ec 2 00 3 Chapter 1 DEPHASING AND DYNAMIC LOCALIZATION IN QUANTUM DOTS

The effects of dynamic localization in a solid-state system – a quantum dot – are considered. The theory of weak dynamic localization is developed for non-interacting electrons in a closed quantum dot under arbitrary time-dependent perturbation and its equivalence to the theory of weak Anderson localization is demonstrated. The dephasing due to inelastic electron scattering is shown to destroy the dynamic localization in a closed quantum dot leading to the classical energy absorption at times much greater than the inelastic scattering time. Finally a realistic case of a dot weakly connected to leads is studied and it is shown that the dynamic localization may lead to a drastic change of the shape of the Coulomb blockade peak in the dc conductance vs the gate voltage. 1. Introduction The process of energy absorption by a quantum system with a time-dependent Hamiltonian underlies a large part of modern physics, both fundamental and applied. A generic Hamiltonian can be written in the form: ˆ H(t) = ˆ H 0 + ˆ V φ(t), (1.1) where we explicitly separated the time-independent partˆH 0 and the external perturbationˆV with the time dependence specified by a given function φ(t). In the textbook example of the classical Drude absorption, φ(t) = E(t) is the time-dependent electric field which is often considered to be a harmonic