Solvable models of many-body chaos from dual-Koopman circuits
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914956056723456 |
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| author | Lakshminarayan, Arul |
| author_facet | Lakshminarayan, Arul |
| contents | Dual-unitary circuits are being vigorously studied as models of many-body quantum chaos that can be solved exactly for correlation functions and time evolution of states. Here we define their classical counterparts as dual-canonical transformations and associated dual-Koopman operators. Like their quantum counterparts, the correlations vanish everywhere except on the light cone, on which they decay with rates governed by a simple contractive map. Providing a large class of such dual-canonical transformations, we study in detail the example of a coupled standard map and show analytically that arbitrarily away from the integrable case, in the thermodynamic limit the system is mixing. We also define ``perfect" Koopman operators that lead to the correlation vanishing everywhere including on the light cone and provide an example of a cat-map lattice which would qualify to be a Bernoulli system at the apex of the ergodic hierarchy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_04950 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Solvable models of many-body chaos from dual-Koopman circuits Lakshminarayan, Arul Chaotic Dynamics Statistical Mechanics Quantum Physics Dual-unitary circuits are being vigorously studied as models of many-body quantum chaos that can be solved exactly for correlation functions and time evolution of states. Here we define their classical counterparts as dual-canonical transformations and associated dual-Koopman operators. Like their quantum counterparts, the correlations vanish everywhere except on the light cone, on which they decay with rates governed by a simple contractive map. Providing a large class of such dual-canonical transformations, we study in detail the example of a coupled standard map and show analytically that arbitrarily away from the integrable case, in the thermodynamic limit the system is mixing. We also define ``perfect" Koopman operators that lead to the correlation vanishing everywhere including on the light cone and provide an example of a cat-map lattice which would qualify to be a Bernoulli system at the apex of the ergodic hierarchy. |
| title | Solvable models of many-body chaos from dual-Koopman circuits |
| topic | Chaotic Dynamics Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2307.04950 |