2021/04/23 by Kohei Yamanaka, Yamanaka, Kohei, Tomohiro Sasamoto +1 · 3 citations
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Quantum Physics (quant-ph) #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2104.11479
openalex publication_date 2021/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We obtain exact formulas for the time-dependence of a few physical observables for the open XX spin chain with Lindbladian dynamics. Our analysis is based on the fact that the Lindblad equation for an arbitrary open quadratic system of N fermions is explicitly solved in terms of diagonalization of a 4N×4N matrix called structure matrix by following the scheme of the third quantization. We mainly focus on the time-dependence of magnetization and spin current. As a short-time behavior at a given site, we observe the plateau regime except near the center of the chain. Basic features of this are explained by the light-cone structure created by propagations of boundary effects from the initial time, but we can explain their more detailed properties analytically using our exact formulas. On the other hand, after the plateau regime, the magnetization and spin current exhibit a slow decay to the steady state values described by the Liouvillian gap. We analytically establish its O(N-3) scaling and also determine its coefficient.