Dynamics of a charged particle on a periodic binary sequence in an external field

The dynamic behavior of a charged particle on a periodic binary sequence under the action of an external electric field is discussed. By the method of the Lie algebra SU(2), the evolution equations of the charged particle are solved analytically, and an expression for the quasienergy bands is obtained. In the limit of a high-frequency ac field, an explicit result for the quasienergies is deduced. Together with the numerical discussion, we find that (i) the hopping disturbance makes the quasienergy spectrum split into two separate quasienergy bands; (ii) the increase of the hopping disturbance changes the band collapse into band suppression and makes the band suppression locations severely deviate from the zeros of the Bessel function of order zero; and (iii) the invasion of the hopping disturbance destroys the dynamic localization. (C) 1998 Elsevier Science B.V.