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Project A4: Light propagation through nonlinear media -- transition from ballistic to dissipative regime.
The goal of this
project is to study systematically the formation, propagation,
and collision of ultra-short light pulses in nonlinear media which in a certain
approximation describe an ensemble of atoms or quantum dots. Our analysis
is based on a sine-Gordon-like equation with dissipative contributions. This
equation for collectively coupled atomic systems includes two limiting cases:
when the dissipative terms are neglected it reduces to the completely integrable
sine-Gordon equation displaying "classical" soliton solutions and preservation of
pairwise colliding solitons, while in the over-damped limit one ends up with a
reaction-diffusion equation that predicts annihilation of traveling wave solutions.
Our focus will be on wave interaction in the transition range between the dissipation
dominated and the ballistic regimes. Increasing the electron-phonon dissipation
parameter (e.g., temperature) beyond a certain threshold, a transition from pairwise
"classically" colliding solitons to anihilation of traveling wave solutions is expected.
In a more general context, our analysis will elucidate the crossover between localized
non-linear waves in conservative and dissipative systems. Investigations combine
analytical tools (inverse scattering method, perturbation techniques for dispersive
effects) and numerical methods (finite difference time domain method, continuation
techniques of numerical bifurcation analysis).
Project leaders: Prof.Dr. A. Knorr , Prof.Dr. H. Engel