Complex Langevin Equation and the Many-Fermion Problem

Details Complex Langevin Equation and the Many-Fermion Problem Complex Langevin Equation and the Many-Fermion Problem

2000-09-07

arxiv.org/abs/nucl-th/0009021v2

Phys.Rev. C63 (2001) 034319

Physics

Nuclear Physics

Nuclear Theory

19 pages, 10 PS figures embedded in text

Scientific paper

10.1103/PhysRevC.63.034319

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 non-positive 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 three examples ranging from simple one-dimensional integrals over quantum mechanical models to a schematic shell model path integral.

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