Quantum projector method on curved manifolds
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Publication:5949322
DOI10.1023/A:1010326231389zbMATH Open1018.82011arXivcond-mat/0001121MaRDI QIDQ5949322
Author name not available (Why is that?)
Publication date: 19 November 2001
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/cond-mat/0001121
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