Curvature as a control field in helicoidal two-body systems

• URL: http://arxiv.org/abs/2608.02659v2
• Date: Thu, 06 Aug 2026 14:04:33 GMT
• Title: Curvature as a control field in helicoidal two-body systems
• Abstract summary: We develop a curvature--gauge framework in which the geometry of an embedded manifold acts as a tunable control parameter.<n>We show that curvature modifies the effective kinetic structure, while the projected gauge field reshapes the conserved momentum landscape.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Geometry is increasingly recognized as an active physical resource capable of modifying the behavior of dynamical systems beyond conventional external control mechanisms. Here, we develop a curvature--gauge framework in which the geometry of an embedded manifold acts as a tunable control parameter for classical trajectories and semiclassical states. By deriving an exact reduced Hamiltonian for a charged two-body system confined to a helicoidal surface, we show that curvature modifies the effective kinetic structure, while the projected gauge field reshapes the conserved momentum landscape. This geometric modification leads to controllable transitions between distinct dynamical regimes, including bounded phase-space structures, zero-energy localization, symmetry-breaking bifurcations, and critical soft-mode behavior. A semiclassical analysis of the geometry-dependent effective potential reveals a spectral reconstruction in which harmonic confinement changes into quartic critical behavior at the localization threshold. These results establish engineered geometry as a route for controlling localization, dynamical stability, and spectral organization in curved classical and semiclassical systems, where deformation itself becomes a functional degree of freedom rather than a passive constraint.

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