Inhomogeneous Mean Fields      

These codes solve for the time evolution of inhomogeneous mean fields in the presence of self-consistently determined quantum fluctuations. The equations being solved are in the leading order 1/N approximation where the mean field interacts with the fluctuations but the fluctuations do not interact with each other directly. Appropriate renormalizations ensure that all physical quantities are independent of cut-offs.

This class of codes is under development and is designed to study the formation and evolution of nonlinear coherent structures such as domain walls and vortices in both equilibrium and nonequilibrium settings. In contrast to the homogeneous case, the mean field is now spatially dependent, which means that a partial differential equation for the mean field has to be solved, coupled in turn to the fluctuations. Thus, in practice, one has now to solve at least hundreds of thousands of coupled ODEs.

We have evaluated two different approaches. The first scheme was to stay in coordinate space and solve the coupled equations using a symplectic finite difference algorithm. The alternative was to work in momentum space as in the homogeneous case. This meant having to deal with convolution integrals and it was not clear a priori which of the two methods was to be preferred. We have now established that the first method is much to be preferred on parallel machines since it avoids global communication.

One-dimensional codes are now running. We will extend these codes to two dimensions (at present, memory restrictions do not allow three dimensional problems to be studied).

The scientific goals for production runs will be to study:

More realistic models for RHIC physics

Quantum transport of kinks

Defect formation in quenches

Salman Habib / LANL / habib@lanl.gov / revised August 00