Universal quantum work statistics in chaotic Fermi liquids

We present a theory of work statistics in generic chaotic, disordered Fermi liquid systems within a driven random matrix formalism. We extend Phil Anderson’s orthogonality determinant formula [1] to compute the full distribution of quantum work at arbitrary temperature [2]. The evolution of quantum work distribution is found to be universal, and characterized by just two parameters: the temperature in units of mean level spacing, and a dimensionless average work [3]. The average work is growing linearly in time, independently of the temperature. For low temperatures fluctuations exhibit superdiffusive behavior [3] and a non-Gaussian work statistics is observed [4], while in the opposite limit the distribution of work becomes Gaussian with diffusive fluctuations.

For large enough absorbed energy, quantum work can be well described in terms of a purely classical Markovian symmetric exclusion process in energy space, at arbitrary temperature, as generated by Landau-Zener transitions, and accurate analytical expressions can be derived for it [2,3]. Our random matrix predictions are compared to and validated by numerical simulations performed on realistic 2D quantum dot models. We propose to verify them experimentally by calorimetric measurements on nanoscale circuits [4].