Dynamic localization in quantum dots: analytical theory

TL;DR

This paper develops an analytical theory to understand how quantum dots respond to time-dependent perturbations, revealing quantum corrections to energy absorption that depend on the nature of the perturbation and symmetry class.

Contribution

It provides a novel analytical framework for quantum corrections in quantum dots under various time-dependent perturbations, linking them to random matrix theory and symmetry classes.

Findings

Quantum corrections depend on dephasing time and perturbation type.

Incommensurate harmonic perturbations mimic d-dimensional Anderson model conductivity.

Periodic perturbations generally lack quantum corrections unless they obey time-reversal symmetry.

Abstract

We analyze the response of a complex quantum-mechanical system (e. g., a quantum dot) to a time-dependent perturbation. Assuming the dot energy spectrum and the perturbation to be described by the Gaussian Orthogonal Ensemble of random matrices we find the quantum corrections to the energy absorption rate as a function of dephasing time. If the perturbation is a sum of d harmonics with incommensurate frequencies, the quantum corrections behave similarly to those of conductivity for the d-dimensional Anderson model of the orthogonal symmetry class. For periodic perturbations, the leading quantum corrections are generically absent as in the systems of the unitary symmetry class. Exceptions are the harmonic perturbation and all other periodic perturbations that obey the generalized time-reversal condition (with an arbitrary time shift). Such cases fall into the quasi-1d orthogonal universality class.