2008/02/29 by Jérôme Roccia, Matthias Brack, M. Brack · 14 citations
Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Circular symmetry #Classical mechanics #Fermion #Geometry #Kinetic energy #Mathematical physics #Nuclear physics research studies #Orbit (dynamics) #Physics #Quantum #Quantum chaos and dynamical systems #Quantum electrodynamics #Quantum mechanics #Semiclassical physics #Simple (philosophy) #Symmetry (geometry) #Virial theorem #cond-mat.other #math-ph #math.MP #nlin.SI #nucl-th
paper · pdf · doi:10.1103/physrevlett.100.200408
published in Physical Review Letters 100(20), 200408 (American Physical Society) · LaTeX, 4 pages, 1 figure; to be published (in slightly shortened form) in Physical Review Letters; (v4) corrected misprint in eq. (21)
arxiv created 2008/05/06 · openalex publication_date 2008/05/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate the particle and kinetic-energy densities for N noninteracting fermions confined in a local potential. Using Gutzwiller's semiclassical Green function, we describe the oscillating parts of the densities in terms of closed nonperiodic classical orbits. We derive universal relations between the oscillating parts of the densities for potentials with spherical symmetry in arbitrary dimensions and a "local virial theorem" valid also for arbitrary nonintegrable potentials. We give simple analytical formulas for the density oscillations in a one-dimensional potential.