Thermal Effects in the Casimir Torque between Birefringent Plates
Benjamin Spreng · Jeremy N. Munday
Abstract and summary · read the original at the source
In one page
Benjamin Spreng and Jeremy Munday, at the University of California, Davis, work out what temperature does to the Casimir torque. Two plates held a fraction of a micrometre apart feel the Casimir force, the pull the vacuum’s own fluctuations exert on them; if the plates are birefringent — crystals whose optical response depends on direction — those same fluctuations also try to twist the two into alignment. That twist has been measured in the laboratory once. Spreng and Munday add the thermal part of the fluctuation spectrum, which nobody had done for the torque, and find that it works against the quantum part rather than adding to it: for barium titanate at room temperature the torque falls by about 99.5 percent, a factor of two hundred, where the same thermal correction trims the ordinary Casimir force between metal plates by only about a third. Temperature also bends the torque away from its textbook angle dependence and, for two unlike crystals, can reverse which way it turns.
Why it matters hereChapter 2 rests on the vacuum being a real, structured medium, and the Casimir torque is its second mechanical signature: not only a pull between surfaces but a twist, sensitive to the direction the material faces. This paper says how strongly the thermal part of the spectrum fights the quantum part, which is exactly the design knob chapter 6 cares about — cool the apparatus and the vacuum torque grows while the Brownian noise shrinks, or hold the gap fixed and change the temperature to flip which way the vacuum turns your plate. The authors’ review of the field is on this site at /library/stm-58df236cfb.
What it claims
01Thermal fluctuations exert a Casimir torque that counteracts the torque coming from quantum vacuum fluctuations, so raising the temperature diminishes rather than adds to the twist: between two barium titanate plates at 300 kelvin the torque is reduced by up to about 99.5 percent, roughly a two-hundred-fold reduction, and the ratio of the 300-kelvin torque to the zero-temperature torque bottoms out near 0.005.Abstract; Figure 1(c) and 1(d)
Published and peer-reviewed02The reduction is far larger than the corresponding thermal correction to the Casimir force between isotropic surfaces, where the same ratio is about 0.69 for two metallic plates and about 0.76 for a sphere and a plane — so lowering the temperature raises the torque signal while lowering the Brownian noise, which favours low-temperature experiments for precise Casimir torque measurements.Paragraph following Figure 1(d), citing references 5 to 7
Published and peer-reviewed03The torque follows a one-over-distance-cubed power law at zero temperature and crosses over to a one-over-distance-squared law, linear in temperature, once the separation exceeds the thermal wavelength of about 7.6 micrometres at 300 kelvin, where only the zero-frequency Matsubara term survives and only the polarisation-preserving element of the reflection matrices contributes.Figure 1(c); Equations 2, 5 and 6
Published and peer-reviewed04For strongly birefringent plates the torque no longer follows the sine-of-twice-the-twist-angle dependence known for weakly birefringent ones: at room temperature and 10 micrometre separation the angle of maximum torque shifts well below 45 degrees, and the deviation grows both at separations beyond the thermal wavelength and at short separations.Figure 2(a) and 2(b)
Published and peer-reviewed05In a pair of unlike birefringent plates the torque reverses direction at a separation that itself depends on temperature — 1.17 micrometres at zero temperature and 1.87 micrometres at 300 kelvin for barium titanate against calcium carbonate — so at a fixed gap of 1.7 micrometres the torque can be tuned from 24 femtonewton-metres per square metre at 100 kelvin to minus 12 at 400 kelvin by changing temperature alone, which the authors offer as a guide for designing a separation sensor read out through the Casimir torque.Figure 4(a) and 4(b); closing paragraph before the summary
Designed, not yet built06The Casimir torque has been verified experimentally only once, between a birefringent plate and a liquid crystal, and a recent self-alignment result on triangular platelets did not reach quantitative agreement with theory; the torque magnitudes computed here for barium borate against barium titanate lie within the range of an already proposed Casimir torque experiment, which is where the thermal prediction would be tested.Introduction, citing references 18 and 19; closing paragraph, citing reference 25
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Read it · abstract
Abstract
The Casimir effect, originating from quantum and thermal fluctuations, is well known for inducing forces between closely spaced surfaces. When these surfaces are optically anisotropic, these interactions can produce a Casimir torque that rotates the surfaces relative to each other. We investigate, for the first time, the influence of thermal fluctuations on the Casimir torque between birefringent plates. Our results reveal that thermal modes significantly diminish the torque, with reductions up to 2 orders of magnitude for highly birefringent materials. Temperature is also shown to alter the angular dependence of the torque, significantly deviating from the typical sinusoidal behavior, and becomes particularly important at large separations that exceed the thermal wavelength. Finally, we demonstrate that systems of dissimilar birefringent plates that exhibit a distance-dependent reversal in the torque’s direction can enable precise control of the torque’s magnitude and sign through temperature manipulation. These findings advance our understanding of quantum and thermal fluctuation interplay and provide a framework for designing innovative nanoscale sensors and devices leveraging Casimir torque phenomena.
Benjamin Spreng and Jeremy N. Munday, Department of Electrical and Computer Engineering, University of California, Davis. Published as Physical Review Letters 135, 013602 (2025); preprint arXiv:2507.02184.
(Abstract only — see the rights note above for why the full text is not reproduced here. The complete Letter, with the four figures carrying the dielectric functions, the torque against separation, the angular dependence, the high-temperature parameter map and the dissimilar-plate sign reversal, together with the Supplemental Material giving the reflection matrix for a diagonal dielectric tensor, is at the source. The authors’ review of the field is on this site at /library/stm-58df236cfb.)
The way in
https://doi.org/10.1103/32gq-dbmsLICENCE. Published as Physical Review Letters 135, 013602 (2 July 2025); the Crossref record carries the APS default licence and the APS default accepted-manuscript licence, and the preprint, arXiv:2507.02184 submitted 2 July 2025, carries the arXiv.org perpetual non-exclusive distribution licence. No Creative Commons statement appears in the text or on the arXiv record, so this page holds the summary, the claims and the authors’ own abstract and sends the reader to the source. The claims below are read from the preprint text. The same group’s review of the field, ’Recent developments on the Casimir torque’, is on this site at /library/stm-58df236cfb.
How to cite it
Benjamin Spreng, Jeremy N. Munday (2025) Thermal Effects in the Casimir Torque between Birefringent Plates. doi:10.1103/32gq-dbms
Where it sits in the curriculum