Year: 2025
Type: preprint
Abstract: We study the quantum dynamics of a particle confined in a twisted tube with a linearly varying cross section. By relating a general linear transformation matrix to the system's Hamiltonian, we use an extended thin-layer method to derive an effective Hamiltonian for tangential motion under mild and general linear transformations. Explicit forms are provided for three fundamental transformations: rotation, scaling, and shearing. Rotation introduces a gauge field coupled to angular momentum, while scaling and shearing produce geometric potentials that lift degeneracies in non-circular cross sections. In square cross sections, these transformations cause energy splittings among formerly degenerate states, whereas circular cross sections retain degeneracy. Through an example combining rotation and squeezing, we analyze state evolution and compute the quantum geometric tensor to quantify geometric response. Our results demonstrate how geometric transformations can tailor quantum states and suggest that circular waveguides are more robust against mode mixing.
Source: arXiv (Cornell University)
Authors: Liang, Guo-Hua, Mei, Ai-Guo, Lai, Men-Yun, Xu, Shu-Sheng
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416683628
Cites:
Cited by:
Related to: