Schrodinger Solvers      

Schrodinger equation solvers solve for the time evolution of the wave function of a quantum system. The memory requirements go as L^(mn) where n is the space dimensionality, L the number of points per dimension, and m the number of degrees of freedom. The basic method of solution is a split-operator technique which may be implemented either in Fourier or coordinate space. The algorithm is fully unitary and also applies to the nonlinear Schrodinger equation. Options for second or fourth order accuracy in time are available. Code performance is controlled typically by the performance achieved by the FFT implementation in the spectral method and by the implementation of shift operators in the coordinate space versions.

We have recently added the capability to solve nonlinear stochastic Schrodinger equations used to model continuous quantum measurements via the so-called ``quantum trajectory'' technique. These codes use tracking methods to reduce memory usage for a given resolution and certain unique capabilities compared to solutions of the quantum Master equation.

This is an HPF and F90/MPI code designed for accurate, very high-resolution, long-term integration of the single-particle Schrodinger equation using a split-operator spectral method. (Unitary nonspectral split-operator solvers also exist.) We have used this code to evaluate various approximation strategies for tracking the dynamics of quantum field theories by testing these schemes in quantum mechanics. The code has proved to be of central importance in our recent studies of chaotic quantum systems where accuracy is an essential requirement. A stochastic version of this code has been used to study quantum decoherence.

Typical system sizes for this code range from 32K to 1024K (one dimension). In two dimensions, we have run 8K X 8K grids. We need to run systems 4 times bigger in each dimension for the next generation of applications (16 GB per array).

This is a version of the code described above that solves the nonlinear Schrodinger equation. This code has applications in soliton transport and studies of Bose-Einstein condensation. Its two-dimensional version has been designed to study vortex dynamics. The coordinate space version of this code is under development.

Except for test runs for vortex dynamics, the rest of the production runs mentioned below will not be carried out at NERSC in FY01 as part of the present project.

The scientific goals for production runs will be to study:

Quantum Control simulations

Microcanonical vortex dynamics (two dimensions)

Dynamics of Bose-Einstein condensates

Quantum chaotic dynamics in two spatial dimensions

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