Quantum breathing mode of interacting particles in a one-dimensional harmonic trap

Extending our previous work, we explore the breathing mode-the (uniform) radial expansion and contraction of a spatially confined system. We study the breathing mode across the transition from weak to moderate couplings and confirm that its frequency is not independent of the pair interaction strength (coupling parameter). We present the results of time-dependent Hartree-Fock simulations for 2 to 20 fermions with Coulomb interaction and show that the breathing frequency has a minimum for a small particle number. We validate the accuracy of our results, comparing them to exact configuration interaction results for up to eight particles.