We consider conditions under which an isolated quantum system approaches a microcanonical equilibrium state. A key component is the eigenstate thermalisation hypothesis, proposes that all energy eigenstates appear thermal. introduce weaker version of this requirement, applying only to average distinguishability from thermal state, and investigate its necessity sufficiency for thermalisation.

Abstract It has previously been shown that ordinary least squares can be used to estimate the coefficients of single-index model under only mild conditions. However, estimator is non-robust leading poor estimates for some models. In this paper we propose a new sliced least-squares utilizes ideas from Sliced Inverse Regression. Slices with problematic observations contribute high variability in ...