Dynamical mean-field solution of coupled quantum wells: a bifurcation analysis.

Abstract

The time evolution of a discrete model of three quantum wells with a localized mean-field electrostatic interaction has been analyzed making use of numerical simulation and bifurcation techniques. The discrete Schrödinger equation can be written as a classical Hamiltonian system with two constants of motion. The frequency spectrum and the Lyapunov exponents show that the system is chaotic as its continuum counterpart. The organizing centers of the dynamical behavior are bifurcations of rotating periodic solutions whose simple structure allows a thorough analytical investigation as the conserved quantities are varied. The global structure of the periodic behavior is organized via subharmonic bifurcations at which tori of nonsymmetric periodic solutions are born. We have found another kind of bifurcation when two pairs of characteristic multipliers split from the unit circle. The chaotic behavior is related to the nonintegrability of the system.