Low lying spectrum of weak-disorder quantum waveguides

Abstract

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 so-called 'initial length scale decay estimates' at they are used in the proof of spectral localization using the multiscale analysis.

Accepted for publication in Journal of Statistical Physics http://www.springerlink.com/content/0022-4715

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Cited by in corpus (7)

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• Quantum Hamiltonians with weak random abstract perturbation. I. Initial length scale estimate
• Expansion of the spectrum in the weak disorder regime for random operators in continuum space
• Expansion of the almost sure spectrum in the weak disorder regime
• Lifshits tails for randomly twisted quantum waveguides
• Quantum Hamiltonians with weak random abstract perturbation. II. Localization in the expanded spectrum
• Lifshitz asymptotics and localization for random breather models