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Main Authors: Feng, Tinglong, Moes, Jesse, Prokopec, Tomislav
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2512.14809
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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