On Thermalization in A Nonlinear Variant of the Discrete NLS Equation
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| Format: | Preprint |
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2026
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| _version_ | 1866915805299474432 |
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| author | Kati, Yagmur Maluckov, Aleksandra Mancic, Ana Kevrekidis, Panayotis |
| author_facet | Kati, Yagmur Maluckov, Aleksandra Mancic, Ana Kevrekidis, Panayotis |
| contents | We study the thermalization properties of a fully nonlinear lattice model originally derived from the two-dimensional cubic defocusing nonlinear Schrödinger equation (NLS) using analytical and numerical methods. Our analysis reveals both ergodic and nonergodic regimes; importantly, we find broad parameter ranges where the dynamics is ergodic even though it lies outside the Gibbsian parameter regime (for both $D=0.25$ and $D=2$), and a higher-energy range where ergodicity breaks down. We observe that in a certain range of parameters, the system requires non-standard statistical descriptions, indicating a breakdown of conventional thermalization. We examine the influence of the nonlinear dispersion parameter $D$ on the system's behavior, showing that increasing $D$ enhances fluctuations and speeds up the crossover of $q(T)$ toward the $\sim 1/T$ scaling. By analyzing excursion times, probability density functions, and localization patterns, we characterize transitions between ergodic and nonergodic behavior. In long-time numerical simulations within the non-ergodic regime for $D>1$, stable localization over two sites is observed, while $D<1$ favors single-site localization in the high energy density regimes. Our results provide insights into the interplay between thermalization, localization, and non-standard statistical behavior in genuinely nonlinear systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_13472 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Thermalization in A Nonlinear Variant of the Discrete NLS Equation Kati, Yagmur Maluckov, Aleksandra Mancic, Ana Kevrekidis, Panayotis Statistical Mechanics Chaotic Dynamics Pattern Formation and Solitons We study the thermalization properties of a fully nonlinear lattice model originally derived from the two-dimensional cubic defocusing nonlinear Schrödinger equation (NLS) using analytical and numerical methods. Our analysis reveals both ergodic and nonergodic regimes; importantly, we find broad parameter ranges where the dynamics is ergodic even though it lies outside the Gibbsian parameter regime (for both $D=0.25$ and $D=2$), and a higher-energy range where ergodicity breaks down. We observe that in a certain range of parameters, the system requires non-standard statistical descriptions, indicating a breakdown of conventional thermalization. We examine the influence of the nonlinear dispersion parameter $D$ on the system's behavior, showing that increasing $D$ enhances fluctuations and speeds up the crossover of $q(T)$ toward the $\sim 1/T$ scaling. By analyzing excursion times, probability density functions, and localization patterns, we characterize transitions between ergodic and nonergodic behavior. In long-time numerical simulations within the non-ergodic regime for $D>1$, stable localization over two sites is observed, while $D<1$ favors single-site localization in the high energy density regimes. Our results provide insights into the interplay between thermalization, localization, and non-standard statistical behavior in genuinely nonlinear systems. |
| title | On Thermalization in A Nonlinear Variant of the Discrete NLS Equation |
| topic | Statistical Mechanics Chaotic Dynamics Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2601.13472 |