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Nonlinear Quantum Mechanics

Banff International Research Station for Mathematical Innovation and Discovery

We model the dynamics of electrons in doped quantum wells driven by terahertz radiation and a superlattice biased by a dc voltage. We compute coherent, self-consistent electron states, density matrix equations of motion, and dipole absorption spectra. The model simultaneously accounts for intersubband transitions and many nonlinear phenomena that have been observed in these systems. We predict a bistable response for strong terahertz fields and bifurcations to coherent time-periodic quantum states. These bifurcation include, period-doubling bifurcations, producing a subharmonic response, Hopf bifurcations producing an incommensurate frequency response, and a cascade of period doubling bifurcations to a strange attractor. We also see a cascade of quasi-periodic orbits on the Hopf torus to a strange attractor. These bifurcation have been difficult to measure in single quantum wells. Therefore we design super-lattice heterostructures of quantum wells where these bifurcations occur and are easier to measure.

Mathematics; Quantum theory; Mechanics of deformable solids; Applied analysis / inverse problems

video/mp4

Author affiliation: Univ. of California, Santa Barbara

2017-02-28

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60726

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/