Time-Dependent Tunneling in the Thin-Barrier Limit
Abstract
The usual WKB analysis for quantum tunneling applies when the tunneling action is large, as it is for tall, wide potential barriers. In contrast we analyze tunneling when the action is small, as it is for tunneling across a tall, thin barrier. We develop a perturbative analysis where the control parameter is the inverse of the area under the potential barrier and apply our technique to several examples in 1+1 dimensions. In resonant situations for bound particles we find that the tunneling probability grows with time as ∝ t2, while in non-resonant situations it grows linearly with time. We evaluate not only the tunneling probability but also the time-dependent tunneling wavefunction for a particle that escapes to infinity, {\it i.e.} from a quasi-bound state to the continuum.
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BibTeX
@misc{vachaspati2026timedependent,
title = {{Time-Dependent Tunneling in the Thin-Barrier Limit}},
author = {Tanmay Vachaspati and Frank Wilczek and Zara Yu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.24032},
eprint = {2608.24032},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.24032},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Time-Dependent Tunneling in the Thin-Barrier Limit
AU - Tanmay Vachaspati
AU - Frank Wilczek
AU - Zara Yu
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2608.24032
UR - https://arxiv.org/abs/2608.24032
AB - The usual WKB analysis for quantum tunneling applies when the tunneling action is large, as it is for tall, wide potential barriers. In contrast we analyze tunneling when the action is small, as it is for tunneling across a tall, thin barrier. We develop a perturbative analysis where the control parameter is the inverse of the area under the potential barrier and apply our technique to several examples in 1+1 dimensions. In resonant situations for bound particles we find that the tunneling probability grows with time as ∝ t^2, while in non-resonant situations it grows linearly with time. We evaluate not only the tunneling probability but also the time-dependent tunneling wavefunction for a particle that escapes to infinity, {\it i.e.} from a quasi-bound state to the continuum.
ER -