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Spontaneous symmetry breaking in linearly coupled disk-shaped Bose-Einstein condensates
linearly coupled disk-shaped Bose-Einstein condensates Spontaneous symmetry breaking
2011/7/7
We study effects of tunnel coupling on a pair of parallel disk-shaped Bose-Einstein condensates with the self-attractive intrinsic nonlinearity. Each condensate is trapped in a combination of in-plane...
Spontaneous symmetry breaking of photonic and matter waves in two-dimensional pseudopotentials
Spontaneous symmetry breaking photonic matter waves two-dimensional pseudopotentials
2011/7/6
We introduce the two-dimensional Gross-Pitaevskii/nonlinear-Schrodinger (GP/NLS) equation with the self-focusing nonlinearity confined to two identical circles, separated or overlapped. The model can ...
Spontaneous Symmetry Breaking during Formation of ZnO Nanocrystals
Crystal structure Growth models Nanomaterials Spontaneous symmetry breaking
2011/3/4
Systemic symmetry is introduced into our work to investigate the symmetries of different ZnO nanocrystals. Result shows that systemic symmetries obey the law of spontaneous symmetry breaking during th...
Symmetry-breaking bifurcation in the nonlinear Schrödinger equation with symmetric potentials
Symmetry-breaking bifurcation nonlinear Schrö dinger equation symmetric potentials
2011/2/22
We consider the focusing (attractive) nonlinear Schr¨odinger (NLS) equation with an external,
symmetric potential which vanishes at infinity and supports a linear bound state. We prove that
the symm...
Symmetry breaking: A tool to unveil the topology of chaotic scattering with three degrees of freedom
Chaotic Dynamics (nlin.CD)
2010/11/10
We shall use symmetry breaking as a tool to attack the problem of identifying the topology of chaotic scatteruing with more then two degrees of freedom. specifically we discuss the structure of the ho...
Radial symmetry and symmetry breaking for some interpolation inequalities
Sobolev spaces interpolation Hardy-Sobolev inequality
2010/12/3
We analyze the radial symmetry of extremals for a class of interpolation inequalities known as Caffarelli-Kohn-Nirenberg inequalities, and for a class of weighted logarithmic Hardy inequalities which ...
Extremal functions in some interpolation inequalities: Symmetry, symmetry breaking and estimates of the best constants
Caffarelli-Kohn-Nirenberg inequality Gagliardo-Nirenberg inequality loga-rithmic Hardy inequality logarithmic Sobolev inequality
2010/12/14
This contribution is devoted to a review of some recent results on existence, symmetry and symmetry breaking of optimal functions for Caffarelli-Kohn-Nirenberg (CKN) and weighted logarithmic Hardy (WL...