Multifractality of random eigenfunctions and generalization of Jarzynski equality

TL;DR

This paper uncovers new universal relations that generalize the Jarzynski equality by linking work dissipation in driven systems to multifractal wave functions near Anderson localization, supported by experimental validation.

Contribution

It introduces a novel connection between work statistics and multifractality, extending the Jarzynski equality to disordered quantum systems.

Findings

Experimental verification of the generalized relations in a driven single-electron box

Identification of universal features of work fluctuations in out-of-equilibrium systems

Insights into the symmetry of multifractal exponents in Anderson localization

Abstract

Systems driven out of equilibrium experience large fluctuations of the dissipated work. The same is true for wave function amplitudes in disordered systems close to the Anderson localization transition.\cite{Mirlin-review} In both cases the probability distribution function (PDF) is given by the large deviation ansatz. Here we exploit the analogy between the PDF of work dissipated in a driven single-electron box (SEB) and that of random multifractal wave function amplitudes and uncover new relations which generalize the Jarzynski equality. We checked the new relations experimentally by measuring the dissipated work in a driven SEB and found a remarkable correspondence. The results represent an important universal feature of the work statistics in systems out of equilibrium and help to understand the nature of the symmetry of multifractal exponents in the theory of Anderson localization.