发表机构
Erzurum Technical University; University of Hradec Králové; California State University, Fresno（埃尔祖鲁姆理工大学; 赫拉德茨-克拉洛韦大学; 加州州立大学弗雷斯诺分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究建立曲率-规范框架，推导螺旋双体系统的精确约化哈密顿量，利用几何调控实现多类动力学行为，为弯曲平台的局域化与谱结构控制提供通用途径。
AI 中文摘要
几何正日益被视为一种主动的物理资源，能够在传统外部控制机制之外调控量子系统的行为。本文中，我们建立了一种曲率-规范框架，其中嵌入流形的几何可作为经典轨迹与量子态的可调控制场。通过推导受限在螺旋面上的双体系统的精确约化哈密顿量，我们证明曲率会修正有效动力学结构，而投影规范场则重构守恒动量图景。这种几何重整化可实现不同动力学 regime 间的可控跃迁，包括有界相空间结构、零能量局域化、对称破缺分岔及临界软模行为。对依赖几何的有效势进行量子化后，会呈现对应的谱重构，其中简谐束缚在局域化阈值处演化为四次临界态。这些结果表明，工程化几何是控制弯曲量子、电子、光子及合成平台中局域化与谱结构的通用途径，其中形变本身成为功能性自由度，而非被动约束。
英文摘要
We study the dynamics and localization of two oppositely charged particles constrained to a helicoidal manifold in a uniform magnetic field. The embedding-induced metric and the pullback of the ambient electromagnetic gauge potential, together with restriction to the reflection-symmetric longitudinal rest frame, lead to an exact reduction of the relative dynamics to a one-dimensional Hamiltonian with a coordinate-dependent kinetic term and a gauge-shifted momentum. We analyze the corresponding effective potential, turning points, and classically allowed regions, and determine how the geometric and magnetic parameters modify the bounded relative motion. For a regularized attractive interaction, we derive the zero-energy condition for localization around the symmetric configuration and obtain the local stiffness governing its stability. When this stiffness changes sign while the quartic coefficient remains positive, the symmetric minimum undergoes a pitchfork-type bifurcation to two symmetry-related finite-separation minima of the relative coordinate. Canonical quantization of the reduced Hamiltonian then gives the low-energy spectrum in the harmonic approximation and the associated zero-energy localization thresholds. At the critical stiffness, the quadratic term vanishes and the quartic term provides the leading contribution to the local low-energy scaling. These results establish how helicoidal geometry and magnetic coupling modify the relative localization and low-energy spectral properties of the two-particle system.
Comments10 pages, 4 figures
