Bogoliubov-de Gennes谱、切连科夫辐射与含三阶色散的孤子反冲：光学类比视界的基础
Bogoliubov-de Gennes spectrum, Cherenkov radiation and recoil of solitons with third-order dispersion underlying optical analogue horizons
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中文总结 AI 辅助
本研究计算三阶色散下非线性薛定谔孤子的谱、切连科夫辐射及反冲，揭示虚假模与稳态谱结构，并建立无需热假设的辐射与反冲模型，适用于克尔介质光学类比视界。
中文摘要 AI 辅助
三阶色散将非线性薛定谔方程的孤子（该方程是光纤中事件视界的光学类比的基础）转变为弱辐射的孤立波。我们在不假设热辐射定律的情况下计算了其三个性质。首先，线性化（Bogoliubov-de Gennes）问题必须围绕色散方程的稳态提出：围绕可积轮廓线性化会产生一个复四重态，该四重态在网格和盒子中收敛，随色散强度的平方根增长，并且是虚假的。在周期网格上，围绕稳态，零模扇区由两个大小为二的若尔当块组成，并且在工作点处谱是实的，包括共振分支的负能量盒子模。其次，我们通过孤子后方辐射的通量，在八个数量级上测量了绝热制备孤子的稳态切连科夫发射。辐射在漂移孤子的参考系中相位匹配，一阶速率比测量值低29至45倍。通过局部孤子的缩放色散系数表示，测量速率描述了三个振幅的发射孤子；利用范数和动量平衡，且没有进一步拟合参数，它再现了它们的反冲和损失率的缓慢衰减；在弱色散下，发射孤子的损失是其发射失配的脱落。第三，渐近通道的普查表明，长波长上游发射要求孤子的化学势（因漂移孤子的共动参考系多普勒频移而降低）位于分析频带内，这限制了孤子振幅。在流动的运动学模型中，表面引力具有封闭形式；热关系及其上构建的纠缠是该模型的强加输入。该构造适用于无拉曼克尔介质。
英文摘要
Third-order dispersion turns the soliton of the nonlinear Schrödinger equation, which underlies optical analogues of event horizons in fibers, into a weakly radiating solitary wave. We compute three of its properties without assuming a thermal emission law. First, the linearized (Bogoliubov-de Gennes) problem must be posed about the stationary state of the dispersive equation: linearizing about the integrable profile produces a complex quartet that is converged in grid and box, grows as the square root of the dispersion strength and is spurious. About the stationary state, on a periodic grid, the zero-mode sector consists of two Jordan blocks of size two and the spectrum is real at the operating point, including negative-energy box modes of the resonant branch. Second, we measure the steady Cherenkov emission of adiabatically prepared solitons from the flux of the radiation behind them, over eight decades. The radiation is phase-matched in the frame of the drifting soliton, and the first-order rate falls short of the measured one by factors of 29 to 45. Expressed through a scaled dispersion coefficient of the local soliton, the measured rate describes launched solitons of three amplitudes; with norm and momentum balance, and no further fitted parameter, it reproduces their recoil and the slow decay of their loss rate; at weak dispersion the loss of a launched soliton is the shedding of its launch mismatch. Third, a census of the asymptotic channels shows that long-wavelength upstream emission requires the chemical potential of the soliton, lowered by the comoving-frame Doppler shift of a drifting soliton, to lie inside the analysis band, which bounds the soliton amplitude. In a kinematic model of the flow the surface gravity has a closed form; the thermal relation and the entanglement built on it are imposed inputs of that model. The construction applies to Raman-free Kerr media.
发表机构
- Istanbul Okan University（伊斯坦布尔奥坎大学）
- Pamukkale University（棉花堡大学）
机构由 AI 辅助整理，请以论文原文为准。
