Random matrix theory of quantum work in metallic grains

We apply a random matrix approach to describe the statistics of work performed on generic disordered, noninteracting fermionic systems during quantum quenches [1]. We generalize and apply Anderson's orthogonality determinant formula to compute the full distribution of quantum work generated by deformations of the Hamiltonian. The energy absorbed increases linearly with time, while its variance exhibits a superdiffusive behavior, reflecting Pauli's exclusion principle. The probability of adiabaticity decays as a stretched exponential. In slowly driven systems work statistics exhibit 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. We test our theory in a 2D hopping model with random on-site energies, finding excellent agreement. Our predictions can be experimentally verified by calorimetric measurements performed on nanoscale circuits.

[1] I. Lovas, A. Grabarits, M. Kormos, G. Zaránd, Phys. Rev. Research 2, 023224 (2020)