The data of article ''Control of the Liouvillian gap in the finite open quantum system''

Relaxation processes in quantum systems coupled to external environments represent one of themost fundamental nonequilibrium phenomena in condensed matter physics. The Lindblad masterequation provides a powerful framework for characterizing such open quantum dynamics. In thiswork, we systematically investigate how different types of quantum jump operators and system geometriesinfluence the Liouvillian gap and the properties of the nonequilibrium steady state (NESS)in finite-size systems. We demonstrate that, due to the intricate structure of the Liouvillian superoperator,multiple NESSs with unphysical characteristics can emerge. The physically meaningfulsteady state must be understood as a superposition of these NESSs that collectively satisfy therequired physical constraints. Furthermore, we find that the Liouvillian gap does not necessarilyincrease monotonically with the system-environment coupling strength. Instead, it can exhibit anontrivial peak structure, corresponding to a minimum in the relaxation time. The magnitude ofthis peak is closely related to the symmetry properties of the system. Our results provide a deeperunderstanding of nonequilibrium behavior in finite quantum systems and offer new insights into thedesign and control of open quantum dynamics.This dataset provides complete Python code for generating all figures in the article. The implementation employs Python technology: the numerical computation core utilizes Numpy for nonequilibrium steady state analysis and Liouvillian gap calculations, while the visualization module uses Matplotlib to plot the system's time evolution under different boundary conditions, Jump-operator type and placement with 600 dpi resolution, along with the non-monotonic dependence of the Liouvillian gap on dissipation strength γ.