Recently it has been proposed and experimentally demonstrated that a spin-orbit coupled multi-component gas in 1d lattice can be viewed as spinless gas in a synthetic 2d lattice with a magnetic flux. In this letter we consider interaction effect of s
uch a Fermi gas, and propose signatures in charge pumping experiment, which can be easily realized in this setting. Using 1/3 filling of the lowest 2d band as an example, in strongly interacting regime, we show that the charge pumping value gradually approaches a universal fractional value for large spin component and low filling of 1d lattice, indicating a fractional quantum Hall type behavior; while the charge pumping value is zero if the 1d lattice filling is commensurate, indicating a Mott insulator behavior. The charge-density-wave order is also discussed.
We study liquid-vapor phase separation under shear via the Shan-Chen lattice Boltzmann model. Besides the rheological characteristics, we analyze the Kelvin-Helmholtz(K-H) instability resulting from the tangential velocity difference of the fluids on
two sides of the interface. We discuss also the growth behavior of droplets. The domains being close to the walls are lamellar-ordered, where the hydrodynamic effects dominate. The patterns in the bulk of the system are nearly isotropic, where the domain growth results mainly from the diffusion mechanism. Both the interfacial tension and the K-H instability make the liquid-bands near the walls tend to rupture. When the shear rate increases, the inequivalence of evaporation in the upstream and coagulation in the downstream of the flow as well as the role of surface tension makes the droplets elongate obliquely. Stronger convection makes easier the transferring of material particles so that droplets become larger.
