arXiv:nucl-th/0009021 · Physical Review C

Complex Langevin equation and the many-fermion problem

Christoph Adami, S. E. Koonin

Published Feb 20, 2001• 14 citations

Abstract

We study the utility of a complex Langevin (CL) equation as an alternative for the Monte Carlo (MC) procedure in the evaluation of expectation values occurring in fermionic many-body problems. We find that a CL approach is natural in cases where nonpositive definite probability measures occur, and remains accurate even when the corresponding MC calculation develops a severe ``sign problem.'' While the convergence of CL averages cannot be guaranteed in principle, we show how convergent results can be obtained in two simple quantum mechanical models, as well as a nontrivial schematic shell model path integral with multiple particles and a noncommuting interaction (the Lipkin model).

DOI: 10.1103/physrevc.63.034319

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