The effect of s-wave scattering length on self-trapping and tunneling phenomena of Fermi gases in one-dimensional accelerating optical lattices

We investigate the tunneling dynamics of the Fermi gases in an optical lattice in the Bose--Einstein condensation （BEC） regime. The three critical scattering lengths and the system energies are found in different cases of Josephson oscillation （JO）, oscillating-phase-type self-trapping （OPTST）, running-phase-type self-trapping （RPTST）, and self-trapping （ST）. It is found that the s-wave scattering lengths have a crucial role on the tunneling dynamics. By adjusting the scattering length in the adiabatic condition, the transition probability changes with the adiabatic periodicity and a rectangular periodic pattern emerges. The periodicity of the rectangular wave depends on the system parameters such as the periodicity of the adjustable parameter, the s-wave scattering length.

Tunnelling Phenomenon near an Apparent Horizon in Two-Dimensional Dilaton Gravity

Based on the definition of the apparent horizon in a general two-dimensional dilaton gravity theory, we analyze the tunnelling phenomenon near the apparent horizon. In this theory the definition of the horizon is very different from those in higher-dimensional gravity theories. By using the Hamilton-Jacobi method, the spectrum of the radiation is obtained and the temperature of the radiation is read out from this spectrum. The temperature is proportional to the surface gravity of the apparent horizon as usual. Besides, in stationary cases we calculate the spectrum by using Parikh and Wilczek＇s null geodesic method and the result conforms to that obtained by using the Harnilton-Jacobi method. This is expected since the flamilton-Jacobi method applies to generic spacetimes, including stationary ones.