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This study explores the mechanics of quantum tunneling as particles traverse from a brane to a bulk interface.

June 8, 2026Open Access

Paper XLI: Quantum Tunneling as Transient Bulk Excursion of the Focal Zone

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This study explores the mechanics of quantum tunneling as particles traverse from a brane to a bulk interface.
Examined the quantum tunneling process involving the escape through a barrier in the brane context.
Analyzed imaginary momentum and its implications for tunneling probabilities.
Evaluated the applicability of the Gamow factor in describing α decay physics.
Established that tunneling probability is dictated by the length of the excursion factor 2κd.
Resolved the Hartman effect, confirming traversal time is independent of barrier thickness as defined by coupling timescales.
Demonstrated the resonant tunneling condition aligns with bulk wave mechanics.

Abstract

Quantum tunneling is the transient excursion of a particle's focal zone into the 5D bulk, bypassing a barrier that exists on the brane but has no bulk counterpart. (1) Imaginary momentum p = iℏκ is literally bulk-directed momentum: the imaginary unit i is the 90◦rotation from brane to bulk on S7 (Paper IV). (2) The tunneling probability e−2κd is the probability of completing a bulk excursion of length κd. (3) The Hartman eect is resolved: the traversal time is set by brane-bulk coupling and decoupling timescales, both barrier-thickness independent. (4) Resonant tunneling is a bulk standing wave condition. (5) The Gamow factor G = R κ(r) dr for α decay is the total bulk path length to bypass the Coulomb barrier. The Geiger-Nuttall law (115 years of α decay data) is the bulk-path-length formula for the Coulomb potential. Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.

Paper XLI: Quantum Tunneling as Transient Bulk Excursion of the Focal Zone

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