Semi-Analytical Engineering of Strongly Driven Nonlinear Systems Beyond Floquet and Perturbation Theory

• URL: http://arxiv.org/abs/2502.17200v2
• Date: Mon, 14 Apr 2025 01:10:44 GMT
• Title: Semi-Analytical Engineering of Strongly Driven Nonlinear Systems Beyond Floquet and Perturbation Theory
• Authors: Kento Taniguchi, Atsushi Noguchi, Takashi Oka,
• Abstract summary: We present a non-perturbative, semi-analytical framework for tailoring strongly driven nonlinear systems.<n>We extend the Floquet theory to nonlinear differential equations using the Harmonic Balance method.<n>We also establish a novel constrained optimization technique inspired by the Lagrange multiplier method.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Strongly driven nonlinear systems are frequently encountered in physics, yet their accurate control is generally challenging due to the intricate dynamics. In this work, we present a non-perturbative, semi-analytical framework for tailoring such systems. The key idea is heuristically extending the Floquet theory to nonlinear differential equations using the Harmonic Balance method. Additionally, we establish a novel constrained optimization technique inspired by the Lagrange multiplier method. This approach enables accurate engineering of effective potentials across a broader parameter space, surpassing the limitations of perturbative methods. Our method offers practical implementations in diverse experimental platforms, facilitating nonclassical state generation, versatile bosonic quantum simulations, and solving complex optimization problems across quantum and classical applications.

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