BY FRANK A. WILCZEK
Institute for Theoretical Physics
University of California, Santa Barbara
Santa Barbara, Calif.
"Multigrid algorithms have traditionally been used in hydrodynamics, where it is often impbrtant to keep track of phenomena occurring on vastly different length scales. Roughly speaking, the idea is to have “average” variables defined on a coarse grid, and separate “local” variables on a fine grid. Lately there has been exciting progress in adapting these ideas to difficult problems in statistical mechanics and quantum field theory.
R.G. Edwards, J. Goodman, A.D. Sokal, “Multigrid method for the random resistor model,” Physical Review Letters, 61 (12), 1333-5, 19 September 1988.
" It has been increasingly appreciated that some of the generic behavior of quantum-mechanical systems can be derived using topological methods. As a simple example, it is often possible to prove the existence of level-crossings on topological grounds that are not related to symmetries....