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Volume 27, Issue 5
How does Gauge Cooling Stabilize Complex Langevin?

Zhenning Cai, Yana Di & Xiaoyu Dong

DOI: 10.4208/cicp.OA-2019-0126

Commun. Comput. Phys., 27 (2020), pp. 1344-1377.

Published online: 2020-03

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  • Abstract

We study the mechanism of the gauge cooling technique to stabilize the complex Langevin method in the one-dimensional periodic setting. In this case, we find the exact solutions for the gauge transform which minimizes the Frobenius norm of link variables. Thereby, we derive the underlying stochastic differential equations by continuing the numerical method with gauge cooling, and thus provide a number of insights on the effects of gauge cooling. A specific case study is carried out for the Polyakov loop model in SU(2) theory, in which we show that the gauge cooling may help form a localized distribution to guarantee there is no excursion too far away from the real axis. 

  • Keywords

Complex Langevin method, gauge cooling, Polyakov loop.

  • AMS Subject Headings

65C05, 65C30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

matcz@nus.edu.sg (Zhenning Cai)

yndi@uic.edu.hk (Yana Di)

dongxiaoyu@lsec.cc.ac.cn (Xiaoyu Dong)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-27-1344, author = {Cai , ZhenningDi , Yana and Dong , Xiaoyu}, title = {How does Gauge Cooling Stabilize Complex Langevin? }, journal = {Communications in Computational Physics}, year = {2020}, volume = {27}, number = {5}, pages = {1344--1377}, abstract = {

We study the mechanism of the gauge cooling technique to stabilize the complex Langevin method in the one-dimensional periodic setting. In this case, we find the exact solutions for the gauge transform which minimizes the Frobenius norm of link variables. Thereby, we derive the underlying stochastic differential equations by continuing the numerical method with gauge cooling, and thus provide a number of insights on the effects of gauge cooling. A specific case study is carried out for the Polyakov loop model in SU(2) theory, in which we show that the gauge cooling may help form a localized distribution to guarantee there is no excursion too far away from the real axis. 

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2019-0126}, url = {http://global-sci.org/intro/article_detail/cicp/15773.html} }
TY - JOUR T1 - How does Gauge Cooling Stabilize Complex Langevin? AU - Cai , Zhenning AU - Di , Yana AU - Dong , Xiaoyu JO - Communications in Computational Physics VL - 5 SP - 1344 EP - 1377 PY - 2020 DA - 2020/03 SN - 27 DO - http://doi.org/10.4208/cicp.OA-2019-0126 UR - https://global-sci.org/intro/article_detail/cicp/15773.html KW - Complex Langevin method, gauge cooling, Polyakov loop. AB -

We study the mechanism of the gauge cooling technique to stabilize the complex Langevin method in the one-dimensional periodic setting. In this case, we find the exact solutions for the gauge transform which minimizes the Frobenius norm of link variables. Thereby, we derive the underlying stochastic differential equations by continuing the numerical method with gauge cooling, and thus provide a number of insights on the effects of gauge cooling. A specific case study is carried out for the Polyakov loop model in SU(2) theory, in which we show that the gauge cooling may help form a localized distribution to guarantee there is no excursion too far away from the real axis. 

Cai , ZhenningDi , Yana and Dong , Xiaoyu. (2020). How does Gauge Cooling Stabilize Complex Langevin? . Communications in Computational Physics. 27 (5). 1344-1377. doi:10.4208/cicp.OA-2019-0126
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