Zitterbewegung and Klein-tunneling phenomena for transient quantum waves

• URL: http://arxiv.org/abs/2003.04417v1
• Date: Mon, 9 Mar 2020 21:27:02 GMT
• Title: Zitterbewegung and Klein-tunneling phenomena for transient quantum waves
• Authors: Fernando Nieto-Guadarrama and Jorge Villavicencio
• Abstract summary: We show that the Zitterbewegung effect manifests itself as a series of quantum beats of the particle density in the long-time limit. We also find a time-domain where the particle density of the point source is governed by the propagation of a main wavefront. The relative positions of these wavefronts are used to investigate the time-delay of quantum waves in the Klein-tunneling regime.
• Score: 77.34726150561087
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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