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Register a new userSimulation of Zitterbewegung by modelling the Dirac equation in Metamaterials
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We develop a dynamic description of an effective Dirac theory in metamaterials, in which the wavefunction is modeled by the corresponding electric and magnetic field in the metamaterial. This electro-magnetic field can be probed in the experimental setup, which means that the wavefunction of the effective theory is directly accessible by measurement. Our model is based on a plane wave expansion, which ravels the identification of Dirac spinors with single-frequency excitations of the electro-magnetic field in the metamaterial. The characteristic Zitterbewegung is shown to emerge in simulations of the effective theory and we verify this signature with an analytic solution.
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We present a physical explanation of Zitterbewegung-like effect near the zero-refractive-index point in a metamaterial slab in this paper. Between the negative and positive refractive index regions centered at the zero-refractive-index point, the transmittance spectrum distribution of the metamaterial slab is asymmetrical. When a symmetrical pulse propagates through the metamaterial slab, its transmitted spectrum becomes asymmetrical due to the asymmetry of the transmittance spectrum of the slab, leading to a transmitted pulse with an asymmetrical temporal shape. The asymmetry manifests a kind of temporally tailed oscillations, i.e., the Zitterbewegung-like effect. Further, the effect of the temporal and spatial widths of pulse, and the thickness of metamaterial slab on the tailed oscillations of the transmitted pulse has also been discussed. Our results agree well with what the other researchers obtained on the strength of relativistic quantum concepts; however, the viewpoint of our analysis is classical and irrelevant to relativistic quantum mechanics.
The validity of the work by Lamata et al [Phys. Rev. Lett. 98, 253005 (2007)] can be further shown by quantum field theory considerations.
We show that Bogoliubovs quasiparticle in superfluid $^3He-B$ undergoes the Zitterbewegung, as a free relativistic Diracs electron does. The expectation value of position, as well as spin, of the quasiparticle is obtained and compared with that of the Diracs electron. In particular, the Zitterbewegung of Bogoliubovs quasiparticle has a frequency approximately $10^5$ lower than that of an electron, rendering a more promising experimental observation.
Ultra-cold atoms which are subject to ultra-relativistic dynamics are investigated. By using optically induced gauge potentials we show that the dynamics of the atoms is governed by a Dirac type equation. To illustrate this we study the trembling motion of the centre of mass for an effective two level system, historically called Zitterbewegung. Its origin is described in detail, where in particular the role of the finite width of the atomic wave packets is seen to induce a damping of both the centre of mass dynamics and the dynamics of the populations of the two levels.
We discuss the structure of the Dirac equation and how the nilpotent and the Majorana operators arise naturally in this context. This provides a link between Kauffmans work on discrete physics, iterants and Majorana Fermions and the work on nilpotent structures and the Dirac equation of Peter Rowlands. We give an expression in split quaternions for the Majorana Dirac equation in one dimension of time and three dimensions of space. Majorana discovered a version of the Dirac equation that can be expressed entirely over the real numbers. This led him to speculate that the solutions to his version of the Dirac equation would correspond to particles that are their own anti-particles. It is the purpose of this paper to examine the structure of this Majorana-Dirac Equation, and to find basic solutions to it by using the nilpotent technique. We succeed in this aim and describe our results.
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