Fidelity in Quasi-1D Systems as a Probe for Anderson Localization

Abstract

We analyze the echo dynamics in quasi-one-dimensional random media to investigate how the transition from localization to delocalization is encoded in its temporal decay properties. Our analysis extends from the standard perturbative regime corresponding to small perturbations (with respect to the mean level spacing) in the echo dynamics, out to the Wigner decay regime. On the theoretical side, our results rely on a banded random matrix modeling, and show in the localized regime under small perturbations a novel decay of the fidelity (Loschmidt echo), differing from the typical Gaussian decay seen within both diffusive and chaotic systems. For larger perturbation strengths, typical Wigner exponential decays are observed. Scattering echo measurements are performed experimentally within a quasi-1D microwave cavity randomly populated with point-like scatterers. Agreements are observed between experiments, numerics, and theoretical predictions.

Microwave experiments in the realm of fidelity

“…But in contrast with (b) the width is larger than the wavelength. (d) Photo of a disordered cavity where the lower wall is shifted and the reflection measurement was performed in the central part of the cavity (details see [22]). (e) Cavity where the coupling with the attached channel can be varied by a diaphragm (details see [23]).…”

Non-Hermitian Dynamics: Examples from Disordered Microwave Cavities and Classical Optics

“…This comparison, and the corresponding experimental set-up will be discussed in the following chapter. from [4] with the parameters renamed.…”

“…The theoretical expression for fidelity defined in the previous chapter is hardly accessible experimentally [4]. Therefore, the notion of the scattering fidelity which makes use of the experimentally accessible scattering matrix was introduced in Ref.…”

“…This figure confirmed the linear behavior σ ν ∼ √ P 2 for localized eigenstates. Figure taken from [4] and referenced herein.…”

“…The fitting parameter, σ 2T is found to be 3.37 which is above the threshold value of 7/3. Figure taken from[4].…”