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arXiv · 2312.08180

On periodic solutions and attractors for the Maxwell--Bloch equations

Alexander Komech
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Abstract

We consider the Maxwell-Bloch system which is a finite-dimensional approximation of the coupled nonlinear Maxwell-Schr\"odinger equations. The approximation consists of one-mode Maxwell field coupled to two-level molecule. We construct time-periodic solutions to the factordynamics which is due to the symmetry gauge group. For the corresponding solutions to the Maxwell--Bloch system, the Maxwell field, current and the population inversion are time-periodic, while the wave function acquires a unit factor in the period. The proofs rely on high-amplitude asymptotics of the Maxwell field and a suitable extension of the Lefschetz theorem on fixed points and the Euler characteristic for noncompact manifolds. We also prove the existence of the global compact attractor.

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Alexander Komech. 2023-12-13. On periodic solutions and attractors for the Maxwell--Bloch equations. https://arxiv.org/abs/2312.08180

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