Spontaneous photon emission from a non-relativistic free charged particle in collapse models: A case study

We study the photon emission rate of a non relativistic charged particle interacting with an external classical noise through its position. Both the particle and the electromagnetic field are quantized. Under only the dipole approximation, the equations of motion can be solved exactly for a free particle, or a particle bounded by an harmonic pot ential. The physical quantity we will be interested in is the spectrum of the radiation emitt ed by the particle, due to the interaction with the noise. We will highlight several properties of the spectrum and clarify some issues appeared in the literature, regarding the exact mathematical formula of a spectrum for a free particle.