Statistical Theory of Energy Transfer to Small and Chaotic Quantum Systems Induced by a Slowly-Varying External Field

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We study nonequilibrium properties of small and chaotic quantum systems, i.e., non-integrable systems whose size is small in the sense that the separations of energy levels are non-negligible as compared with other relevant energy scales. The energy change ΔE induced by a slowly-varying external field λ(t) is evaluated when the range of the variation Δλ is large so that the linear response theory breaks down. A new statistical theory is presented, by which we can predict <ΔE>, the average of ΔE over a finite energy resolution δE, as a function of λ(t) if we are given the density of states smeared over δE, the average distance of the anticrossings, and a constant K 1.