Atomic, Molecular, and Optical Physics Seminar
Department of Physics and Astronomy, University of Oklahoma
The resources required for an exact solution of the quantum N-body problem are widely believed to scale exponentially with N, typically doubling for every particle added. With current numerical resources, this problem hits an “exponential wall” around N=10 (within a factor of 2). Even the advent of quantum computers is not expected to solve this problem, since recent studies have predicted that exact solutions of N-body wave functions for fermions or bosons are unlikely to have efficient algorithms on quantum computers. This exponential wall has prompted the creation of many approximate methods to avoid this exponential scaling. In this talk, I will present a method which performs an exact rearrangement of this exponential wall using analytic building blocks so that N is a parameter, i.e. the method scales as N0 . Group theory and graphical techniques do the “heavy lifting” to allow a direct transformation from microscopic two-body interactions to macroscopic motions of large-N systems. I will show that the exponential complexity of the quantum wave function has been shifted to an exponential wall that now scales with the order of the perturbation series. This approach thus allows the study of arbitrarily large systems of identical particles through low order in our perturbation series.