Spectral gaps of local quantum channels in the weak-dissipation limit

• URL: http://arxiv.org/abs/2409.17238v1
• Date: Wed, 25 Sep 2024 18:00:07 GMT
• Title: Spectral gaps of local quantum channels in the weak-dissipation limit
• Authors: J. Alexander Jacoby, David A. Huse, Sarang Gopalakrishnan,
• Abstract summary: We consider the dynamics of generic chaotic quantum many-body systems with no conservation laws, subject to weak bulk dissipation. The generator of these dissipative dynamics, a quantum channel $mathcalE$, retains a nonzero gap as the dissipation strength $gamma to 0$ if the thermodynamic limit is taken first. We argue that the gap in the $gamma to 0$ limit can change nonanalytically as one tunes the parameters of the unitary dynamics.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the dynamics of generic chaotic quantum many-body systems with no conservation laws, subject to weak bulk dissipation. It was recently observed [T. Mori, arXiv:2311.10304] that the generator of these dissipative dynamics, a quantum channel $\mathcal{E}$, retains a nonzero gap as the dissipation strength $\gamma \to 0$ if the thermodynamic limit is taken first. We use a hydrodynamic description of operator spreading in the presence of dissipation to estimate the gap of $\mathcal{E}$ as $\gamma \to 0$; to calculate the operator-size distribution of the low-lying eigenmodes of $\mathcal{E}$; and to relate the gap to the long-time decay rates of autocorrelation functions under unitary dynamics. We provide a microscopic derivation of this hydrodynamic perspective for random unitary circuits. We argue that the gap in the $\gamma \to 0$ limit can change nonanalytically as one tunes the parameters of the unitary dynamics.

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