Quick Navigation

Overview Topics Abstract Importance Paper Tools References Reactions Discussion Publication Related

Topics

Open Quantum Systems Decoherence Quantum Simulation Quantum State Preparation Representation Entanglement Theory Quantum Correlations

Rotation angles of a rotating disc as the holonomy of the Hopf fibration

arXiv
Authors: Takuya Matsumoto

Year

2025

Paper ID

16215

Status

Preprint

Abstract Read

~2 min

Abstract Words

121

Citations

N/A

Abstract

This article investigates a simple kinematical model of a disc (Disc B) rolling on the edge of a fixed disc (Disc A) to study the geometric nature of rotation. The total rotation angle Δ of Disc B after one cycle is decomposed into a dynamical phase Δd and a geometric phase Δg. The paper's main contribution is to demonstrate that this geometric phase can be essentially described as the U(1) holonomy of the Hopf fibration with the canonical connection. By using a Gauss map to represent the disc's motion as a curve on a two-sphere $S2$, the work connects the physical rotation to the underlying geometry of the Hopf fiber bundle S3 → S2 and clarifies the origin of the geometric phase.

Why This Paper Matters

  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
  • It adds a 2025 reference point for readers tracking recent quantum research.
  • This article investigates a simple kinematical model of a disc (Disc B) rolling on the edge of a fixed disc (Disc A) to study the geometric nature of rotation.

Paper Tools

Become a member to use research tools

Sign in to open papers, visit source links, share, cite, compare, copy DOI links, request category corrections, and build your reading list.

Become a member Sign in
Show Paper arXiv Publisher Share Cite This Paper Copy URL Compare Copy DOI Add to Reading List Category Correction Request

References & Citation Signals

[1] DOI https://doi.org/arXiv:2512.04481 [2] arXiv https://arxiv.org/abs/2512.04481 [3] Publisher https://arxiv.org/abs/2512.04481

Local Citation Graph (Related-Paper Links)

Current Paper #16215 #69027 Computational Superiority of No... #68993 Tomography of quantum states wi... #68981 Affine Filtering Measurements a... #68971 On solutions of the Schrödinger...

External citation index: OpenAlex citation signal

Community Reactions

Quick sentiment from readers on this paper.

Score: 0
Likes: 0 Dislikes: 0

Sign in to react to this paper.

Discussion & Reviews (Moderated)

Average Rating: 0.0 / 5 (0 ratings)

No written reviews yet.