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

In a series of publications (see review), one of them selected as the EPL editorial board highlight of 2006, and another as the Editor's choice of 2007-2008, we develop (in various collaborations involved) a new paradigm for energy absorption of driven chaotic systems, called "semi-linear response theory". The theory uses a resistor network picture of transitions, and gives different results compared with linear response theory (Kubo) whenever the perturbation matrix in the Hamiltonian is "textured" or "sparse" [notably if its elements have log-normal or log-box rather than Gaussian distribution]. The theory has been applied to obtain novel results for the mesoscopic conductance of rings with very strong or very weak disorder, and also in order to resolve long standing questions regarding the applicability of the variable range hopping picture and the absorption of low frequency radiation by small metallic grains.
The figure illustrates model systems of interest: a Billiard with a moving wall, and a Ring with a time dependent magnetic flux. The "sparsity" of the perturbation matrix (right panel) reflects the slight deviation from intelligibility due to a deformation of the boundary, or due to the presence of weak disorder.
Additional highlights of the quantum chaos group can be found here