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arXiv 1507.07005hep-thmath-phmath.MP
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Schwinger效应中的多维量子隧穿

Multidimensional quantum tunneling in the Schwinger effect

Cesim K. Dumlu

摘要:

我们研究了Schwinger效应,其中具有时空轮廓的外场通过多维量子隧穿产生电子-正电子对。我们的处理是基于迹公式的QED有效作用量,其虚部表示的总和超过复杂的世界线解决方案。世界线是多周期的,运动的周期共同取决于空间和时间不均匀性的强度。我们认为,经典的行动,导致正确的隧道振幅必须考虑到整个周期,$\tilde{T}$和第一个基本周期,$T_1$。鉴于这一论点,我们调查对生产指数阻尼正弦字段,并发现,多周期轨迹的初始动量位于抛物线曲线,使在每个曲线上的比例$\tilde{T}/T_1$保持一致。使用这些轨迹的隧穿振幅的评估表明,真空衰减率减少了一个数量级,相对于纯粹的时间依赖的情况下,由于存在的磁场。

英文摘要:

We study the Schwinger effect, in which the external field having a spatiotemporal profile creates electron-positron pairs via multidimensional quantum tunneling. Our treatment is based on the trace formula for the QED effective action, whose imaginary part is represented by a sum over complex worldline solutions. The worldlines are multiperiodic, and the periods of motion collectively depend on the strength of spatial and temporal inhomogeneity. We argue that the classical action that leads to the correct tunneling amplitude must take into account both the full period, $\tilde{T}$ and the first fundamental period, $T_1$. In view of this argument we investigate pair production in an exponentially damped sinusoidal field and find that the initial momenta for multiperiodic trajectories lie on parabolic curves, such that on each curve the ratio $\tilde{T}/T_1$ stays uniform. Evaluation of the tunneling amplitude using these trajectories shows that vacuum decay rate is reduced by an order of magnitude, with respect to the purely time-dependent case, due to the presence of magnetic field.

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