We show that a non-Fermi-liquid state of interacting electrons in two dimensions is stable in the presence of disorder and is a perfect conductor, provided the interactions are sufficiently strong. Otherwise, the disorder leads to localization as in the case of noninteracting electrons. This conclusion is established by examining the replica field theory in the weak-disorder limit, but in the presence of arbitrary electron-electron interaction. Thus, a disordered two-dimensional metal is a perfect metal, but not a Fermi liquid.

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.

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.

We study the pairing instability and mechanical collapse of a dilute homogeneous Bose gas with an attractive interaction. The pairing phase is found to be a saddle point and is unstable against pairing fluctuations. This pairing saddle point exists above a critical temperature. Below this critical temperature, the system is totally unstable in the pairing channel. Thus the system could collapse in the pairing channel in addition to mechanical collapse. The critical temperatures of pairing instability and mechanical collapse are higher than the Bose-Einstein condensation (BEC) temperature of an ideal Bose gas with the same density. When fluctuations are taken into account, we find that the critical temperature of mechanical collapse is even higher. The difference between the collapse temperature and the BEC temperature is proportional to (nuasu3)2/9, where n is the density and as is the scattering length.

The phase diagram of the double-exchange model is studied in the large-S limit at zero temperature in two and three dimensions. We find that the spiral state has lower energy than the canted antiferromagnetic state in the region between the antiferromagnetic phase and the ferromagnetic phase. At small doping, the spiral phase is unstable against phase separation due to its negative compressibility. When the Hund coupling is small, the system separates into spiral regions and antiferromagnetic regions. When the Hund coupling is large, the spiral phase disappears completely and the system separates into ferromagnetic regions and antiferromagnetic regions.