Quantum breathing mode of trapped bosons and fermions at arbitrary coupling

An analysis of the quantum breathing behavior of few-particle Coulomb systems in one- and two-dimensional harmonic traps is presented. We report the existence of \emph{two independent breathing modes} and present exact numerical results for two particles at any coupling strength which smoothly connect the two known limits of an \emph {ideal} quantum and a strongly coupled \emph {classical} system. Substantial differences in the breathing frequency of two-dimensional fermions and bosons are observed which may be used as a sensitive experimental tool to probe confined interacting quantum systems.