Quantum Breathing Mode of Trapped Systems in One and Two Dimensions

We investigate the quantum breathing mode (monopole oscillation) of trapped fermionic particles with Coulomb and dipole interaction in one and two dimensions. This collective oscillation has been shown to reveal detailed information on the many-particle state of interacting trapped systems and is thus a sensitive diagnostics for a variety of finite systems, including cold atomic and molecular gases in traps and optical lattics, electrons in metal clusters and in quantum confined semiconductor structures or nanoplasmas. An improved sum rule formalism allows us to accurately determine the breathing frequencies from the ground state of the system, avoiding complicated time-dependent simulations. In combination with the Hartree-Fock and the Thomas-Fermi approximations this enables us to extend the calculations to large particle numbers N on the order of several million. Tracing the breathing frequency to large N as a function of the coupling parameter of the system reveals a surprising difference of the asymptotic behavior of one-dimensional and two-dimensional harmonically trapped Coulomb systems.