Singularities in radiative heat generation and interaction forces for two rotating nanoparticles caused by the anomalous Doppler effect

The quantum heat generation, interaction force, and friction torque for two rotating spherical nanoparticles with the radius $R$ are calculated. In contrast to a static case where an upper bound in the radiative heat transfer between two particles exists, the quantum heat generation for two rotating particles diverges at distances between particles $d <d_0= R(3/\varepsilon''(\omega_0))^{1/3}$ (where $\varepsilon''(\omega_0)$ is the imaginary part of the dielectric function for the material of a particle at the resonance frequency $\omega_0$), when the rotation frequency coincides with poles in the excitation generation rate at $\Omega=2\omega_0$. These poles are due to the anomalous Doppler effect and the mutual polarization of particles and exist even in the presence of dissipation in particles. The anomalous heat generation is associated with the conversion of mechanical rotation energy into heat mediated by quantum friction. Similar singularities also exist for the interaction force and friction torque. The results can be of significant importance for biomedical applications.