2025/06/18 by Roy, Basudha, Das, Adway Kumar, Ghosh, Anandamohan +1 · 2 citations
#Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Other Condensed Matter (cond-mat.other) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2506.15283
The β-ensemble is a prototypical model of a single particle system on a one-dimensional disordered lattice with inhomogeneous nearest neighbor hopping. Corresponding nonergodic phase has an anomalous critical energy scale, Ec: correlations are present above and absent below Ec as reflected in the number variance. We study the dynamical properties of the β-ensemble where the critical energy controls the characteristic timescales. In particular, the spectral form factor equilibrates at a relaxation time, tR ≡ Ec-1, which is parametrically smaller than the Heisenberg time, tH, given by the inverse of the mean level spacing. Incidentally, the dimensionless relaxation time, τR ≡ tR/tH ≪ 1 is equal to the Dyson index, β. We show that the energy correlations are absent within a temporal window tR < t < tH, which we term as the correlation void. This is in contrast to the mechanism of equilibration in a typical many-body system. We analytically explain the qualitative behavior of the number variance and the spectral form factor of the β-ensemble by a spatially local mapping to the Anderson model.