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arXiv · 2609.02370

Surprises of Klein paradox

T. R. Ahmadov·E. T. Akhmedov·V. I. Lapushkin
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Abstract

We consider second quantized $1+1$ dimensional Dirac fermions with mass $m$ in background electric fields. This theory mimics the following situations. We consider two parallel capacitors with opposite directions of the electric field $E$ in them. The potential energy difference in one of them is equal to $V_0 > 2m$ and in the other to $V+V_0$, with $0 2m$. We also consider the same theory in the presence of the infinite wall and a deep well $V_0>2m$. We show that in such a potential the limiting expectation value of the current is zero in the Gaussian approximation. We discuss the relation of these observations to the Schwinger effet and to the decay of supercritical nuclei.

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T. R. Ahmadov, E. T. Akhmedov, V. I. Lapushkin. 2026-09-02. Surprises of Klein paradox. https://arxiv.org/abs/2609.02370

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