Dynamic Compressibility and Aging in Wigner Crystals and Quantum Glasses

We study the nonequilibrium linear response of quantum elastic systems pinned by quenched disorder with Schwinger-Keldysh real-time techniques complemented by a mean-field variational approach. We find (i) a quasiequilibrium regime in which the analytic continuation from the imaginary-time replica results holds provided the marginality condition is enforced, and (ii) an aging regime. The conductivity and compressibility are computed. The latter is found to cross over from its dynamic to static value on a scale set by the waiting time after a quench, an effect which can be probed in experiments in, e.g., Wigner glasses.

Figure 1

Sketch of the variation of the chemical potential; dc (solid line) and ac (dashed line), for a system quenched at time $t=0$. The density is measured at time $t$.