Classical Theory of Quantum Work Distribution in Chaotic Fermion Systems

Abstract

We present a theory of quantum work statistics in generic chaotic, disordered Fermi liquid systems within a driven random matrix formalism. By extending P. W. Anderson's orthogonality determinant formula to compute quantum work distribution, we find that work statistics is non-Gaussian and is characterized by a few dimensionless parameters. At longer times, quantum interference effects become irrelevant and the quantum work distribution is well-described in terms of a purely classical ladder model with a symmetric exclusion process in energy space, while bosonization and mean field methods provide accurate analytical expressions for the work statistics. Our random matrix and mean field predictions are validated by numerical simulations for a two-dimensional disordered quantum dot, and can be verified by calorimetric measurements on nanoscale circuits.

Superdiffusive quantum work and adiabatic quantum evolution in finite temperature chaotic Fermi systems

“…As we demonstrate, the universal behavior found at T = 0 temperature carries over to finite temperatures too, and is well captured by the simple classical 'ladder' model constructed in Ref. 41.…”

“…Real systems are, however, always subject to finite temperature. Here we therefore extend our previous, T = 0 temperature fermionic random matrix approach [40,41] to finite temperatures. The random matrix models studied here capture the properties of driven chaotic and disordered Fermi-systems such as metallic nano-grains [45].…”

“…While the average energy absorption has been investigated in chaotic and disordered systems quite some time ago in the pioneering works of Wilkinson [27][28][29][30] and Kravtsov [31][32][33], the full distribution, P (W, t), has started to attract attention much more recently. Most of the works on disordered systems have focused on sudden quenches [34][35][36][37][38][39], while the first results on generic quench protocols in driven fermionic random systems considered only the zero temperature limit [40,41].…”

“…40 and 41, we have shown at T = 0 temperature that, in chaotic Fermi systems, described by random matrix theory, P ad T =0 (t) decays as a stretched exponential, and we have derived approximate expressions for the non-Gaussian regular part, P reg T =0 (W, t), using bosonization and mean field methods. Work, in particular, has been shown to display a superdiffusive behavior [40,41], and the work statistics has been found to exhibit interesting universal features at T = 0 temperature.…”

“…In the context of work statistics in disordered nanograins, an even stronger sense of universality appears to emerge [41]. For sufficiently large injected work, the work statistics is independent not only of such microscopic details as the metallic grains' level spacing, δǫ, but even of the symmetry of the underlying Hamiltonian (unitary, orthogonal, or symplectic).…”