Numerical evaluation of Casimir forces using the discontinuous Galerkin time-domain method
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917312720797696 |
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| author | Farràs, Carles Martí Beverungen, Bettina Kristensen, Philip Trøst Intravaia, Francesco Busch, Kurt |
| author_facet | Farràs, Carles Martí Beverungen, Bettina Kristensen, Philip Trøst Intravaia, Francesco Busch, Kurt |
| contents | We present a time-domain scheme for computing Casimir forces within the Maxwell stress tensor formalism, together with a specific realization using the finite-element-based discontinuous Galerkin time-domain method. The approach enables accurate evaluation of Casimir--Lifshitz interactions for a wide range of geometries and material properties at finite temperature. At the core of the method, the electromagnetic Green's tensor is expressed as the system's response to dipolar excitations, thereby recasting the Maxwell stress tensor into a set of classical scattering problems driven by electric and magnetic dipoles. We validate the approach against reference calculations of the Casimir interaction between parallel half-spaces at both zero and nonzero temperature. We further demonstrate its applicability to finite, cylindrically symmetric geometries for which closed-form solutions are unavailable, obtaining accurate agreement with asymptotic predictions based on physical considerations. These findings illustrate the method's potential for studying Casimir interactions in realistic micro- and nanoscale structures, relevant to nanodevice design and experimental settings. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_03888 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Numerical evaluation of Casimir forces using the discontinuous Galerkin time-domain method Farràs, Carles Martí Beverungen, Bettina Kristensen, Philip Trøst Intravaia, Francesco Busch, Kurt Quantum Physics Computational Physics We present a time-domain scheme for computing Casimir forces within the Maxwell stress tensor formalism, together with a specific realization using the finite-element-based discontinuous Galerkin time-domain method. The approach enables accurate evaluation of Casimir--Lifshitz interactions for a wide range of geometries and material properties at finite temperature. At the core of the method, the electromagnetic Green's tensor is expressed as the system's response to dipolar excitations, thereby recasting the Maxwell stress tensor into a set of classical scattering problems driven by electric and magnetic dipoles. We validate the approach against reference calculations of the Casimir interaction between parallel half-spaces at both zero and nonzero temperature. We further demonstrate its applicability to finite, cylindrically symmetric geometries for which closed-form solutions are unavailable, obtaining accurate agreement with asymptotic predictions based on physical considerations. These findings illustrate the method's potential for studying Casimir interactions in realistic micro- and nanoscale structures, relevant to nanodevice design and experimental settings. |
| title | Numerical evaluation of Casimir forces using the discontinuous Galerkin time-domain method |
| topic | Quantum Physics Computational Physics |
| url | https://arxiv.org/abs/2603.03888 |