Low lying spectrum of weak-disorder quantum waveguides
We study the low-lying spectrum of the Dirichlet Laplace operator on a randomly wiggled strip. More precisely, our results are formulated in terms of the eigenvalues of finite segment approximations of the infinite waveguide. Under appropriate weak-disorder assumptions we obtain deterministic and probabilistic bounds on the position of the lowest eigenvalue. A Combes-Thomas argument allows us to obtain a so-called ‘initial length scale decay estimate’ as they are employed in the proof of spectral localization using the multiscale analysis method.
Abstract A self-consistent quasilinear model of the interaction between VLF emissions and geomagnetic pulsation is set forth. As a result an explicit expression of a modulation frequency dependence can be obtained.