# Anomalous Doppler Effect Singularities in the Radiative Heat Generation, Interaction Force and Frictional Torque for two Rotating Nanoparticles

## TL;DR

This paper investigates the divergence in heat generation, force, and torque between two rotating nanoparticles caused by anomalous Doppler effect singularities, revealing critical behavior at specific angular velocities.

## Contribution

It introduces the concept of anomalous Doppler effect singularities in rotating nanoparticles, showing divergence in radiative heat transfer, force, and torque at specific velocities, a novel insight into nanoparticle interactions.

## Key findings

- Heat generation rate diverges at specific angular velocities.
- Singularities occur due to the anomalous Doppler effect and mutual polarization.
- Results are relevant for biomedical applications.

## Abstract

We calculate the quantum heat generation, the interaction force and the frictional torque for two rotating spherical nanoparticles with a radius $R$. In contrast to the static case, when there is an upper limit in the radiative heat transfer between the particles, for two rotating nanoparticles the quantum heat generation rate diverges when the angular velocity becomes equal to the poles in the photon emission rate. These poles arise for the separation $d <d_0= R(3/\varepsilon''(\omega_0))^{1/3}$ (where $\varepsilon''(\omega_0)$ is the imaginary part of the dielectric function for the particle material at the surface phonon or plasmon polariton frequency $\omega_0$ ) due to the anomalous Doppler effect and the mutual polarization of the particles and they exist even for the particles with losses. Similar singularities exist also for the interaction force and the frictional torque. The obtained results can be important for biomedical applications.