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Complex Langevin dynamics as a cure for the sign problem. / Frank James

Swansea University Author: Frank James

Abstract

Theories with a chemical potential are difficult to treat numerically because the action is complex and therefore methods based on a probability interpretation of the weight break down. This is an issue known as the sign problem. Complex Langevin dynamics was first proposed in the early 1980s and do...

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Published: 2012
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
URI: https://cronfa.swan.ac.uk/Record/cronfa42679
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last_indexed 2018-08-03T10:10:48Z
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spelling 2018-08-02T16:24:30.0866121 v2 42679 2018-08-02 Complex Langevin dynamics as a cure for the sign problem. 5c727164133d8e9e8a7361af54863edf NULL Frank James Frank James true true 2018-08-02 Theories with a chemical potential are difficult to treat numerically because the action is complex and therefore methods based on a probability interpretation of the weight break down. This is an issue known as the sign problem. Complex Langevin dynamics was first proposed in the early 1980s and does not rely in a probability interpretation of the weight, so it can in principle l)e applied even where there is a severe sign problem. However, the combined problems of numerical instabilities and incorrect convergence impeded such early studies. In this work, the problem of runaway trajectories is cured l)y the use of a general adaptive stepsize procedure, which can be applied to both abelian and non-abelian theories. A study of the three-dimensional XY model at non-zero chemical potential follows, in which the problem of incorrect convergence is encountered. A formal justification of complex Langevin dynamics is given, from which a set of criteria are derived which can be used to test the validity of results. These ideas are applied to the SU(3) spin model, which is found to pass them all and therefore give correct results. An improved integration algorithm, which eliminates leading order step size corrections, is outlined and shown to give improved results. E-Thesis Theoretical physics. 31 12 2012 2012-12-31 COLLEGE NANME Physics COLLEGE CODE Swansea University Doctoral Ph.D 2018-08-02T16:24:30.0866121 2018-08-02T16:24:30.0866121 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics Frank James NULL 1 0042679-02082018162513.pdf 10807448.pdf 2018-08-02T16:25:13.4700000 Output 6928480 application/pdf E-Thesis true 2018-08-02T16:25:13.4700000 false
title Complex Langevin dynamics as a cure for the sign problem.
spellingShingle Complex Langevin dynamics as a cure for the sign problem.
Frank James
title_short Complex Langevin dynamics as a cure for the sign problem.
title_full Complex Langevin dynamics as a cure for the sign problem.
title_fullStr Complex Langevin dynamics as a cure for the sign problem.
title_full_unstemmed Complex Langevin dynamics as a cure for the sign problem.
title_sort Complex Langevin dynamics as a cure for the sign problem.
author_id_str_mv 5c727164133d8e9e8a7361af54863edf
author_id_fullname_str_mv 5c727164133d8e9e8a7361af54863edf_***_Frank James
author Frank James
author2 Frank James
format E-Thesis
publishDate 2012
institution Swansea University
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Biosciences, Geography and Physics - Physics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Biosciences, Geography and Physics - Physics
document_store_str 1
active_str 0
description Theories with a chemical potential are difficult to treat numerically because the action is complex and therefore methods based on a probability interpretation of the weight break down. This is an issue known as the sign problem. Complex Langevin dynamics was first proposed in the early 1980s and does not rely in a probability interpretation of the weight, so it can in principle l)e applied even where there is a severe sign problem. However, the combined problems of numerical instabilities and incorrect convergence impeded such early studies. In this work, the problem of runaway trajectories is cured l)y the use of a general adaptive stepsize procedure, which can be applied to both abelian and non-abelian theories. A study of the three-dimensional XY model at non-zero chemical potential follows, in which the problem of incorrect convergence is encountered. A formal justification of complex Langevin dynamics is given, from which a set of criteria are derived which can be used to test the validity of results. These ideas are applied to the SU(3) spin model, which is found to pass them all and therefore give correct results. An improved integration algorithm, which eliminates leading order step size corrections, is outlined and shown to give improved results.
published_date 2012-12-31T03:53:26Z
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score 11.016235

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