Relativistic tunneling through opaque barriers

2011/02/28 by Stefano De Leo, Vinicius Leonardi, Vinícius Leonardi · 1 citation
Mathematics · Physics and Astronomy · #Atomic and Molecular Physics #Cold Atom Physics and Bose-Einstein Condensates #Limit (mathematics) #Mathematical analysis #Mathematics #Opacity #Phase (matter) #Physics #Quantum mechanics #Quantum optics and atomic interactions #Quantum tunnelling #Upper and lower bounds #hep-th #quant-ph

paper · pdf · doi:10.1103/physreva.83.022111

published as Physical Review A 83, (2011) 022111-5 · 11 pages, 3 figures

openalex publication_date 2011/02/28 · arxiv created 2011/03/14 · arxiv updated 2015/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We propose an analytical study of relativistic tunneling through opaque barriers. We obtain a closed formula for the phase time. This formula is in excellent agreement with the numerical simulations and corrects the standard formula obtained by the stationary phase method. An important result is found when the upper limit of the incoming energy distribution coincides with the upper limit of the tunneling zone. In this case, the phase time is proportional to the barrier width.

Citations

• Above barrier Dirac multiple scattering and resonances
• Tunneling time, the Hartman effect, and superluminality: A proposed resolution of an old paradox
• Barrier paradox in the Klein zone
• Tunneling of a Wave Packet
• Unified time analysis of photon and particle tunnelling
• Lower Limit for the Energy Derivative of the Scattering Phase Shift
• Planar Dirac diffusion
• TIME AS A QUANTUM OBSERVABLE

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• Dirac solutions for quaternionic potentials