Optimizing mixing in the Rudner–Levitov lattice

Abstract

Here we discuss the optimization of mixing in finite linear and circular Rudner–Levitov lattices (Su–Schrieffer–Heeger lattices with a dissipative sublattice). We show that the 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 logarithmic. When operating in the region between maximal and minimal exceptional points, it is always possible to restore 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 arbitrarily large number of lattice nodes.