Exact quantum revivals for the Dirac equation

Abstract

In the present work, the results obtained by Strange [Phys. Rev. Lett. 104, 120403 (2010)] about the revivals of a relativistic fermion wave function on a torus are considerably expanded. In fact, all the possible quantum states exhibiting revivals are fully characterized. The revivals are exact, that is, are true revivals without taking any particular limit such as the nonrelativistic one. The present results are of interest since they generalize the Talbot effect and the revivals of the Schrödinger equation to a relativistic situation with nonzero mass. This makes the problem nontrivial, as the dispersion relation is modified and is not linear. The present results are obtained by the use of arithmetic tools, which are described in certain detail. In addition, several plots of the revivals are presented, which are useful for exemplifying the procedure proposed in the present paper.