Propagation of a wave packet in the presence of random scatterers and nonlinearity
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Venue:
KIT - Campus South - Wolfgang-Gaede-Str.1
Seminar Room 10.01, Bldg. 30.23 (Physikhochhaus) -
Date:
18.05.2009
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Speaker:
Dr. Georg Schwiete
Texas A & M University, U.S.A. -
Time:
14:00
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Abstract: In recent experiments on laser beams propagating in photonic crystals and on expanding atomic Bose-Einstein condensates the evolution of a wave-packet has been studied in the presence of random scatterers. We derive a non-linear diffusion equation determining the energy distribution and the spatial profile of a wave-packet for such systems when they are effectively two-dimensional. We find that the time evolution depends crucially on the sign and strength of non-linearity. Nevertheless, the average width of the wave-packet changes as $sqrt{t}$, like for ordinary diffusion, because of the constraint imposed by energy conservation. Physical effects such as a "locked explosion" and "diffusive collapse" are discussed in the case of repulsive and attractive non-linearities.