Semi-classical Imprint of Horizon Induced Instability
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910229353988096 |
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| author | Chakraborty, Arnab Islam, Onirban Momen, Arshad |
| author_facet | Chakraborty, Arnab Islam, Onirban Momen, Arshad |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_17586 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Semi-classical Imprint of Horizon Induced Instability Chakraborty, Arnab Islam, Onirban Momen, Arshad High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics 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. |
| title | Semi-classical Imprint of Horizon Induced Instability |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2605.17586 |