论文标题
Zitterbewegung和Klein-Tunneling现象，用于瞬态量子波
Zitterbewegung and Klein-tunneling phenomena for transient quantum waves
论文作者
论文摘要
我们通过使用具有点源初始条件的klein-gordon方程的精确解决方案来探索潜在步骤中相对论量子波的动力学。我们表明，在繁殖和克莱因隧道式方案中，Zitterbewegung效应在长期极限中表现为粒子密度的一系列量子节拍。我们证明了跳动现象的特征是Zitterbewegung频率，并且这些振荡的幅度衰减为$ t^{ - 3/2} $。我们表明，跳动效应也表现在量子快门设置中的自由klein-gordon和dirac方程中，这涉及截止量子状态的动力学。我们还找到了一个时间域，其中点源的粒子密度受主波的传播控制，在非偏爱系统中观察到的时间现象类似于时间现象的振荡模式。这些波前的相对位置用于研究klein-Tunnelning状态中量子波的时间延迟。我们表明，根据能源差，源和潜在步骤之间的$ {\ cal e} $，时间延迟可以为正，负或零。后一种情况对应于超级klein-tunneling配置，其中$ {\ cal e} $等于潜在步骤的一半。
We explore the dynamics of relativistic quantum waves in a potential step by using an exact solution to the Klein-Gordon equation with a point source initial condition. We show that in both the propagation, and Klein-tunneling regimes, the Zitterbewegung effect manifests itself as a series of quantum beats of the particle density in the long-time limit. We demonstrate that the beating phenomenon is characterized by the Zitterbewegung frequency, and that the amplitude of these oscillations decays as $t^{-3/2}$. We show that beating effect also manifests itself in the free Klein-Gordon and Dirac equations within a quantum shutter setup, which involve the dynamics of cut-off quantum states. We also find a time-domain where the particle density of the point source is governed by the propagation of a main wavefront, exhibiting an oscillating pattern similar to the diffraction in time phenomenon observed in non-relativistic systems. The relative positions of these wavefronts are used to investigate the time-delay of quantum waves in the Klein-tunneling regime. We show that, depending on the energy difference, ${\cal E}$, between the source and the potential step, the time-delay can be positive, negative or zero. The latter case corresponds to a super-Klein-tunneling configuration, where ${\cal E}$ equals to half the energy of the potential step.
