Optimizing mixing in the Rudner-Levitov lattice

TL;DR

This paper investigates how exceptional points in Rudner-Levitov lattices influence mixing times, revealing conditions for optimal mixing scaling and the impact of lattice geometry and initial states.

Contribution

It demonstrates how exceptional points affect mixing time scaling and shows methods to restore logarithmic scaling in various lattice configurations.

Findings

Exceptional points cause mixing time scaling to vary from quadratic to logarithmic.

Choosing the initial state can restore logarithmic mixing time scaling.

Asymmetric circular lattices maintain logarithmic scaling regardless of size.

Abstract

Here we discuss optimization of mixing in finite linear and circular Rudner-Levitov lattices, i.e., Su-Schrieffer-Heeger lattices with a dissipative sublattice. We show that presence of exceptional points in the systems spectra can lead to drastically different scaling of the mixing time with the number of lattice nodes, varying from quadratic to the logarithmic one. When operating in the region between the maximal and minimal exceptional points, it is always possible to restore the logarithmic scaling by choosing the initial state of the chain. Moreover, for the same localized initial state and values of parameters, a longer lattice might mix much faster than the shorter one. Also we demonstrate that an asymmetric circular Rudner-Levitov lattice can preserve logarithmic scaling of the mixing time for an arbitrary large number of lattice nodes.