On the well-posedness of the inviscid multi-layer quasi-geostrophic equations

The inviscid multi-layer quasi-geostrophic equations are considered over an arbitrary bounded domain. The no-flux but non-homogeneous boundary conditions are imposed to accommodate the free fluctuations of the top and layer interfaces. Using the barotropic and baroclinic modes in the vertical direction, the elliptic system governing the streamfunctions and the potential vorticity is decomposed into a sequence of scalar elliptic boundary value problems, where the regularity theories from the two-dimensional case can be applied. With the initial potential vorticity being essentially bounded, the multi-layer quasi-equations are then shown to be globally well-posed, and the initial and boundary conditions are satisfied in the classical sense

Fermi surface evolution in the antiferromagnetic state for the electron-doped t-t'-t''-J model

By use of the slave-boson mean-field approach, we have studied the electron-doped t-t'-t''-J model in the antiferromagnetic (AF) state. It is found that at low doping the Fermi surface (FS) pockets appear around $(\pm\pi,0)$ and $(0,\pm\pi)$, and upon increasing doping the other ones will form around $(\pm{\pi\over 2},\pm{\pi\over 2})$. The evolution of the FS with doping as well as the calculated spectral weight are consistent with the experimental results.Comment: Fig. 4 is updated, to appear in Phys. Rev.