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Updated: Jun 27, 2026
11:33
All-electronic Nanosecond-resolved Scanning Tunneling Microscopy: Facilitating the Investigation of Single Dopant Charge Dynamics
Published on: January 19, 2018
Superluminal Tunneling and the Sauter-Schwinger Effect
1Department of Chemistry and Chemical Biology, McMaster University, Hamilton, ON L8S 4M1, Canada.
Entropy (Basel, Switzerland)
|June 26, 2026
Summary
Relativistic electron wavepackets exhibit superluminal tunneling, but vacuum electron-positron pair production complicates signaling. This study derives densities for pair production, clarifying its role in quantum tunneling phenomena.
Area of Science:
- Quantum Field Theory
- Relativistic Quantum Mechanics
- High-Energy Physics
Background:
- Previous 1+1-dimensional Dirac wavepacket calculations indicated superluminal tunneling for relativistic electrons.
- Adapting superluminal tunneling for signaling was limited by low tunneling probability, resulting in subluminal signaling.
- The barriers used in prior studies were supercritical concerning the Sauter-Schwinger effect, implying vacuum pair production.
Purpose of the Study:
- To investigate the impact of spontaneous electron-positron production on relativistic electron wavepacket tunneling.
- To derive and analyze formulas for electron and positron densities in supercritical barriers.
- To compare numerical results with a semiclassical resonance model for pair production.
Main Methods:
- Derivation of compact formulas for electron and positron densities, considering an initial electron and vacuum pair production.
- Application of these formulas to a fourth-order super-Gaussian barrier exhibiting superluminal electron tunneling.
- Numerical calculation of densities at various times and comparison with a semiclassical resonance model.
Main Results:
- The evolved electron wavepacket contribution enhances the vacuum-produced electron density.
- Pauli blocking reduces positron density due to the negative-energy component of the propagated electron.
- The semiclassical model accurately reproduces the numerical growth of the pair yield and clarifies resonance phenomena.
Conclusions:
- Spontaneous electron-positron production is a crucial factor in supercritical barrier tunneling of relativistic electrons.
- The interplay between wavepacket propagation and vacuum effects modifies particle densities.
- The study provides a foundation for extending these calculations to 1+3 dimensions.
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