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| Format: | Preprint |
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2026
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| Online-Zugang: | https://arxiv.org/abs/2605.28875 |
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| _version_ | 1866913171920388096 |
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| author | Hernández, Kevin Maamache, Mustapha |
| author_facet | Hernández, Kevin Maamache, Mustapha |
| contents | We develop a systematic framework for the quantum and thermal properties of a Klein-Gordon scalar field subject to an inverted harmonic potential $-{1\over2} m^2ω^2 x^2$. Starting from a non-Hermitian momentum substitution $P \to P - mωx$, we employ a symplectic phase-space rotation $V = \exp\!\left[-\tfracπ{8}(xp+px)\right]$ to map the system onto an analytically tractable effective harmonic oscillator evaluated at $xe^{iπ/4}$. This allows us to define a well-regulated partition function $Z(β,ω,m)$ and derive closed-form expressions for the free energy, entropy, and thermal correlation functions. We then apply this framework to three physical settings: (i) scalar field fluctuations during cosmological inflation, (ii) quantum fields near black-hole horizons, and (iii) order-parameter dynamics near second-order phase transitions in condensed matter. Our results unify previously scattered results in the literature and provide new predictions for the finite-temperature spectral density and entanglement entropy of unstable quantum systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28875 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum and Thermal Properties of the Klein-Gordon Inverted Harmonic Oscillator with Physical Applications Hernández, Kevin Maamache, Mustapha Quantum Physics We develop a systematic framework for the quantum and thermal properties of a Klein-Gordon scalar field subject to an inverted harmonic potential $-{1\over2} m^2ω^2 x^2$. Starting from a non-Hermitian momentum substitution $P \to P - mωx$, we employ a symplectic phase-space rotation $V = \exp\!\left[-\tfracπ{8}(xp+px)\right]$ to map the system onto an analytically tractable effective harmonic oscillator evaluated at $xe^{iπ/4}$. This allows us to define a well-regulated partition function $Z(β,ω,m)$ and derive closed-form expressions for the free energy, entropy, and thermal correlation functions. We then apply this framework to three physical settings: (i) scalar field fluctuations during cosmological inflation, (ii) quantum fields near black-hole horizons, and (iii) order-parameter dynamics near second-order phase transitions in condensed matter. Our results unify previously scattered results in the literature and provide new predictions for the finite-temperature spectral density and entanglement entropy of unstable quantum systems. |
| title | Quantum and Thermal Properties of the Klein-Gordon Inverted Harmonic Oscillator with Physical Applications |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2605.28875 |