2009/05/31 by Kumar Abhinav, Chandrasekhar Bhamidipati, B. Chandrasekhar +3
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Dimension (graph theory) #Fermion #Geometry #Harmonic #Harmonic oscillator #Mathematics #Physics #Quantum many-body systems #Quantum mechanics #Quantum, superfluid, helium dynamics #Scaling #Symmetry (geometry) #Unitary state #cond-mat.other #cond-mat.quant-gas
paper · pdf · doi:10.1016/j.physleta.2016.12.018
published in Physics Letters A 381(5), 457-461 (Elsevier BV) · 5 pages, revamped version for clarity
arxiv created 2015/11/09 · openalex publication_date 2016/12/09 · arxiv updated 2017/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The correlated fermionic many-particle system, near infinite scattering length, reveals an underlying Heisenberg symmetry in one dimension, as compared to an SO(2,1) symmetry in two dimensions. This facilitates an exact map from the interacting to the non-interacting system, both with and without a harmonic trap, and explains the short-distance scaling behavior of the wave-function. Taking advantage of the phenomenological Calogero-Sutherland-type interaction, motivated by the density functional approach, we connect the ground-state energy shift, to many-body correlation effect. For the excited states, modes at integral values of the harmonic frequency ω, are predicted in one dimension, in contrast to the breathing modes with frequency 2ω in two dimensions.