Quantum Projector Method on Curved Manifolds

Details Quantum Projector Method on Curved Manifolds Quantum Projector Method on Curved Manifolds

2000-01-10

arxiv.org/abs/cond-mat/0001121v1

Physics

Condensed Matter

Statistical Mechanics

28 pages, 6 figures

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Quantum Projector Method on Curved Manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Quantum Projector Method on Curved Manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum Projector Method on Curved Manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-364501