Photon Torpedoes and Rytov Pinwheels: Integral-Equation Modeling of Non-Equilibrium Fluctuation-Induced Forces and Torques on Nanoparticles

We present new theoretical tools, based on fluctuational electrodynamics and the integral-equation approach to computational electromagnetism, for numerical modeling of forces and torques on bodies of complex shapes and materials due to emission of thermal radiation out of thermal equilibrium. This extends our recently-developed fluctuating-surface-current (FSC) and fluctuating-volume-current (FVC) techniques for radiative heat transfer to the computation of non-equilibrium fluctuation-induced forces and torques; as we show, the extension is non-trivial due to the greater computational cost of modeling radiative momentum transfer, including new singularities that must be carefully neutralized. We introduce a new analytical cancellation technique that addresses these challenges and allows, for the first time, accurate and efficient prediction of non-equilibrium forces and torques on bodies of essentially arbitrary shapes---including asymmetric and chiral particles---and complex material properties, including continuously-varying and anisotropic dielectrics. We validate our approach by showing that it reproduces known results, then present new numerical predictions of non-equilibrium self-propulsion, self-rotation, and momentum-transfer phenomena in complex geometries that would be difficult or impossible to study with existing methods. Our findings indicate that the fluctuation-induced dynamics of micron-size room-temperature bodies in cold environments involve microscopic length scales but macroscopic time scales, with typical linear and angular velocities on the order of microns/second and radians/second; For a micron-scale gear driven by thermal radiation from a nearby chiral emitter, we find a strong and non-monotonic dependence of the magnitude and even the \textit{sign} of the induced torque on the temperature of the emitter.