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.

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.

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.