Lifshitz Tails for Acoustic Waves in Random Quantum Waveguide

In this study, we consider acoustic operators in a random quantum waveguide. Precisely we deal with an elliptic operator in the divergence form 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. 2000 Mathematics Subject Classification: 81Q10, 35P05, 37A30, 47F05