Quantum Projector Method on Curved Manifolds
Abstract
A generalized stochastic method for projecting out the ground state of the quantum many-body Schr\"odinger equation on curved manifolds is introduced. This random-walk method is of wide applicability to any second order differential equation (first order in time), in any spatial dimension. The technique reduces to determining the proper ``quantum corrections'' for the Euclidean short-time propagator that is used to build up their path-integral Monte Carlo solutions. For particles with Fermi statistics the ``Fixed-Phase'' constraint (which amounts to fixing the phase of the many-body state) allows one to obtain stable, albeit approximate, solutions with a variational property. We illustrate the method by applying it to the problem of an electron moving on the surface of a sphere in the presence of a Dirac magnetic monopole.
Cite
@article{arxiv.cond-mat/0001121,
title = {Quantum Projector Method on Curved Manifolds},
author = {V. Melik-Alaverdian and G. Ortiz and N. E. Bonesteel},
journal= {arXiv preprint arXiv:cond-mat/0001121},
year = {2007}
}
Comments
28 pages, 6 figures