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| Natura: | Preprint |
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2024
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| Accesso online: | https://arxiv.org/abs/2407.06470 |
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| _version_ | 1866916321974812672 |
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| author | Mackrory, Jonathan B. Zheng, He Steck, Daniel A. |
| author_facet | Mackrory, Jonathan B. Zheng, He Steck, Daniel A. |
| contents | The worldline method is a powerful numerical path-integral framework for computing Casimir and Casimir-Polder energies. An important challenge arises when one desires derivatives of path-integral quantities--standard finite-difference techniques, for example, yield results of poor accuracy. In this work we present methods for computing derivatives of worldline-type path integrals of scalar fields to calculate forces, energy curvatures, and torques. In Casimir-Polder-type path integrals, which require derivatives with respect to the source point of the paths, the derivatives can be computed by a simple reweighting of the path integral. However, a partial-averaging technique is necessary to render the differentiated path integral computationally efficient. We also discuss the computation of Casimir forces, curvatures, and torques between macroscopic bodies. Here a different method is used, involving summing over the derivatives of all the intersections with a body; again, a different partial-averaging method makes the path integral efficient. To demonstrate the efficiency of the techniques, we give the results of numerical implementations of these worldline methods in atomplane and plane-plane geometries. Being quite general, the methods here should apply to path integrals outside the worldline context (e.g., financial mathematics). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06470 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pathwise Differentiation of Worldline Path Integrals Mackrory, Jonathan B. Zheng, He Steck, Daniel A. Quantum Physics The worldline method is a powerful numerical path-integral framework for computing Casimir and Casimir-Polder energies. An important challenge arises when one desires derivatives of path-integral quantities--standard finite-difference techniques, for example, yield results of poor accuracy. In this work we present methods for computing derivatives of worldline-type path integrals of scalar fields to calculate forces, energy curvatures, and torques. In Casimir-Polder-type path integrals, which require derivatives with respect to the source point of the paths, the derivatives can be computed by a simple reweighting of the path integral. However, a partial-averaging technique is necessary to render the differentiated path integral computationally efficient. We also discuss the computation of Casimir forces, curvatures, and torques between macroscopic bodies. Here a different method is used, involving summing over the derivatives of all the intersections with a body; again, a different partial-averaging method makes the path integral efficient. To demonstrate the efficiency of the techniques, we give the results of numerical implementations of these worldline methods in atomplane and plane-plane geometries. Being quite general, the methods here should apply to path integrals outside the worldline context (e.g., financial mathematics). |
| title | Pathwise Differentiation of Worldline Path Integrals |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2407.06470 |