Energy absorption by "sparse" systems: beyond linear response theory

TL;DR

This paper explores energy absorption in weakly chaotic or interacting systems, introducing a resistor network approach to go beyond linear response theory, with applications to billiards and mesoscopic rings.

Contribution

It develops a semi-linear response framework using resistor network models to analyze energy absorption beyond traditional linear response theory.

Findings

Modified response formula replacing algebraic average with resistor network average

Semi-linear response behavior observed in prototype systems

Contrasts with Wall and Drude formulas in specific applications

Abstract

The analysis of the response to driving in the case of weakly chaotic or weakly interacting systems should go beyond linear response theory. Due to the "sparsity" of the perturbation matrix, a resistor network picture of transitions between energy levels is essential. The Kubo formula is modified, replacing the "algebraic" average over the squared matrix elements by a "resistor network" average. Consequently the response becomes semi-linear rather than linear. Some novel results have been obtained in the context of two prototype problems: the heating rate of particles in Billiards with vibrating walls; and the Ohmic Joule conductance of mesoscopic rings driven by electromotive force. Respectively, the obtained results are contrasted with the "Wall formula" and the "Drude formula".