克莱因佯谬的意外之处
Surprises of Klein paradox
- Azerbaijan State Oil and Industry University（阿塞拜疆国立石油工业大学）
- Moscow Institute of Physics and Technology（莫斯科物理技术学院）
- NRC ”Kurchatov Institute”（库尔恰托夫国家研究中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究1+1维狄拉克费米子在特定电场势能下的电流极限期望值，发现瞬时开启满足0<V<2m的势能时总电流为零，仅V>2m时非零，还分析了无限势垒与深势阱情形，关联施温格效应和超临界核衰变。
AI中文摘要：
我们考虑在背景电场中的质量为$m$的1+1维二次量子化狄拉克费米子，该理论可模拟如下情形：两个平行电容器内的电场$E$方向相反，其中一个电容器的势能差为$V_0 > 2m$，另一个为$V+V_0$，且$0<V<2m$。根据对施温格效应的一般物理理解，每个电容器单独都会产生粒子对，且会出现方向相反的电流，二者并不相等，总电流不会消失。本文表明这一观察过于简单：若以瞬时开启上述满足$0<V<2m$的势能形式，当$t\to +\infty$时，电流算符的极限期望值实际为零，仅当$V>2m$时才会得到非零电流。我们还考虑了无限势垒和深势阱$V_0>2m$存在下的同一理论，证明在高斯近似下，该势能中电流的极限期望值为零，并讨论了这些观测结果与施温格效应及超临界核衰变的关系。
英文摘要：
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 $0<V<2m$. According to general physical understanding of the Schwinger effect, each capacitor separately will create pairs and there will be oppositely directed currents, which will not be equal to each other. The total current will not vanish. In this paper we show that this is too naive an observation: the limiting expectation value of the current operator, as $t\to +\infty$, is actually zero, if the above form of the potential with $0<V<2m$ is instantaneously turned on. The non-vanishing current is obtained only if $V>2m$. 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.
