Reducing the sign problem with line integrals
Abstract We present a novel strategy to strongly reduce the severity of the sign problem, using line integrals along paths of changing imaginary action. Highly oscillating regions along these paths cancel out, decreasing their contributions. As a result, sampling with standard Monte-Carlo techniques...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-02-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP02(2025)041 |
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| _version_ | 1823863428634116096 |
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| author | Rasmus N. Larsen |
| author_facet | Rasmus N. Larsen |
| author_sort | Rasmus N. Larsen |
| collection | DOAJ |
| description | Abstract We present a novel strategy to strongly reduce the severity of the sign problem, using line integrals along paths of changing imaginary action. Highly oscillating regions along these paths cancel out, decreasing their contributions. As a result, sampling with standard Monte-Carlo techniques becomes possible in cases that otherwise require methods taking advantage of complex analysis, such as Lefschetz-thimbles or Complex Langevin. We lay out how to write down an ordinary differential equation for the line integrals. As an example of its usage, we apply the results to a 1d quantum mechanical anharmonic oscillator with a x 4 potential in real time, finite temperature. |
| format | Article |
| id | doaj-art-80fd5d797fa949048639e3480919f711 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-80fd5d797fa949048639e3480919f7112025-02-09T12:08:26ZengSpringerOpenJournal of High Energy Physics1029-84792025-02-012025211410.1007/JHEP02(2025)041Reducing the sign problem with line integralsRasmus N. Larsen0Department of Mathematics and Physics, University of StavangerAbstract We present a novel strategy to strongly reduce the severity of the sign problem, using line integrals along paths of changing imaginary action. Highly oscillating regions along these paths cancel out, decreasing their contributions. As a result, sampling with standard Monte-Carlo techniques becomes possible in cases that otherwise require methods taking advantage of complex analysis, such as Lefschetz-thimbles or Complex Langevin. We lay out how to write down an ordinary differential equation for the line integrals. As an example of its usage, we apply the results to a 1d quantum mechanical anharmonic oscillator with a x 4 potential in real time, finite temperature.https://doi.org/10.1007/JHEP02(2025)041Algorithms and Theoretical DevelopmentsStochastic ProcessesLattice Quantum Field Theory |
| spellingShingle | Rasmus N. Larsen Reducing the sign problem with line integrals Journal of High Energy Physics Algorithms and Theoretical Developments Stochastic Processes Lattice Quantum Field Theory |
| title | Reducing the sign problem with line integrals |
| title_full | Reducing the sign problem with line integrals |
| title_fullStr | Reducing the sign problem with line integrals |
| title_full_unstemmed | Reducing the sign problem with line integrals |
| title_short | Reducing the sign problem with line integrals |
| title_sort | reducing the sign problem with line integrals |
| topic | Algorithms and Theoretical Developments Stochastic Processes Lattice Quantum Field Theory |
| url | https://doi.org/10.1007/JHEP02(2025)041 |
| work_keys_str_mv | AT rasmusnlarsen reducingthesignproblemwithlineintegrals |