Lifshitz tails for Schrödinger operators with random breather potential

Abstract

We prove a Lifshitz tail bound on the integrated density of states of random breather Schrödinger operators. The potential is composed of translated single site potentials. The single site potential is an indicator function of set $tA$ where $t$ is from the unit interval and $A$ is a measurable set contained in the unit cell. The challenges of this model are: Since $A$ is not assumed to be star-shaped the dependence of the potential on the parameter $t$ is not monotone. It is also non-linear and not differentiable.

accepted in Comptes rendus - Mathématique

References in corpus (3)

• Scale-free unique continuation principle, eigenvalue lifting and Wegner estimates for random Schrödinger operators
• Scale-free uncertainty principles and Wegner estimates for random breather potentials
• Conditional Wegner estimate for the standard random breather potential

Cited by in corpus (3)

• Band edge localization beyond regular Floquet eigenvalues
• Wegner estimate for random divergence-type operators monotone in the randomness
• Lifshitz asymptotics and localization for random breather models