Experimental Width Shift Distribution: A Test of Nonorthogonality for Local and Global Perturbations

TL;DR

This paper experimentally investigates the universal statistics of resonance width shifts in open systems under perturbations, testing nonorthogonality indicators in microwave cavities and chambers, and compares results with theory and simulations.

Contribution

It extends the theory of width shift distribution to local perturbations and validates it through experiments and simulations in multi-channel open systems.

Findings

Good agreement between theory, experiments, and simulations.

Width shift distribution is more sensitive to perturbation type in many-channel systems.

Experimental results confirm the universality of the width shift statistics.

Abstract

The change of resonance widths in an open system under a perturbation of its interior has been recently introduced by Fyodorov and Savin [Phys. Rev. Lett. 108, 184101 (2012)] as a sensitive indicator of the nonorthogonality of resonance states. We experimentally study universal statistics of this quantity in weakly open two-dimensional microwave cavities and reverberation chambers realizing scalar and electromagnetic vector fields, respectively. We consider global as well as local perturbations, and also extend the theory to treat the latter case. The influence of the perturbation type on the width shift distribution is more pronounced for many-channel systems. We compare the theory to experimental results for one and two attached antennas and to numerical simulations with higher channel numbers, observing a good agreement in all cases.