Speaker
Description
In random matrix theory, the β ensemble is a generalization of the Wigner-Dyson ensembles to arbitrary values of β. Dumitriu and Edelman proposed a matrix model of the β ensemble, which is equivalent to a single-particle Hamiltonian with inhomogeneous disorder in the hopping amplitudes. The β ensemble exhibits a non-ergodic phase which has many distinctive features: weak long-range energy correlation despite the absence of short-range correlation, coexistence of localized and extended states without forming any mobility edge, fast eqiulibration of quench dynamics. All these anomalous properties can be understood from a spatially local equivalence to the 1D Anderson model. In the zero temperature limit (β → ∞), the β ensemble reduces to a deterministic Hamiltonian, which has an energy-coordinate duality to the quantum Harmonic oscillator. We find that corresponding bulk states have energy dependent multifractality.