Integrals of motion as slow modes in dissipative many-body operator dynamics
Published in arXiv preprint, 2025
In this work, we studied the spectrum of Lindbladian superoperators. We consider the Hamiltonian part having integrals of motion (IOMs), while the dissipation part consist of weak and local jump operators. Building on previous results that showed the dissipative decay of an operator in such setting is roughly proportional to the size of the operator, we showed that IOMs would have slower decay than generic operators due to their immunity to operator growth. With this, we showed that diagonalizing the Lindbladian can reveal the IOMs of the system, with both numerical evidence and a perturbation theory argument.