Abstract:
We study the response of a cold gas (all particles are initially at rest) to a sudden kick when one particle suddenly starts moving. The outcome is a spherical shock wave advancing as $t^\frac{2}{d+2}$. The density, velocity, and temperature behind the shock are described by Euler equations. Deviations from the predictions of non-dissipative hydrodynamics arise in the central region whose size increases slower than the radius $R$ of the shock wave, viz. as $R^{4/5}$ in 2D and $R^{31/35}$ n 3D. In a one-dimensional semi-infinite setting, when the left-most particle suddenly starts moving to the right, a growing number of ``splatter" particles penetrate the initially empty half-line. The total energy and momentum of the splatter particles exhibit counterintuitive behaviors.