凝聚态物理中的一个反问题
An inverse problem from condense matter physics
摘要：
本文研究了由非线性Gross-Pitaevskii方程中涡旋偶极子的轨迹重构弱各向异性背景势的问题。在首阶，涡旋偶极子的动力学由一个哈密顿系统给出。如果背景势足够平滑和平坦，则可以使用来自边界和透镜刚性问题的想法来重建背景。我们证明了重建是唯一的，推导出一个近似的重建公式，并给出数值例子。
英文摘要：
We consider the problem of reconstructing the features of a weak anisotropic background potential by the trajectories of vortex dipoles in a nonlinear Gross-Pitaevskii equation. At leading order, the dynamics of vortex dipoles are given by a Hamiltonian system. If the background potential is sufficiently smooth and flat, the background can be reconstructed using ideas from the boundary and the lens rigidity problems. We prove that reconstructions are unique, derive an approximate reconstruction formula, and present numerical examples.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
