Lifshitz tails for acoustic waves in random quantum waveguide

Hatem Najar (1)

1 IPEI - Département de Mathématiques Physiques

In this study, we consider acoustic operators in a random quantum waveguide. Precisely we deal with the acoustic operator of the form $-\nabla \varrho \nabla$ on a random strip. We prove that the integrated density of states of the relevant operator exhibits Lifshitz behavior at the bottom of the spectrum. This result could be used to prove localization of acoustic waves at the bottom of the spectrum.

Mots clés: spectral theory; random operators; integrated density of states; Lifshitz tails; localization. waveguide

Domaines: Théorie spectrale [math.SP]

Hatem Najar. Lifshitz tails for acoustic waves in random quantum waveguide. 2006. ⟨hal-00069624⟩