Dynamical effects of a one-dimensional multibarrier potential of finite range

Abstract

We discuss the properties of a large number N of one-dimensional (bounded) locally periodic potential barriers in a finite interval. We show that the transmission coefficient, the scattering cross section $\sigma$, and the resonances of $\sigma$ depend sensitively upon the ratio of the total spacing to the total barrier width. We also show that a time dependent wave packet passing through the system of potential barriers rapidly spreads and deforms, a criterion suggested by Zaslavsky for chaotic behaviour. Computing the spectrum by imposing (large) periodic boundary conditions we find a Wigner type distribution. We investigate also the S-matrix poles; many resonances occur for certain values of the relative spacing between the barriers in the potential.

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• Phase transitions in a one-dimensional multibarrier potential of finite range
• Ordered and periodic chaos of the bounded one dimensinal multibarrier potential
• The band-gap structure and the singular character of the bounded large array of potential barriers