Negative group velocity and Kelvin-like wake in superfluid $^{4}He$

Eugene B. Kolomeisky, Jonathan Colen, Joseph P. Straley

Published 2021-06-01Version 1

The dispersion law $\Omega(k)$ of elementary excitations in superfluid $^{4}He$ is a non-monotonic function of the wave number $k$. After an initial increase, the function $\Omega(k)$ reaches a maximum followed by a "roton" minimum at finite $k$. As a result, there is a range of $k$ between these extrema where the elementary excitations have negative group velocity. These excitations are generated when a fast heavy impurity travels through the superfluid or the latter flows past an obstacle with the speed exceeding $60~m/s$. Their interference leads to a pattern resembling the Kelvin ship wake.