The equilibrium distribution function for strongly nonlinear systems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913936051273728 |
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| author | Zhang, Jialin Zhang, Yong Zhao, Hong |
| author_facet | Zhang, Jialin Zhang, Yong Zhao, Hong |
| contents | The equilibrium distribution function determines macroscopic observables in statistical physics. While conventional methods correct equilibrium distributions in weakly nonlinear or near-integrable systems, they fail in strongly nonlinear regimes. We develop a framework to get the equilibrium distributions and dispersion relations in strongly nonlinear many-body systems, incorporating corrections beyond the random phase approximation and capturing intrinsic nonlinear effects. The theory is verified on the nonlinear Schrodinger equation, the Majda-McLaughlin-Tabak model, and the FPUT-beta model, demonstrating its accuracy across distinct types of nonlinear systems. Numerical results show substantial improvements over existing approaches, even in strong nonlinear regimes. This work establishes a theoretical foundation for equilibrium statistical properties in strongly nonlinear systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_07600 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The equilibrium distribution function for strongly nonlinear systems Zhang, Jialin Zhang, Yong Zhao, Hong Statistical Mechanics Mathematical Physics Chaotic Dynamics Classical Physics The equilibrium distribution function determines macroscopic observables in statistical physics. While conventional methods correct equilibrium distributions in weakly nonlinear or near-integrable systems, they fail in strongly nonlinear regimes. We develop a framework to get the equilibrium distributions and dispersion relations in strongly nonlinear many-body systems, incorporating corrections beyond the random phase approximation and capturing intrinsic nonlinear effects. The theory is verified on the nonlinear Schrodinger equation, the Majda-McLaughlin-Tabak model, and the FPUT-beta model, demonstrating its accuracy across distinct types of nonlinear systems. Numerical results show substantial improvements over existing approaches, even in strong nonlinear regimes. This work establishes a theoretical foundation for equilibrium statistical properties in strongly nonlinear systems. |
| title | The equilibrium distribution function for strongly nonlinear systems |
| topic | Statistical Mechanics Mathematical Physics Chaotic Dynamics Classical Physics |
| url | https://arxiv.org/abs/2507.07600 |