We provide further evidence for the nontrivial interplay between geometry and temperature in the Casimir effect. We investigate the temperature dependence of the Casimir force between an inclined semi-infinite plate above an infinite plate in D dimensions using the worldline formalism. Whereas the high-temperature behavior is always found to be linear in T in accordance with dimensional-reduction arguments, different power-law behaviors at small temperatures emerge. Unlike the case of infinite parallel plates, which shows the well-known T^D behavior of the force, we find a T^{D-1} behavior for inclined plates, and a ~T^{D-0.3} behavior for the edge effect in the limit where the plates become parallel. The strongest temperature dependence ~T^{D-2} occurs for the Casimir torque of inclined plates. Numerical as well as analytical worldline results are presented.Comment: 17 pages, 12 figures, revtex
We investigate the nontrivial interplay between geometry and temperature in the Casimir effect for the sphere-plate and cylinder-plate configurations. At low temperature, the thermal contribution to the Casimir force is dominated by this interplay, implying that standard approximation techniques such as the proximity force approximation (PFA) are inapplicable even in the limit of small surface separation. Thermal fluctuations on scales of the thermal wavelength lead to a delocalization of the thermal force density at low temperatures. As a consequence, the temperature dependence strongly differs from naive expectations. Most prominently, thermal forces can develop nonmonotonic behavior below a critical temperature. We perform a comprehensive study of such geothermal phenomena in these Casimir geometries, using analytical and numerical worldline techniques for Dirichlet scalar fluctuations.
The geometry dependence of Casimir forces is significantly more pronounced in the presence of thermal fluctuations due to a generic geometry-temperature interplay. We show that the thermal force for standard sphere-plate or cylinder-plate geometries develops a non-monotonic behavior already in the simple case of a fluctuating Dirichlet scalar. In particular, the attractive thermal force can increase for increasing distances below a critical temperature. This anomalous behavior is triggered by a reweighting of relevant fluctuations on the scale of the thermal wavelength. The essence of the phenomenon becomes transparent within the worldline picture of the Casimir effect. PACS numbers:Fluctuations of the radiation field between mesoscopic or macroscopic test bodies give rise to the fascinating Casimir effect [1] -a dispersive quantum and relativistic force phenomenon in the absence of net charges, see [2] for reviews. Experimental verifications [3] typically involve spheres or cylinders and plates. For standard materials, the Casimir force is generally attractive [4] and decreases monotonically with distance. The latter seems intuitively clear from spectral properties of the fluctuations: in this picture, the Casimir effect arises from the difference between the fluctuation spectrum in the presence of the surfaces and that of the trivial vacuum (at infinite surface separation). For increasing separation, the spectrum is expected to monotonically approach the vacuum spectrum, implying a monotonic force depletion.A first non-monotonic behavior has been observed in a more involved piston-like geometry of two squares moving between metal walls [5]; similar observations hold for two cylinders near a sidewall [6]. Here, the non-monotonic behavior arises from a competition between the TE and TM modes of the electromagnetic fluctuations. Its strength is governed by the dependence of the force on a lateral geometry parameter. The example demonstrates that an unexpected behavior of the Casimir force may occur in the presence of competing scales (in this case: normal and lateral distances).In this work, we show that a non-monotonic behavior already exists for a single fluctuating scalar obeying Dirichlet boundary conditions on the surfaces (similar to a TM mode in a cavity-like configuration). This anomalous phenomenon requires a nonzero temperature and occurs for the thermal contribution to the Casimir force which we abbreviate by "thermal force" in the following.This phenomenon is a prime example of the general geometry-temperature or geothermal interplay [7]. As first conjectured in [8], the thermal correction to the Casimir effect can vary qualitatively for different geometries, as both the zero-and finite-temperature Casimir effect are based on the underlying fluctuation spectrum. Analytical and numerical evidence for this geothermal interplay has been collected using perpendicular-or inclined-plates configurations [7,9,10]. At low temperatures, the temperature dependence is more pronounced in open geometries which do n...
The study shows that workplace health promotion (WHP) in German small and medium-sized enterprises is not yet installed to a wide extent. The smaller the enterprises the less WHP is found. The results are verified by similar studies. Small and medium-sized enterprises have a need for consultation in cases of illness or health prevention. But there is not yet an organised structure available for getting advice. The study is the basis for a national project "Gesunde Arbeit", which will establish these consulting structures.
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