Vector and Spinor Decomposition of SU(2) Gauge Potential, their quivalence and Knot Structure in SU(2) Chern-Simons Theory

In this paper, spinor and vector decomposition of SU(2) gauge potential are presented and their equivalence is constructed using a simply proposal. We also obtain the action of Faddeev nonlinear O(3) sigma model from the SU(2) massive gauge field theory which is proposed according to the gauge invariant principle. At last, the knot structure in SU(2) Chern-Simons filed theory is discussed in terms of the $\phi$--mapping topological current theory. The topological charge of the knot is characterized by the Hopf indices and the Brouwer degrees of $\phi$-mapping.Comment: 10 pages, ni figur

Dynamical Response of Fermi Condensate to Varying Magnetic Fields

We investigate the dynamical response of strongly interacting ultra-cold fermionic atoms near Feshbach resonance to varying magnetic fields. Following the experimental practices, we calculate the response of the atoms to oscillating and to linearly ramped magnetic fields respectively. For oscillating magnetic fields, depending on the frequencies and the amplitudes of the oscillations, the response of the pair excitation gap shows either linear or rich non-linear behaviour. In addition, both the spectral studies through the linear response theory and the time-domain simulations suggest the existence of a resonant frequency corresponding to the pair dissociation threshold. For linearly ramped magnetic fields, the response of the excitation gap shows damped oscillations. The final value of the excitation gap depends on the rate of the field sweep.Comment: 6 pages, 6 figure