2006/10/31 by Shoichi Sasaki, Takeshi Yamazaki · 50 citations
Mathematics · Physics and Astronomy · #Bound state #Energy (signal processing) #Finite volume method #Geometry #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Scattering #Sign (mathematics) #Theoretical and Computational Physics #Upper and lower bounds #Volume (thermodynamics) #hep-lat
paper · pdf · doi:10.1103/physrevd.74.114507
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 74(11) (American Physical Society) · 25 pages, 30 figures; v2: typos corrected and two references added, v3: final version to appear in PRD
openalex publication_date 2006/12/19 · arxiv created 2006/12/20 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We discuss formation of an S-wave bound state in finite volume on the basis of L"uscher's phase-shift formula. It is found that although a bound-state pole condition is fulfilled only in the infinite-volume limit, its modification by the finite-size corrections is exponentially suppressed by the spatial extent L in a finite box L3. We also confirm that the appearance of the S-wave bound state is accompanied by an abrupt sign change of the S-wave scattering length even in finite volume through numerical simulations. This distinctive behavior may help us to distinguish the loosely bound state from the lowest energy level of the scattering state in finite-volume simulations.