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

Abstract

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 $K \lesssim 1$.