Dynamic Localization in Quantum Dots: Analytical Theory

Abstract

We analyze the response of a complex quantum-mechanical system (e.g., a quantum dot) to a time-dependent perturbation $\ensuremath{\phi}(t)$. Assuming the dot to be described by random-matrix theory for the Gaussian orthogonal ensemble, we find the quantum correction to the energy absorption rate as a function of the dephasing time ${t}_{\ensuremath{\varphi}}$. If $\ensuremath{\phi}(t)$ is a sum of $d$ harmonics with incommensurate frequencies, the correction behaves similarly to that for the conductivity $\ensuremath{\delta}{\ensuremath{\sigma}}_{d}({t}_{\ensuremath{\varphi}})$ in the $d$-dimensional Anderson model of the orthogonal symmetry class. For a generic periodic perturbation, the leading quantum correction is absent as in the systems of the unitary symmetry class, unless $\ensuremath{\phi}(\ensuremath{-}t+\ensuremath{\tau})=\ensuremath{\phi}(t+\ensuremath{\tau})$ for some $\ensuremath{\tau}$, which falls into the quasi-1D orthogonal universality class.