The interplay of finite and infinite size stability in quadratic bosonic Lindbladians

A hallmark of systems whose time evolution is governed by a non-normal dynamical matrix is sensitivity to small perturbations, including changes in system parameters, system size, and boundary conditions. Among highly non-normal systems is a class of quadratic bosonic Lindbladians (QBLs), describing systems of non-interacting bosons subject to Markovian dissipation. Non-normality in QBLs, which can arise from both coherent and incoherent mechanisms, may cause spectral properties of finite- and infinite-size systems to be dramatically different. This has been linked to anomalous dynamical phenomena in truncated systems, notably, dynamical metastability – transient amplification preceding asymptotic relaxation, in parameter regimes where the finite-size system is dynamically stable. In this work, we report on the identification of QBLs which host an opposite flavor of dynamical metastability, namely, such QBLs that are dynamically stable in the infinite-size limit, but become unstable under open boundaries, for arbitrary system size. These systems reflect their stable infinite-size limits by appearing stable for a transient period whose duration grows with system size, before the instabilities set in. We discuss consequences for linear-response behavior and entanglement entropy.