Semi-classical Imprint of Horizon Induced Instability

Arnab Chakraborty; Onirban Islam; Arshad Momen

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arXiv · 2605.17586

Semi-classical Imprint of Horizon Induced Instability

Arnab Chakraborty·Onirban Islam·Arshad Momen

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Abstract

We consider an inverted harmonic oscillator in the space $L^{2} (\mathbb{S})$ of square-integrable functions on the circle $\mathbb{S}$ and compute its density of states employing the stationary phase approximation. Our computation is based on an oscillatory integral representation of the Schwartz kernel of the time-evolution operator. This demonstrates thermalisation as a semi-classical manifestation of the classical Lyapunov instability -- reported earlier in [Phys. Rev. D 102, 044006; Phys. Rev. D 102, 124047] using heuristic analytic continuation. Our spectral analysis of the Hamiltonian points out and closes the conceptual and mathematical gaps in the preceding literature.

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Arnab Chakraborty, Onirban Islam, Arshad Momen. 2026-05-17. Semi-classical Imprint of Horizon Induced Instability. https://arxiv.org/abs/2605.17586

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