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arXiv:2606.24723

Rotational Vacuum Friction of Nonabsorbing Particles

F. Javier García de Abajo, Alejandro Manjavacas

quant-phSubmitted Jun 23, 2026• Announced Jun 24, 2026
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Abstract

A nonabsorbing particle rotating in vacuum can lose angular momentum only by converting mechanical energy into electromagnetic radiation. Here, we develop a quantum theory of rotational vacuum friction for small lossless particles and show that axial symmetry qualitatively changes the leading dissipation channel. At zero temperature, the frictional torque scales as $M\proptoΩ^7$ with rotation frequency $\ Omega$ in anisotropic particles due to the emission of correlated photon pairs whose frequencies sum to $2Ω$, while a contribution to the torque linear in $\ Omega$ is found at finite temperature. In contrast, axisymmetric particles are protected against photon-assisted friction regardless of temperature.

Comments
13 pages, 3 figures, 54 references

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A nonabsorbing particle rotating in vacuum can lose angular momentum only by converting mechanical energy into electromagnetic radiation. Here, we develop a quantum theory of rotational vacuum friction for small lossless particles and show that axial symmetry qualitatively changes the leading dissipation channel. At zero temperature, the frictional torque scales as M∝Ω7M\proptoΩ^7M∝Ω7 with rotation frequency  Omega\ Omega Omega in anisotropic particles due to the emission of correlated photon pairs whose frequencies sum to 2Ω2Ω2Ω, while a contribution to the torque linear in  Omega\ Omega Omega is found at finite temperature. In contrast, axisymmetric particles are protected against photon-assisted friction regardless of temperature.
Casimir torque is conventionally associated with explicit breaking of rotational symmetry, arising from material dielectric anisotropy, geometric asymmetry, or externally applied fields that themselves break rotational invariance. Here we demonstrate a fundamentally different mechanism: an axially symmetric magnetic field can generate a Casimir torque by inducing an axially asymmetric Casimir energy - and can even reverse the torque's sign. Focusing on two-dimensional altermagnets, we show that a magnetic field applied perpendicular to the plane - while preserving in-plane rotational symmetry - activates an orientation-dependent vacuum interaction through the combined crystalline symmetry CnT\mathrm{C_n T}Cn​T inherent to altermagnetic order. The resulting torque emerges continuously and scales quadratically with the magnetic field strength. We further analyze its temperature and distance dependence, revealing scaling behaviors that are qualitatively different from those found in uniaxial bulk materials. Our results identify time-reversal symmetry breaking as a powerful route for engineering both the sign and strength of Casimir torque and establish altermagnets as an exciting platform for exploring phenomena driven by vacuum quantum fluctuations.
A fascinating effect belonging to the field of vacuum forces and fluctuations is that of quantum friction. It refers to the prediction of a dissipative force acting on a moving object due to the quantum vacuum field. In this work, we investigate rotational quantum friction where a diatomic polar molecule rotates around its own center of mass in free space. We quantize the rotational motion and investigate the resulting dissipation due to spontaneous decay. We find in the Markovian regime that a friction torque ∝Ω3\propto Ω^3∝Ω3 persists even for zero temperature, and in agreement with the classical result in the limit of large rotational quantum number lll. Within the non-Markovian short-time regime we find a friction ∝Ω\proptoΩ∝Ω.
Electromagnetic fluctuations can transfer not only energy but also angular momentum, leading to forces, torques, heat currents, and friction in out-of-equilibrium setups. In enclosing configurations, we show that if at least one of two objects is rotationally symmetric, the torque is bounded by heat transfer, since both arise from photon transfers with angular momentum ℏn\hbar nℏn and energy ℏω\hbarωℏω. With only one object assumed to be rotationally symmetric, it may be possible to obtain a nonzero torque with reciprocal media, but nonreciprocal media are required to break the symmetry between nnn and −n-n−n and produce a nonzero torque if both objects are rotationally symmetric. We then specialize to concentric cylinders with a nonreciprocal dielectric response and use Rytov fluctuational electrodynamics to express heat transfer and torque in terms of an angular-momentum-resolved flux density, Φn(ω)Φ_n(ω)Φn​(ω). We also analyze the conditions for stable levitation of the inner cylinder using the proximity force approximation, in the process obtaining a new analytic formula for the normal Casimir force between dilute plates at different temperatures. Finally, to find the extracted work in a contactless engine setup, we compute the fluctuation-induced friction for a slowly rotating inner cylinder, and we find a bound between torque, friction, and heat transfer. Due to this bound, the efficiency of the heat engine remains bounded by the Carnot limit.
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Quantum mechanics predicts the occurrence of random electromagnetic field fluctuations, or virtual photons, in vacuum. The exchange of virtual photons between two bodies in relative motion could lead to non-contact quantum vacuum friction or Casimir friction. Despite its theoretical significance, the non-contact Casimir frictional force has not been observed and its theoretical predictions have varied widely. In this work, we report the first measurement of the non-contact Casimir frictional force between two moving bodies. By employing two mechanical oscillators with resonant frequencies far lower than those in Lorentz models of electrons in dielectric materials, we have amplified the Casimir frictional force at low relative velocities by several orders of magnitude. We directly measure the non-contact Casimir frictional force between the two oscillators and show its linear dependence on velocity, proving the dissipative nature of Casimir friction. This advancement marks a pivotal contribution to the field of dissipative quantum electrodynamics and enhances our understanding of friction at the nanoscale.