We study the properties of a phase slip in a superfluid Fermi gas near a Feshbach resonance. The phase slip can be generated by the phase imprinting method. Below the superfluid transition temperature, it appears as a dip in the density profile and becomes more pronounced when the temperature is lowered. Therefore the phase slip can provide direct evidence of the superfluid state. The condensation energy of the superfluid state can be extracted from the density profile of the phase slip, due to the unitary properties of the Fermi gas near the resonance. The width of the phase slip is inversely proportional to the square root of the difference between the transition temperature and the temperature. The signature of the phase slip in the density profile becomes more robust across the BCS-Bose-Einstein-condensate crossover.

Motivated by the recent discoveries of spin-1 and pseudo-spin-1 2 Bose gas, we have studied the general structure of the Bose gases with arbitrary spin. A general method is developed to uncover the elementary building blocks of the angular momentum eigenstates, as well as the relations (or interactions) between them. Applications of this method to Bose gas with integer spins (f=1,2,3) and half integer spins (f=1,2,3,2) reveal many surprising structures.

Recent neutron scattering experiments in optimally doped YBCO exhibit an unusual magnetic peak that appears only below the superconducting transition temperature. The experimental observations are explained within the context of the interlayer tunneling theory of high temperature superconductors.

In this paper, we study the three-body recombination rate of a homogeneous dilute Bose gas with a Feshbach resonance at zero temperature. The ground state and excitations of this system are obtained. The three-body recombination in the ground state is due to the breakup of an atom pair in the quantum depletion and the formation of a molecule by an atom from the broken pair and an atom from the condensate. The rate of this process is in good agreement with the experiment on 23Na in a wide range of magnetic fields.

The existence of a dynamical potential with both local and global meanings in general nonequilibrium processes has been controversial. Following an earlier heuristic argument in a letter by one of us, in the present paper we show rigorously its existence for a generic class of situations in physical and biological sciences. The local dynamical meaning of this potential function is demonstrated via a special stochastic differential equation and its global steadystate meaning via a novel and explicit form of the Fokker-Planck equation. We also give a procedure to obtain the special stochastic differential equation for any given Fokker-Planck equation. No detailed balance condition is required in our demonstration. For the first time we obtain here a formula to describe the noise-induced shift in drift force compared to the steady-state distribution, a phenomenon extensively observed in numerical studies.