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

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".

8 pages, 7 figures, short pedagogical review. Proceedings of FQMT conference (Prague, 2011). Ref corrected

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• Mesoscopic "Rydberg" atom in a microwave field
• The mesoscopic conductance of disordered rings, its random matrix theory, and the generalized variable range hopping picture
• Multiphoton Processes in Driven Mesoscopic Systems
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Cited by in corpus (2)

• Minimal Fokker-Planck theory for the thermalization of mesoscopic subsystems
• Quantum thermalization via percolation