Abstract
Abstract
We study the relativistic dynamics of electrons submitted to a uniform harmonic electric fields longitudinally applied to the electron velocity. In order to obtain explicitly the set of time-dependent equations for the bi-spinors components, we write down the corresponding Dirac equation for this system. By performing a suitable transformation to this set of equations, we get a matrix equation whose eigenvalues can be found directly. We found analytically the band structure and show a break of degeneracy and the existence of three bands: two total and one partial. The thicker band preventing from the Schwinger mechanisms can be shortened by proper combination of the frequency and amplitude of the applied electric field.
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics