Multiple Timescales in Open Kitaev Chains: Renormalization Group Analysis and Insights From Nonintegrability

We analyze the multiple timescales that appear in the dissipative dynamics of an open Kitaev chain. Starting from the unified quantum master equation (UQME), we reduce the problem to a singularly perturbed three-dimensional system that describes the nearly degenerate subspace spanned by a pair of Majorana zero modes (MZMs). Application of Chiba’s renormalization-group (RG) method yields an explicit β-function for the slow amplitude and the asymptotic expansions λ1=−ɛ24γ+Oɛ3, λ2=−2γ+Oɛ,of the slow and fast eigenvalues, together with rigorous error bounds on the timescale t=O1/ɛ2. A weak longitudinal field, which renders the underlying closed system nonintegrable, produces a quadratic correction of structural type to the same β-function. The sign of the correction implies a shortening of the slow timescale; the prefactor k is not evaluated numerically. The analytic predictions are confirmed by numerical integration of both the reduced master equation and a short chain. The resulting framework provides a mathematically controlled description of how dissipation and the loss of integrability jointly determine the long-time fate of topological edge modes.MSC2020 Classification: 81T17, 34E13, 82C10, 81Q80, 37A60