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Intermediate energy scale physics plays a very important role innon-equilibrium dynamics of quasi-low dimensional cold atom systems. In thisarticle we obtain the universal scaling relations for the generalizedreflection coefficient, i.e., the fraction of atoms scattered out of theinitial state, at intermediate energies scales. These intermediate energies arelarger than the trap frequency, but necessarily smaller than the effectiverange of the inter-atomic potential. For harmonically confined one and twodimensional geometries, whenever the energy of the system is commensurate witha transverse energy level, it is shown that the system becomes non-interacting.For energies close to a transverse energy level, the reflection coefficient andscattering dynamics take on universal scaling forms, only depending on thedifference between the energy of the particles and the transverse energy level.In this article, the universal power law behaviors of these scatteringobservables are obtained.

Universal Scaling Properties of Cold Atom Scattering Dynamics in Confined Low Dimensional Geometries