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Relation between chaos probability and zero-point number of the Melnikov function for a Bose-Einstein condensate

100%
Zhu Q., Hai W., Rong S.
Open Physics
|
2009
|
vol. 7
|
issue 4
738-746
EN
We investigate an attractive Bose-Einstein condensate perturbed by a weak traveling optical superlattice. It is demonstrated that under a stochastic initial set and in a given parameter region solitonic chaos appears with a certain probability that is tightly related to the zero-point number of the Melnikov function; the latter depends on the potential parameters. Effects of the lattice depths and wave vectors on the chaos probability are studied analytically and numerically, and different chaotic regions of the parameter space are found. The results suggest a feasible method for strengthening or weakening chaos by modulating the potential parameters experimentally.
2
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A direct connection between quantum Hall plateaus and exact pair states in a 2D electron gas

100%
Hai W., Li Z., Xiao K.
Open Physics
|
2011
|
vol. 9
|
issue 6
1509-1517
EN
It is previously found that the two-dimensional (2D) electron-pair in a homogeneous magnetic field has a set of exact solutions for a denumerably infinite set of magnetic fields. Here we demonstrate that as a function of magnetic field a band-like structure of energy associated with the exact pair states exists. A direct and simple connection between the pair states and the quantum Hall effect is revealed by the band-like structure of the hydrogen “pseudo-atom”. From such a connection one can predict the sites and widths of the integral and fractional quantum Hall plateaus for an electron gas in a GaAs-AlxGa1−x As heterojunction. The results are in good agreement with the existing experimental data.
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