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The calculation of the heating rate of cold atoms in vibrating traps requiresa theory that goes beyond the Kubo linear response formulation. If a strong"quantum chaos" assumption does not hold, the analysis of transitions showssimilarities with a percolation problem in energy space. We show how thetexture and the sparsity of the perturbation matrix, as determined by thegeometry of the system, dictate the result. An improved sparse random matrixmodel is introduced: it captures the essential ingredients of the problem, andleads to a generalized variable range hopping picture.

Semilinear response for the heating rate of cold atoms in vibrating traps