  Shock waves are examples of the far-from-equilibrium behaviour of matter;
they are ubiquitous in nature, yet the underlying microscopic mechanisms behind
their formation are not well understood. Here, we study the dynamics of
dispersive quantum shock waves in a one-dimensional Bose gas, and show that the
oscillatory train forming from a local density bump expanding into a uniform
background is a result of quantum mechanical self-interference. The amplitude
of oscillations, i.e., the interference contrast, decreases with the increase
of both the temperature of the gas and the interaction strength due to the
reduced phase coherence length. Furthermore, we show that vacuum and thermal
fluctuations can significantly wash out the interference contrast, seen in the
mean-field approaches, due to shot-to-shot fluctuations in the position of
interference fringes around the mean.
