2025/04/23 by Teepanis Chachiyo, Chachiyo, Teepanis · 1 citation
Physics and Astronomy · #Classical Physics (physics.class-ph) #Cold Atom Physics and Bose-Einstein Condensates #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Mathematical Physics (math-ph) #Mechanical and Optical Resonators #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2504.16816
openalex publication_date 2025/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
Pendulum-like dynamics is a universal motif across many areas of physics, underlying systems ranging from classical nonlinear oscillators to superconducting qubits and cold-atom tunneling platforms. Here we present an exact frequency-domain formulation of the pendulum equation that applies uniformly across oscillatory, separatrix, and rotational regimes. The resulting spectral representation reveals a previously hidden unification: all regimes share the same analytic spectral structure and characteristic frequency scale. We discover that all regimes arise from a single universal spectral kernel, with parity selection distinguishing the periodic motions and the separatrix representing their discrete-to-continuum limit. Regime changes thus correspond to symmetry-driven reorganizations in frequency space rather than changes in the underlying spectral structure, with the stopping trajectory representing the continuum limit reached without system-size scaling. The spectral structure can be derived via a spectral discretization approach starting from the separatrix solution, without relying on the classical Jacobi elliptic formulation. Beyond providing closed-form solutions, the framework reveals a transparent spectral structure underlying a broad class of classical and quantum pendulum-like systems.