Theory of Quantum Work in Metallic Grains

We generalize Anderson's orthogonality determinant formula to describe the statistics of work performed on generic disordered, non-interacting fermionic nanograins during quantum quenches. The energy absorbed increases linearly with time, while its variance exhibits a superdiffusive behavior due to Pauli's exclusion principle. The probability of adiabatic evolution decays as a stretched exponential. In slowly driven systems, work statistics exhibits universal features, and can be understood in terms of fermion diffusion in energy space, generated by Landau-Zener transitions. This diffusion is very well captured by a Markovian symmetrical exclusion process, with the diffusion constant identified as the energy absorption rate. The energy absorption rate shows an anomalous frequency dependence at small energies, reflecting the symmetry class of the underlying Hamiltonian. Our predictions can be experimentally verified by calorimetric measurements performed on nanoscale circuits.