Complex Langevin method: When can it be trusted?

By Gert Aarts, E. Seiler, I. Stamatescu. 2009

222 citations recorded by the source corpus.

We analyze to what extent the complex Langevin method, which is in principle capable of solving the so-called sign problems, can be considered as reliable. We give a formal derivation of the correctness and then point out various mathematical loopholes. The detailed study of some simple examples leads to practical suggestions about the application of the method.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/91b5cb5241bfaf9d5fbb445d056f831a0128dc27

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. V. Koch
2. T. Schaefer
3. P. Braun-Munzinger
4. J. Stachel
5. T. Hatsuda
6. Kenji Fukushima

In Statistical and Nonlinear Physics

1. V. Koch
2. T. Schaefer
3. T. Hatsuda
4. Kenji Fukushima

Citations in the corpus

• The phase diagram of dense QCD (2010, background): “The complex Langevin dynamics can evade the sign problem and correctly describe the system at finite density for some simple models, while there are also cases where it may fall into a wrong answer [142, 143].”
• Properties of hot and dense matter from relativistic heavy ion collisions (2015, methodology): “This includes new approaches, like integration over Lefshetz thimbles [96, 97], as well as novel variants of old approaches, like the complex Langevin method [98, 99], or the use of dual variables [100].”