Quantum breathing mode of interacting particles in harmonic traps

The breathing mode – the uniform radial expansion and contraction of a system of interacting particles – is analyzed. Extending our previous work [Bauch et al 2009 Phys. Rev. B.80 054515] we present a systematic analysis of the breathing mode for fermions with an inverse power law interaction potential w(r) ~ r^−dwith d = 1,2,3 in the whole range of coupling parameters. The results thus cover the range from the ideal "gas" to the Wigner crystal-like state. In addition to exact results for two particles obtained from a solution of the time-dependent Schrödinger equation we present results for N = 4,6 from multiconfiguration time-dependent Hartree-Fock simulations.