Speaker
Description
We study the spectral properties of a tridiagonal matrix ensemble that is isospectral to random matrices, in which strength of level repulsion (β) can be tuned continuously to interpolate between integrable and chaotic regimes. Our analysis reveals that the spatial inhomogeneity in the β-ensemble gives rise to Non-Ergodic Extended (NEE) states and is devoid of any mobility edge. This NEE phase is associated with an unconventional energy scale which is captured by the Spectral Form Factors (SFF). The relaxation dynamics in β-ensemble is significantly different from those observed in standard many-body systems. Furthermore, using finite temperature spectral form factors we systematically probe distinct energy scales and extract the system-size scaling laws of the associated relaxation times.