogoliubov mode, in contrast to a hydrodynamicscenario. We propose to detect this regime via step-pulse density perturbation,which simultaneously detects both sound modes

Sound propagation in a two-dimensional Bose gas across the superfluid transition