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 the ideal quantum to the classical regime and confirm that it 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 how the quantum breathing mode depends on the particle number. We validate the accuracy of our results, comparing them to exact Configuration Interaction results for up to 8 particles. 
Jan Willem Abraham, Karsten Balzer, David Hochstuhl, and Michael   Bonitz
cond-mat.str-el physics.plasm-ph