Schematic baryon models, their tight binding description and their microwave realization

A schematic model for baryon excitations is presented in terms of a symmetric Dirac gyroscope, a relativistic model solvable in closed form, that reduces to a rotor in the non-relativistic limit. The model is then mapped on a nearest neighbour tight binding model. In its simplest one-dimensional form this model yields a finite equidistant spectrum. This is experimentally implemented as a chain of dielectric resonators under conditions where their coupling is evanescent and good agreement with the prediction is achieved.Comment: 17 pages, 15 figure

First experimental realization of the Dirac oscillator

We present the first experimental microwave realization of the one-dimensional Dirac oscillator, a paradigm in exactly solvable relativistic systems. The experiment relies on a relation of the Dirac oscillator to a corresponding tight-binding system. This tight-binding system is implemented as a microwave system by a chain of coupled dielectric disks, where the coupling is evanescent and can be adjusted appropriately. The resonances of the finite microwave system yields the spectrum of the one-dimensional Dirac oscillator with and without mass term. The flexibility of the experimental set-up allows the implementation of other one-dimensional Dirac type equations.Comment: 6 figures, 5 page

Relativistic echo dynamics and the stability of a beam of Landau electrons

We extend the concepts of echo dynamics and fidelity decay to relativistic quantum mechanics, specifically in the context of Klein-Gordon and Dirac equations under external electromagnetic fields. In both cases we define similar expressions for the fidelity amplitude under perturbations of these fields, and a covariant version of the echo operator. Transformation properties under the Lorentz group are established. An alternate expression for fidelity is given in the Dirac case in terms of a 4-current. As an application we study a beam of Landau electrons perturbed by field inhomogeneities.Comment: 8 pages, no figure