Multifractality of random eigenfunctions and generalization of Jarzynski equality
Abstract
Systems driven out of equilibrium experience large fluctuations of the dissipated work. The same is true for wavefunction amplitudes in disordered systems close to the Anderson localization transition. In both cases, the probability distribution function is given by the largedeviation ansatz. Here we exploit the analogy between the statistics of work dissipated in a driven singleelectron box and that of random multifractal wavefunction amplitudes, and uncover new relations that generalize the Jarzynski equality. We checked the new relations theoretically using the rate equations for sequential tunnelling of electrons and experimentally by measuring the dissipated work in a driven singleelectron box 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.
 Publication:

Nature Communications
 Pub Date:
 April 2015
 DOI:
 10.1038/ncomms8010
 arXiv:
 arXiv:1411.1852
 Bibcode:
 2015NatCo...6.7010K
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Strongly Correlated Electrons;
 Condensed Matter  Superconductivity
 EPrint:
 5 pages of the main text, 4 pages of the supplementary materials, 4 figures