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Klein paradox for bosons, wave packets and negative tunnelling times
X Gutiérrez de la Cal1, M Alkhateeb2, M Pons3
1Departamento de Química-Física, Universidad del País Vasco, UPV/EHU, Leioa, Spain.
Scientific Reports
|November 6, 2020
Summary
The Klein paradox reveals that Klein-Gordon bosons can cross supercritical barriers acausally. Causal solutions are problematic for rectangular barriers but resolved for smooth ones, with enhanced pair production.
Area of Science:
- Quantum mechanics
- Relativistic quantum mechanics
Background:
- The Klein paradox describes unusual phenomena for relativistic particles encountering potential barriers.
- Investigating acausal transmission and negative time-delay in quantum systems is crucial for understanding relativistic effects.
Purpose of the Study:
- To analyze a lesser-known aspect of the Klein paradox concerning Klein-Gordon bosons and supercritical barriers.
- To investigate the causality of particle transmission and the behavior of causal solutions for different barrier shapes.
Main Methods:
- Analysis of the Klein-Gordon equation for a boson encountering a supercritical rectangular barrier.
- Examination of the transmission mechanism for acausality and time-delay.
- Investigation of causal solutions and their relation to divergent series.
- Comparison with results for a smooth barrier.
Main Results:
- Klein-Gordon bosons exhibit acausal transmission across supercritical rectangular barriers with negative time-delay.
- Attempts to construct a causal solution for the rectangular barrier fail, linked to a divergent multiple-reflections series.
- For a smooth barrier, the causality issue is resolved, and pair production is enhanced but finite.
Conclusions:
- Acausal transmission and negative time-delay are key features of the Klein paradox for supercritical barriers.
- Barrier shape critically influences the causality of relativistic boson transmission.
- Smooth barriers offer a physically realistic scenario where acausal effects are mitigated, with controlled pair production.
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