Hubbard-like Interactions and Emergent Dynamical Regimes Between Modulational Instability and Self-Trapping
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| Format: | Preprint |
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2025
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| author | Bezerra Jr., L. J. R. Dias, W. S. |
| author_facet | Bezerra Jr., L. J. R. Dias, W. S. |
| contents | We investigate the modulational instability of uniform wave packets governed by a discrete third-order nonlinear Schrödinger equation in finite square lattices, modeling light propagation in two-dimensional nonlinear waveguide arrays. We analyze how initially stable uniform distributions evolve into self-trapped (localized) regimes and the influence of a refractive index detuning selectively applied along the diagonal waveguides on this transition. This detuning effectively emulates the effect of on-site Hubbard-like interactions $U$ in photonic analogs of interacting particles in a one-dimensional lattice. While for $U = 0$ the system exhibits the known direct transition from stable uniform states to asymptotically localized profiles, we show that $U > 0$ induces an emergence of intermediate dynamical regimes. These regimes include coherent breathing modes that can be either confined along diagonal or off-diagonal waveguides, as well as chaotic-like propagation patterns. At higher nonlinearities, we identify distinct self-trapped regimes characterized by diagonal or off-diagonal localized modes, depending on the strength of $U$. The critical nonlinear strengths separating the existing regimes are shown in the phase diagram, underscoring the competing trends imposed by the Hubbard-like interaction on the optical field. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_08781 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hubbard-like Interactions and Emergent Dynamical Regimes Between Modulational Instability and Self-Trapping Bezerra Jr., L. J. R. Dias, W. S. Pattern Formation and Solitons Other Condensed Matter Quantum Physics We investigate the modulational instability of uniform wave packets governed by a discrete third-order nonlinear Schrödinger equation in finite square lattices, modeling light propagation in two-dimensional nonlinear waveguide arrays. We analyze how initially stable uniform distributions evolve into self-trapped (localized) regimes and the influence of a refractive index detuning selectively applied along the diagonal waveguides on this transition. This detuning effectively emulates the effect of on-site Hubbard-like interactions $U$ in photonic analogs of interacting particles in a one-dimensional lattice. While for $U = 0$ the system exhibits the known direct transition from stable uniform states to asymptotically localized profiles, we show that $U > 0$ induces an emergence of intermediate dynamical regimes. These regimes include coherent breathing modes that can be either confined along diagonal or off-diagonal waveguides, as well as chaotic-like propagation patterns. At higher nonlinearities, we identify distinct self-trapped regimes characterized by diagonal or off-diagonal localized modes, depending on the strength of $U$. The critical nonlinear strengths separating the existing regimes are shown in the phase diagram, underscoring the competing trends imposed by the Hubbard-like interaction on the optical field. |
| title | Hubbard-like Interactions and Emergent Dynamical Regimes Between Modulational Instability and Self-Trapping |
| topic | Pattern Formation and Solitons Other Condensed Matter Quantum Physics |
| url | https://arxiv.org/abs/2510.08781 |