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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2512.14809 |
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| _version_ | 1866918251663982592 |
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| author | Feng, Tinglong Moes, Jesse Prokopec, Tomislav |
| author_facet | Feng, Tinglong Moes, Jesse Prokopec, Tomislav |
| contents | Metastable decay exhibits a familiar exponential regime bracketed by early-time deviations and late-time power-law tails. We adopt the real-time, flux-based definition of the decay rate in the spirit of Andreassen et al.\ direct method and present a complete analysis of one-dimensional quantum-mechanical resonance models. We show that the kernel admits a universal pole--plus--branch decomposition and use it to define two computable time scales: a dawn time, when a single resonant contribution starts dominating and exponential decay sets in, and a twilight time, when the branch-cut tail overtakes exponential decay. The latter can be expressed in closed form via the Lambert $W$ function, making its parametric dependence manifest without fitting. For square, modified square, and Pöschl--Teller barriers we obtain simple thick-barrier formulas, clarify the relation $ΓT = T_{\text{trans}}$ between the decay rate $Γ$, oscillation period $T$, and transmission probability $T_{\text{trans}}$, and indicate how our spectral picture can be naturally extended to quantum field theoretic vacuum decay. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14809 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dawn and Twilight Time in Quantum Tunneling Feng, Tinglong Moes, Jesse Prokopec, Tomislav Quantum Physics High Energy Physics - Theory Metastable decay exhibits a familiar exponential regime bracketed by early-time deviations and late-time power-law tails. We adopt the real-time, flux-based definition of the decay rate in the spirit of Andreassen et al.\ direct method and present a complete analysis of one-dimensional quantum-mechanical resonance models. We show that the kernel admits a universal pole--plus--branch decomposition and use it to define two computable time scales: a dawn time, when a single resonant contribution starts dominating and exponential decay sets in, and a twilight time, when the branch-cut tail overtakes exponential decay. The latter can be expressed in closed form via the Lambert $W$ function, making its parametric dependence manifest without fitting. For square, modified square, and Pöschl--Teller barriers we obtain simple thick-barrier formulas, clarify the relation $ΓT = T_{\text{trans}}$ between the decay rate $Γ$, oscillation period $T$, and transmission probability $T_{\text{trans}}$, and indicate how our spectral picture can be naturally extended to quantum field theoretic vacuum decay. |
| title | Dawn and Twilight Time in Quantum Tunneling |
| topic | Quantum Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2512.14809 |