Single-particle eigenstate thermalization in quantum-chaotic quadratic Hamiltonians

Abstract

We study the matrix elements of local and nonlocal operators in the single-particle eigenstates of two paradigmatic quantum-chaotic quadratic Hamiltonians; the quadratic Sachdev-Ye-Kitaev (SYK2) model and the three-dimensional Anderson model below the localization transition. We show that they display eigenstate thermalization for normalized observables. Specifically, we show that the diagonal matrix elements exhibit vanishing eigenstate-to-eigenstate fluctuations, and a variance proportional to the inverse Hilbert space dimension. We also demonstrate that the ratio between the variance of the diagonal and the off-diagonal matrix elements is 2, as predicted by the random matrix theory. We study distributions of matrix elements of observables and establish that they need not be Gaussian. We identify the class of observables for which the distributions are Gaussian.

Typicality of nonequilibrium (quasi-)steady currents

“…In the future we will consider adding an intermediate system between the baths so as to study conditions for the emergence of a (quasi-)steady current within this intermediate system. Furthermore, it would be important to consider whether the conditions for the emergence of the (quasi-)steady current can be loosened, for example considering also integrable baths [55,[62][63][64][65][66]]. In this section we derive the perturbative current expression (Eq.…”