An analytical expression for the quantum breathing frequency ${\omega }_b$ of harmonically trapped quantum particles with inverse power-law repulsion is derived. It is verified by ab initio numerical calculations for electrons confined in a lateral (2D) quantum dot. We show how this relation can be used to express the ground state properties of harmonically trapped quantum particles as functions of the breathing frequency by presenting analytical results for the kinetic, trap, and repulsive energy and for the linear entropy. Measurement of ${\omega }_b$ together with these analytical relations represents a tool to characterize the state of harmonically trapped interacting particles—from the Fermi gas to the Wigner crystal regime.

• Received 7 November 2012

DOI:https://doi.org/10.1103/PhysRevLett.111.256801