Transmission through a noisy network (Q2921130)

This article studies the influence of a time dependent random noise perturbation on the transmission through quantum graphs with leads to infinity.NEWLINENEWLINEQuantum graphs are on the one side convenient and simple models for chaotic quantum systems in mathematical and theoretical physics [\textit{G. Berkolaiko} and \textit{P. Kuchment}, Introduction to quantum graphs. Providence, RI: American Mathematical Society (AMS) (2013; Zbl 1318.81005)] and on the other side in the focus of current experimental realisations [\textit{O. Hul} et al., ``Experimental simulation of quantum graphs by microwave networks'', Phys. Rev. E 69, Article ID 056205 (2004; \url{doi:10.1103/PhysRevE.69.056205}); \textit{M. Allgaier} et al., Phys. Rev. E 89, No. 2, Article ID 022925 (2014; \url{doi:10.1103/PhysRevE.89.022925})]. NEWLINENEWLINENEWLINE In this article quantum graphs with leads to infinity are taken as a model for open chaotic scattering. Such systems are usually described via stationary scattering theory by a sequence of complex resonances. In order to study the influence of noise on such systems the authors add a delta potential of fixed strength, but at a time dependent position, as a perturbation on an arbitrary edge of the graph. The position fluctuations of the delta perturbation is assumed to perform a one-dimensional Brownian motion of a particle in a harmonic potential (Ornstein-Uhlenbeck process). Under this assumptions the authors obtain results on the transmission through these graphs by using perturbation theory on the time dependent Schrödinger equation. Their results show that the effect of noise is particularly strong in the vicinity of narrow topological resonances which were recently studied in [\textit{S. Gnutzmann} et al., ``Topological resonances in scattering on networks (graphs)'', Phys. Rev. Lett. 110, No. 4, Article ID 094101 (2013; \url{doi:10.1103/PhysRevLett.110.094101}); \textit{D. Waltner} and \textit{U. Smilansky}, ``Scattering from a ring graph -- a simple model for the study of resonances '', Acta Phys. Pol. A 124, No. 12, 1087--1090 (2013; \url{doi:10.12693/APhysPolA.124.1087})].