Universal Ladder Structure Across Scales: From Quantum to Black Hole Physics

• URL: http://arxiv.org/abs/2604.06249v1
• Date: Mon, 06 Apr 2026 18:29:56 GMT
• Title: Universal Ladder Structure Across Scales: From Quantum to Black Hole Physics
• Abstract summary: We present a unified symmetry-based framework that provides a litmus-test criterion'' to determine when a system admits a hierarchical ladder structure.<n>This approach uncovers a previously underappreciated connection to supersymmetric quantum mechanics and a deep commonality among diverse physical problems.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Second-order ordinary linear differential equations appear ubiquitously across physics, describing the behavior of systems from the quantum world of atoms to the classical world of gravitating bodies. We present a unified symmetry-based framework that provides a ``litmus-test criterion'' to determine when such a system admits a hierarchical ladder structure, and, whenever it does, explicitly constructs the ladder. This approach uncovers a previously underappreciated connection to supersymmetric quantum mechanics and a deep commonality among diverse physical problems. Applications to the quantum harmonic oscillator and dynamical tidal response of Kerr black holes are presented to illustrate the framework.

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