Localization crossover for the continuous Anderson Hamiltonian in $1$-d

no code implementations • 18 Feb 2021 • Laure Dumaz, Cyril Labbé

We investigate the behavior of the spectrum of the continuous Anderson Hamiltonian $\mathcal{H}_L$, with white noise potential, on a segment whose size $L$ is sent to infinity.

Probability Statistical Mechanics Mathematical Physics Analysis of PDEs Mathematical Physics

The delocalized phase of the Anderson Hamiltonian in $1$-d

no code implementations • 10 Feb 2021 • Laure Dumaz, Cyril Labbé

This allows to answer a conjecture of Rifkind and Vir\'ag (2018) on the behavior of the eigenvectors of $\mathcal{H}_L$.

Probability Statistical Mechanics Mathematical Physics Mathematical Physics 60H25, 60J60, 60B20