Harmonic potential theorem: \\extension to spin-, velocity- and density-dependent interactions

Abstract

One of the few exact results for the description of the time-evolution of an inhomogeneous, interacting many-particle system is given by the Harmonic Potential Theorem (HPT). The relevance of this theorem is that it sets a tight constraint on time-dependent many-body approximations. In this contribution, we show that the original formulation of the HPT is valid also for the case of spin-, velocity- and density-dependent interactions. This result is completely general and relevant, among the rest, for nuclear structure theory both in the case of ab initio and of more phenomenological approaches. As an example, we report on a numerical implementation by testing the small-amplitude limit of the time-dependent Hartree-Fock -- also known as Random Phase Approximation (RPA) -- for the translational frequencies of a neutron system trapped in a harmonic potential.

arXiv comment5 pages, 1 figure. Submitted to Phys. Rev. Lett

References in corpus (22)

• Modern Theory of Nuclear Forces
• Half-metallic ferromagnets: From band structure to many-body effects
• Exotic modes of excitation in atomic nuclei far from stability
• Current-dependent exchange-correlation potential for dynamical linear response theory
• From low-momentum interactions to nuclear structure
• Three-body forces: From cold atoms to nuclei
• Chiral interactions up to next-to-next-to-next-to-leading order and nuclear saturation
• Microscopic determination of the nuclear incompressibility within the non-relativistic framework
• Chiral Three-Nucleon Interactions in Light Nuclei, Neutron-$\alpha$ Scattering, and Neutron Matter
• Nuclear Equation of State from ground and collective excited state properties of nuclei
• Electric dipole polarizability of ${}^{48}$Ca and implications for the neutron skin
• Spin-dependent phenomena and device concepts explored in (Ga,Mn)As
• A new Skyrme interaction with improved spin-isospin properties
• Center of mass and relative motion in time dependent density functional theory
• Cold neutrons trapped in external fields
• Universal features of dynamic heterogeneity in supercooled liquids
• Multi-speed prethermalization in spin models with power-law decaying interactions
• Properties of trapped neutrons interacting with realistic nuclear Hamiltonians
• Ab Initio study of neutron drops with chiral Hamiltonians
• Relativistic Brueckner-Hartree-Fock theory for neutron drops
• Onset of the Limit Cycle and Universal Three-Body Parameter in Efimov Physics
• New density-independent interactions for nuclear structure calculations