Deterministic many-body dynamics with multifractal response
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913947401060352 |
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| author | Kasim, Yusuf Prosen, Tomaž |
| author_facet | Kasim, Yusuf Prosen, Tomaž |
| contents | Dynamical systems can display a plethora of ergodic and ergodicity breaking behaviors, ranging from simple periodicity to ergodicity and chaos. Here we report an unusual type of non-ergodic behavior in a many-body discrete-time dynamical system, specifically a multi-periodic response with multi-fractal distribution of equilibrium spectral weights at all rational frequencies. This phenomenon is observed in the momentum-conserving variant of the newly introduced class of the so-called parity check reversible cellular automata, which we define with respect to an arbitrary bi-partite lattice. Although the models display strong fragmentation of phase space of configurations, we demonstrate that the effect qualitatively persists within individual fragmented sectors, and even individual typical many-body trajectories. We provide detailed numerical analysis of examples on 2D (honeycomb, square) and 3D (cubic) lattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19779 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deterministic many-body dynamics with multifractal response Kasim, Yusuf Prosen, Tomaž Statistical Mechanics Cellular Automata and Lattice Gases Dynamical systems can display a plethora of ergodic and ergodicity breaking behaviors, ranging from simple periodicity to ergodicity and chaos. Here we report an unusual type of non-ergodic behavior in a many-body discrete-time dynamical system, specifically a multi-periodic response with multi-fractal distribution of equilibrium spectral weights at all rational frequencies. This phenomenon is observed in the momentum-conserving variant of the newly introduced class of the so-called parity check reversible cellular automata, which we define with respect to an arbitrary bi-partite lattice. Although the models display strong fragmentation of phase space of configurations, we demonstrate that the effect qualitatively persists within individual fragmented sectors, and even individual typical many-body trajectories. We provide detailed numerical analysis of examples on 2D (honeycomb, square) and 3D (cubic) lattices. |
| title | Deterministic many-body dynamics with multifractal response |
| topic | Statistical Mechanics Cellular Automata and Lattice Gases |
| url | https://arxiv.org/abs/2411.19779 |