### 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).

Original language | English (US) |
---|---|

Pages (from-to) | 343191-3431910 |

Number of pages | 3088720 |

Journal | Physical Review C - Nuclear Physics |

Volume | 63 |

Issue number | 3 |

DOIs | |

State | Published - Mar 2001 |

### Fingerprint

### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Nuclear and High Energy Physics

### Cite this

*Physical Review C - Nuclear Physics*,

*63*(3), 343191-3431910. https://doi.org/10.1103/PhysRevC.63.034319

**Complex langevin equation and the many-fermion problem.** / Adami, Chris; Koonin, Steven E.

Research output: Contribution to journal › Article

*Physical Review C - Nuclear Physics*, vol. 63, no. 3, pp. 343191-3431910. https://doi.org/10.1103/PhysRevC.63.034319

}

TY - JOUR

T1 - Complex langevin equation and the many-fermion problem

AU - Adami, Chris

AU - Koonin, Steven E.

PY - 2001/3

Y1 - 2001/3

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=18744421134&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18744421134&partnerID=8YFLogxK

U2 - 10.1103/PhysRevC.63.034319

DO - 10.1103/PhysRevC.63.034319

M3 - Article

VL - 63

SP - 343191

EP - 3431910

JO - Physical Review C - Nuclear Physics

JF - Physical Review C - Nuclear Physics

SN - 0556-2813

IS - 3

ER -