We derive the leading order radiation through tunneling of an oscillating soliton in a well. We use the hydrodynamic formulation with a rigorous control of the errors for finite times.
Recent experiments [1] suggest that the ferromagnetism (FM) in GaAs: Mn is determined by the impurity band rather than holes in the valence band. We discuss here the physical mechanism of FM mediated by the carriers in impurity band, where the Mn d-l
evel play a crucial role. The theory is based on the first principle approach.
We investigate macroscopic tunneling from an elongated quasi 1-d trap, forming a cigar shaped BEC. Using recently developed formalism we get the leading analytical approximation for the right hand side of the potential wall, i.e. outside the trap, an
d a formalism based on Wigner functions, for the left side of the potential wall, i.e. inside the BEC. We then present accomplished results of numerical calculations, which show a blip in the particle density traveling with an asymptotic shock velocity, as resulted from previous works on a dot-like trap, but with significant differences from the latter. Inside the BEC a pattern of a traveling dispersive shock wave is revealed. In the attractive case, we find trains of bright solitons frozen near the boundary.
