Quantum Projector Method on Curved Manifolds |
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Authors: | V Melik-Alaverdian G Ortiz N E Bonesteel |
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Institution: | (1) Department of Physics, University of Rhode Island, Kingston, Rhode Island, 02881;(2) Theoretical Division, Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, New Mexico, 87545;(3) National High Magnetic Field Laboratory and Department of Physics, Florida State University, Tallahassee, Florida, 32306-4005 |
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Abstract: | A generalized stochastic method for projecting out the ground state of the quantum many-body Schrödinger 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. |
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Keywords: | stochastic or statistical methods quantum Monte Carlo fermion methods generalized diffusion equation quantum hell physics |
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