Sonic propagation and causal evolution for dissipative relativistic superfluid hydrodynamics

Abstract

For the first time in this paper, we have studied sonic propagation and causal evolution for dissipative relativistic superfluid in the framework of second-order dissipative theory. General features of the evolution modes are provided and the sound speeds are identified as the propagation of discontinuity, in agreement with earlier theoretical studies. Moreover, the growth equation is obtained to describe the decay and growth of the discontinuity propagating along its normal trajectory. The solution is in an integral form and various cases are discussed. Some important features of the second-order theory are also presented for the first time, which may be meaningful for future experiments to identify the dissipative theory of relativistic superfluidity.