Localization of soft modes at the depinning transition

CAO, XIANGYU; BOUZAT, SEBASTIAN; KOLTON, ALEJANDRO B.; ROSSO, ALBERTO

Physical Review E

American Physical Society

Lugar: New York; Año: 2018 vol. 97 p. 221181 - 2211817

2470-0045

We characterize the soft modes of the dynamical matrix at the depinning transition, and compare the matrixwith the properties of the Anderson model (and long-range generalizations). The density of states at the edge ofthe spectrum displays a universal linear tail, different from the Lifshitz tails. The eigenvectors are instead verysimilar in the two matrix ensembles. We focus on the ground state (soft mode), which represents the epicenter ofavalanche instabilities. We expect it to be localized in all finite dimensions, and make a clear connection betweenits localization length and the Larkin length of the depinning model. In the fully connected model, we show thatthe weak-strong pinning transition coincides with a peculiar localization transition of the ground state.