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Journal Article

Complex Langevin and boundary terms

MPS-Authors

Scherzer,  Manuel
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Seiler,  Erhard
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Sexty,  Denes
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Stamatescu,  Ion-Olimpiu
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

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Citation

Scherzer, M., Seiler, E., Sexty, D., & Stamatescu, I.-O. (2019). Complex Langevin and boundary terms. Physical Review D, 99, 014512. Retrieved from https://publications.mppmu.mpg.de/?action=search&mpi=MPP-2018-215.


Cite as: https://hdl.handle.net/21.11116/0000-0005-D6AF-5
Abstract
It is well known that the Complex Langevin (CL) method sometimes fails to converge or converges to the wrong limit. We identified one reason for this long ago: insufficient decay of the probability density either near infinity or near poles of the drift, leading to boundary terms that spoil the formal argument for correctness. To gain a deeper understanding of this phenomenon, we analyze the emergence of such boundary terms thoroughly in a simple model, allowing some analytic results for comparing with numerics. We also show how some simple modification stabilizes the CL process in such a way that it produces results agreeing with direct integration.