Spectral gaps of local quantum channels in the weak-dissipation limit
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| Format: | Preprint |
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2024
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| _version_ | 1866915286584655872 |
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| author | Jacoby, J. Alexander Huse, David A. Gopalakrishnan, Sarang |
| author_facet | Jacoby, J. Alexander Huse, David A. Gopalakrishnan, Sarang |
| contents | 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 $γ\to 0$ 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 $γ\to 0$; 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 $γ\to 0$ limit can change nonanalytically as one tunes the parameters of the unitary dynamics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_17238 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectral gaps of local quantum channels in the weak-dissipation limit Jacoby, J. Alexander Huse, David A. Gopalakrishnan, Sarang Quantum Physics Statistical Mechanics Strongly Correlated Electrons 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 $γ\to 0$ 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 $γ\to 0$; 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 $γ\to 0$ limit can change nonanalytically as one tunes the parameters of the unitary dynamics. |
| title | Spectral gaps of local quantum channels in the weak-dissipation limit |
| topic | Quantum Physics Statistical Mechanics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2409.17238 |