Exact Accumulated-Field Determined Steady States with Boundary-Controlled Relaxation in Dissipative Quantum Link Chains

Abstract: In open quantum lattice systems, changing the boundary condition would appear to alter both the steady state and the nonzero Liouvillian spectrum. Here we show that these two boundary-induced changes do not necessarily occur together in a globally reciprocal dissipative quantum link chain. The steady state is determined by an accumulated field defined by link-resolved dissipative asymmetries, and a gauge-generated transformation built from this field gives exact symmetry-resolved steady states with nonuniform, accumulated-field-dependent reduced matter occupations. We then construct a reciprocal cyclic boundary condition that preserves these matter occupations while changing the nonzero Liouvillian spectrum. Consequently, open and cyclic chains relax to the same reduced matter steady-occupation profile with different Liouvillian gaps, with the cyclic closure accelerating relaxation. In the strong-dissipation limit, this relaxation difference can be reduced to a spectral comparison of effective exclusion processes with open and cyclic boundaries.