For Lindblad quantum spin systems on infinite lattices, the paper proves that thermodynamic and long-time limits defining NESS and TANESS commute under spectral-gap plus condition-number assumptions, and gives a model where spectral gaps alone fail.
Automorphic Equivalence within Gapped Phases of Quan- tum Lattice Systems
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Nonequilibrium steady state in Lindblad dynamics for infinite quantum spin systems
For Lindblad quantum spin systems on infinite lattices, the paper proves that thermodynamic and long-time limits defining NESS and TANESS commute under spectral-gap plus condition-number assumptions, and gives a model where spectral gaps alone fail.