Fermionic shock waves: Distinguishing dissipative versus dispersive regularizations

The collision of two clouds of Fermi gas at unitarity (UFG) has been recently observed to lead to shock waves whose regularization mechanism, dissipative or dispersive, is being debated. While classical, dissipative shocks, as in gas dynamics, develop a steep, localized shock front that translates at a well-defined speed, dispersively regularized shocks are distinguished by an expanding region of short wavelength oscillations with two speeds, those of the leading and trailing edges. For typical UFG experimental conditions, the theoretical oscillation length scale is smaller than the resolution of present imaging systems so it is unclear how to determine the shock type from its structure alone. Two experimental methods to determine the appropriate regularization mechanism are proposed: measurement of the shock speed and observation of a one-dimensional collision experiment with sufficiently tight radial confinement.

Figure 1

Nondimensional shock speeds by type of regularization. $v_{\mathrm{L}}$ and $v_{\mathrm{S}}$ correspond to the leading and trailing edge speeds of a UFG DSW, respectively. $V$ is the dissipative shock speed. The vertical dotted line at ${\rho }_0=2.7$ is for comparison with the particular discontinuity simulated in Fig. 2.

Figure 2

Numerical simulation of the gNLS equation (solid) [from Eqs. (5) and (6)] for a DSW with ${\rho }_0=2.7$ and corresponding VSW solution (dashed). The right panels depict the filtered solutions.

Figure 3

Numerical simulation of the gNLS equation (solid) and dissipative hydrodynamic equations (dashed) for the collision problem. The right panels depict the filtered solutions.