Some aspects of the Anderson Hamiltonian in 1D

In this talk, I will present several results on the Anderson Hamiltonian with white noise potential in dimension 1. This operator formally writes « minus Laplacian plus white noise ». It arises as the scaling limit of various discrete models and its explicit potential allows for a detailed description of its spectrum. We will discuss localization of its eigenfunctions as well as the behaviour of the local statistics of its eigenvalues. Around large energies, we will see that the eigenfunctions are delocalized and the operator limit takes a simple form “J partial_t + 2*2 noise matrix’’ that can be linked to the hyperbolic carousel operators of Valko and Virag. Based on joint works with Cyril Labbé.

• Speaker: Laure Dumaz (CNRS, ENS Paris)
• Tuesday 23 January 2024, 14:00–15:00
• Venue: MR12.
• Series: Probability; organiser: ww295.