Spectral properties of generic local Lindbladians: Implications for open system dynamics

The advent of noisy quantum simulators has led to a lot of interest in exploring the dynamical aspects of generic open quantum systems. We study the implications of generic features in the spectrum of interacting Lindbladians for the dynamics of open quantum systems. Notably, previous work has demonstrated that in certain classes of random Lindbladians, the rate of decay of an operator is closely correlated with its "weight” (i.e. the number of sites on which it acts non-trivially). We show that the correlation between weight and decay rates is a general feature of local Lindbladian dynamics. We justify this both numerically, by studying one-dimensional spin chains evolving under a generic interacting local Lindbladian and analytically using a simple non-interacting model. We discuss the implications of this result for the dynamics of local observables, operator spreading, and other information-theoretic quantities.