Non-Gaussian work statistics in fermionic nanostructures

We investigate the statistical properties of work performed on generic disordered fermionic nanograins under the effect of external fields during non-equilibrium quantum quenches. We construct a simple mean field theory yielding amazingly precise analytic expressions for the distribution of work in the case of zero temperature for arbitrarily fast driven quantum systems. The tail of the work distribution for large work is found to decay exponentially rather than being Gaussian. Using an effective temperature formalism, we obtain an analytic expression for the work statistics for large enough injected works via bosonization. We compare our predictions with numerical simulations in a 2D hopping model with random on-site energies, finding remarkable agreement.
For quenches at finite temperature we derive an exact determinant formula for the characteristic function of the work statistics. In contrast to the zero temperature case, in the limit of large temperatures, it converges to a Gaussian distribution with the average work increasing linearly in time. We also verified that for symmetrical cyclic driving our results satisfy the Crooks fluctuation relation.