Breathing dynamics for systems of interacting particles in the microcanonical and canonical descriptions

By means of a dynamical ansatz, we study the breathing dynamics in systems of trapped interacting particles in a unified context, including a wide range of power law interactions and interaction strengths, at linear and nonlinear levels. We present detailed numerical tests of the general theory, and, motivated by Magneto-Optical Traps modeling, we extend it to the case of space-dependent friction and diffusion.