Discrete Bound States in a Toy Model for Weak Turbulence and Implications for the Invariant Measure
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915576552620032 |
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| author | Marzuola, Jeremy L. Mattingly, Jonathan C. |
| author_facet | Marzuola, Jeremy L. Mattingly, Jonathan C. |
| contents | A model Hamiltonian dynamical system has been derived to study frequency cascades in the cubic defocusing nonlinear Schrödinger equation on the torus. Here, we explore the framework for exploring a canonical ensemble formulation of the dynamics through classification of energy minimizers for fixed mass and characterizing the invariant measure in a neighborhood of those minimizers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_22090 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Discrete Bound States in a Toy Model for Weak Turbulence and Implications for the Invariant Measure Marzuola, Jeremy L. Mattingly, Jonathan C. Classical Analysis and ODEs Analysis of PDEs 35Q55 A model Hamiltonian dynamical system has been derived to study frequency cascades in the cubic defocusing nonlinear Schrödinger equation on the torus. Here, we explore the framework for exploring a canonical ensemble formulation of the dynamics through classification of energy minimizers for fixed mass and characterizing the invariant measure in a neighborhood of those minimizers. |
| title | Discrete Bound States in a Toy Model for Weak Turbulence and Implications for the Invariant Measure |
| topic | Classical Analysis and ODEs Analysis of PDEs 35Q55 |
| url | https://arxiv.org/abs/2510.22090 |