Fractional short-time dynamics in driven quantum gases

Quantum gases with short-range attractive interaction have a tendency to form pairs. For time-dependent interaction we find that the pairing amplitude at small separation satisfies a fractional differential equation (FDE). We derive analytic solutions of the pairing evolution for sudden interaction quenches and power-law drives toward resonant scattering. We observe universal short-time dynamics governed by a conformal fixed point at which the momentum distribution exhibits nonthermal, self-similar scaling in time, in quantitative agreement with experiment. At longer times, many-body effects induce relaxation toward an equilibrium state. In this limit, the FDE turns into a M\"uller-Israel-Stewart type equation that describes a hydrodynamic attractor approaching equilibrium.