dorsal/arxiv
View SchemaGeometry of the Casimir Effect
| Authors | Roger Balian, Bertrand Duplantier |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0408124 |
| URL | https://arxiv.org/abs/quant-ph/0408124 |
| Journal | Recent Developments in Gravitational Physics, Institute of Physics Conference Series 176, Ed. Ciufiolini et al, Oct 2004 |
Abstract
When the vacuum is partitioned by material boundaries with arbitrary shape, one can define the zero-point energy and the free energy of the electromagnetic waves in it: this can be done, independently of the nature of the boundaries, in the limit that they become perfect conductors, provided their curvature is finite. The first examples we consider are Casimir's original configuration of parallel plates, and the experimental situation of a sphere in front of a plate. For arbitrary geometries, we give an explicit expression for the zero-point energy and the free energy in terms of an integral kernel acting on the boundaries; it can be expanded in a convergent series interpreted as a succession of an even number of scatterings of a wave. The quantum and thermal fluctuations of vacuum then appear as a purely geometric property. The Casimir effect thus defined exists only owing to the electromagnetic nature of the field. It does not exist for thin foils with sharp folds, but Casimir forces between solid wedges are finite. We work out various applications: low temperature, high temperature where wrinkling constraints appear, stability of a plane foil, transfer of energy from one side of a curved boundary to the other, forces between distant conductors, special shapes (parallel plates, sphere, cylinder, honeycomb).
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"abstract": "When the vacuum is partitioned by material boundaries with arbitrary shape,\none can define the zero-point energy and the free energy of the electromagnetic\nwaves in it: this can be done, independently of the nature of the boundaries,\nin the limit that they become perfect conductors, provided their curvature is\nfinite. The first examples we consider are Casimir\u0027s original configuration of\nparallel plates, and the experimental situation of a sphere in front of a\nplate. For arbitrary geometries, we give an explicit expression for the\nzero-point energy and the free energy in terms of an integral kernel acting on\nthe boundaries; it can be expanded in a convergent series interpreted as a\nsuccession of an even number of scatterings of a wave. The quantum and thermal\nfluctuations of vacuum then appear as a purely geometric property. The Casimir\neffect thus defined exists only owing to the electromagnetic nature of the\nfield. It does not exist for thin foils with sharp folds, but Casimir forces\nbetween solid wedges are finite. We work out various applications: low\ntemperature, high temperature where wrinkling constraints appear, stability of\na plane foil, transfer of energy from one side of a curved boundary to the\nother, forces between distant conductors, special shapes (parallel plates,\nsphere, cylinder, honeycomb).",
"arxiv_id": "quant-ph/0408124",
"authors": [
"Roger Balian",
"Bertrand Duplantier"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech",
"gr-qc",
"math-ph",
"math.MP"
],
"journal_ref": "Recent Developments in Gravitational Physics, Institute of Physics\n Conference Series 176, Ed. Ciufiolini et al, Oct 2004",
"title": "Geometry of the Casimir Effect",
"url": "https://arxiv.org/abs/quant-ph/0408124"
},
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