Theory of the quantum breathing mode in harmonic traps and its use as a diagnostic tool.
An analytical expression for the quantum breathing frequency ωb 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 ωb 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.
Department of Physics, University of Ottawa, Ottawa, Ontario K1N6N5, Canada.
C R
CR
McDonald
Department of Physics, University of Ottawa, Ottawa, Ontario K1N6N5, Canada.
G
G
Orlando
Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany.
J W
JW
Abraham
Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany.
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D
Hochstuhl
Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany.
M
M
Bonitz
Department of Physics, University of Ottawa, Ottawa, Ontario K1N6N5, Canada.
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Brabec