Symmetry mismatch between SU(2) Hamiltonian and U(1) Liouvillian in a long-range XXZ chain with dephasing selects fast eigenmodes, enabling size-independent fast relaxation and a strong quantum Mpemba effect.
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In U(1)-symmetric random circuits, initial states with lower stabilizer Rényi entropy generate nonstabilizerness faster than those with higher entropy, with the effect also depending on spatial charge structure and extending to SU(2) circuits and Hamiltonian dynamics.
Bath memory reshapes transport patterns in the extended phase of the AAH transition but mainly renormalizes timescales in the localized phase.
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