Transport and spectral signatures of transient fluctuating superfluids in the absence of long-range order

Abstract: Results are presented for the quench dynamics of a clean and interacting electron system, where the quench involves varying the strength of the attractive interaction along arbitrary quench trajectories. The initial state before the quench is assumed to be a normal electron gas, and the dynamics is studied in a regime where long-range order is absent, but nonequilibrium superconducting fluctuations need to be accounted for. A quantum kinetic equation using a two-particle irreducible formalism is derived. Conservation of energy, particle-number, and momentum emerge naturally, with the conserved currents depending on both the electron Green's functions and the Green's functions for the superconducting fluctuations. The quantum kinetic equation is employed to derive a kinetic equation for the current, and the transient optical conductivity relevant to pump-probe spectroscopy is studied. The general structure of the kinetic equation for the current is also justified by a phenomenological approach that assumes model-F in the Halperin-Hohenberg classification, corresponding to a non-conserved order-parameter coupled to a conserved density. Linear response conductivity and the diffusion coefficients in thermal equilibrium are also derived, and connections with Aslamazov-Larkin fluctuation corrections are highlighted. Results are also presented for the time-evolution of the local density of states. It is shown that Andreev scattering processes result in an enhanced density of states at low frequencies. For a quench trajectory corresponding to a sudden quench to the critical point, the density of states is shown to grow in a manner where the time after the quench plays the role of the inverse detuning from the critical point.