An Effective Scaling Framework for Non-Adiabatic Mode Dynamics
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910231531880448 |
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| author | Tishin, A. M. |
| author_facet | Tishin, A. M. |
| contents | This study proposes an effective theoretical framework for non-adiabatic parametric excitation in structured media, incorporating a nonlinear frequency regulator U as a stabilizing mechanism. We introduce the non-adiabaticity parameter as a time-local diagnostic for driven non-stationary systems and analyze its competition with nonlinear spectral detuning through the scaling ratio. The principal physical result is that strongly nonlinear oscillatory systems can exhibit saturation of non-adiabatic parametric amplification: when the nonlinear regulator becomes sufficiently strong, exponential mode growth is dynamically suppressed and the excitation evolves toward a bounded low-occupancy regime. Using numerical verification in an expanded 100-level bosonic Fock basis, we demonstrate a crossover from hyperbolic amplification dynamics toward an effectively bounded response associated with spectral blockade and suppression of higher-order mode occupation. These results suggest that nonlinear spectral stabilization may represent a general mechanism for finite-amplitude non-adiabatic dynamics in driven structured media. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_13376 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Effective Scaling Framework for Non-Adiabatic Mode Dynamics Tishin, A. M. Mesoscale and Nanoscale Physics This study proposes an effective theoretical framework for non-adiabatic parametric excitation in structured media, incorporating a nonlinear frequency regulator U as a stabilizing mechanism. We introduce the non-adiabaticity parameter as a time-local diagnostic for driven non-stationary systems and analyze its competition with nonlinear spectral detuning through the scaling ratio. The principal physical result is that strongly nonlinear oscillatory systems can exhibit saturation of non-adiabatic parametric amplification: when the nonlinear regulator becomes sufficiently strong, exponential mode growth is dynamically suppressed and the excitation evolves toward a bounded low-occupancy regime. Using numerical verification in an expanded 100-level bosonic Fock basis, we demonstrate a crossover from hyperbolic amplification dynamics toward an effectively bounded response associated with spectral blockade and suppression of higher-order mode occupation. These results suggest that nonlinear spectral stabilization may represent a general mechanism for finite-amplitude non-adiabatic dynamics in driven structured media. |
| title | An Effective Scaling Framework for Non-Adiabatic Mode Dynamics |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2605.13376 |