A closed, quantum, double barrier, GaAs/AlGaAs heterostructure is made chaotic by adding a nonlinear potential term, α〈Q(t)〉, to the time-dependent Schrödinger equation, and the dynamical behavior of an electron cloud moving in the heterostructure biased by a dc electric field is examined numerically. Using phase-space diagrams, power spectrums, and Lyapunov exponents, both qualitative and quantitative measures of the chaos in the system were taken. In general, for all values of α, the nonlinearity parameter, the Lyapunov exponent, λ, increases as the applied dc field, β, increases. However, for values of α ⩽ 1.376, we notice a sharp drop in λ for the value of β = −9.2×107 V/m corresponding to an average dc voltage of −.085 eV in the central well. This first order type transition to high values of λ for α>1.376 corresponds to a similar increase in the mean charge trapped in the heterostructure and in the average nonlinear potential in the central well for that dc field. This behavior is attributed to the fact that for α ⩽ 1.376 and β = −9.2×107 V/m, the field effects dominate, but for α>1.376, the nonlinearity term dominates.
Journal of Applied Physics
J. Appl. Phys. 82, 1687 (1997)