2005/08/23 by Dae-Yup Song · 3 citations
Mathematics · Physics and Astronomy · #Anharmonicity #Atomic and Subatomic Physics Research #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Electron #Fermi gas #Geometry #Harmonic #Harmonic oscillator #Invariant (physics) #Inverse #Isotropy #Mathematics #Physics #Quantum #Quantum mechanics #Quantum, superfluid, helium dynamics #Simple harmonic motion #cond-mat.mes-hall #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreva.72.023614
published in Physical Review A 72(2) (American Physical Society) · Typos in the printed verions are corrected
openalex publication_date 2005/08/23 · arxiv created 2006/09/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Single-component quantum gas confined in a harmonic potential, but otherwise isolated, is considered. From the invariance of the system of the gas under a displacement-type transformation, it is shown that the center of mass oscillates along a classical trajectory of a harmonic oscillator. It is also shown that this harmonic motion of the center has, in fact, been implied by Kohn's theorem. If there is no interaction between the atoms of the gas, the system in a time-independent isotropic potential of frequency \ensuremathνc is invariant under a squeeze-type unitary transformation, which gives collective radial breathing motion of frequency 2\ensuremathνc to the gas. The amplitudes of the oscillating and breathing motions from the exact invariances could be arbitrarily large. For a Fermi system, appearance of 2\ensuremathνc mode of the large breathing motion indicates that there is no interaction between the atoms, except for a possible long-range interaction through the inverse-square-type potential.