Circuits as a simple platform for the emergence of hydrodynamics in deterministic chaotic many-body systems
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915192504320000 |
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| author | Kim, Sun Woo P. Hübner, Friedrich Garrahan, Juan P. Doyon, Benjamin |
| author_facet | Kim, Sun Woo P. Hübner, Friedrich Garrahan, Juan P. Doyon, Benjamin |
| contents | The emergence of hydrodynamics is one of the deepest phenomena in many-body systems. Arguably, the hydrodynamic equations are also the most important tools for predicting large-scale behaviour. Understanding how such equations emerge from microscopic deterministic dynamics is a century-old problem, despite recent progress in fine-tuned integrable systems. Due to the universality of hydrodynamics, the specific microscopic implementation should not matter. Here, we show that classical deterministic circuits provide a minimal, exact, and efficient platform that admits non-trivial hydrodynamic behaviour for deterministic but chaotic systems. By developing new techniques and focusing on 1D circuits as a proof of concept, we obtain the characteristic dynamics, including relaxation to Gibbs states, exact Euler equations, shocks, diffusion, and exact KPZ super-diffusion. Our methods can be easily generalised to higher dimensions or quantum circuits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08788 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Circuits as a simple platform for the emergence of hydrodynamics in deterministic chaotic many-body systems Kim, Sun Woo P. Hübner, Friedrich Garrahan, Juan P. Doyon, Benjamin Statistical Mechanics Mathematical Physics The emergence of hydrodynamics is one of the deepest phenomena in many-body systems. Arguably, the hydrodynamic equations are also the most important tools for predicting large-scale behaviour. Understanding how such equations emerge from microscopic deterministic dynamics is a century-old problem, despite recent progress in fine-tuned integrable systems. Due to the universality of hydrodynamics, the specific microscopic implementation should not matter. Here, we show that classical deterministic circuits provide a minimal, exact, and efficient platform that admits non-trivial hydrodynamic behaviour for deterministic but chaotic systems. By developing new techniques and focusing on 1D circuits as a proof of concept, we obtain the characteristic dynamics, including relaxation to Gibbs states, exact Euler equations, shocks, diffusion, and exact KPZ super-diffusion. Our methods can be easily generalised to higher dimensions or quantum circuits. |
| title | Circuits as a simple platform for the emergence of hydrodynamics in deterministic chaotic many-body systems |
| topic | Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2503.08788 |