2012/05/01 by Simon Kreuzer, Sebastian Kreuzer, Harald W. Grießhammer · 2 citations
Mathematics · Physics and Astronomy · #Boson #Boundary (topology) #Boundary value problem #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Finite volume method #Lattice (music) #Mathematical analysis #Mathematics #Nuclear physics research studies #Periodic boundary conditions #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Scattering #hep-lat #nucl-th
paper · pdf · doi:10.1140/epja/i2012-12093-6
21 pages, 4 figures, 2 tables
arxiv created 2012/05/01 · openalex publication_date 2012/07/01 · arxiv updated 2016/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Lattice simulations of light nuclei necessarily take place in finite volumes, thus affecting their infrared properties. These effects can be addressed in a model-independent manner using Effective Field Theories. We study the model case of three identical bosons (mass m) with resonant two-body interactions in a cubic box with periodic boundary conditions, which can also be generalized to the three-nucleon system in a straightforward manner. Our results allow for the removal of finite volume effects from lattice results as well as the determination of infinite volume scattering parameters from the volume dependence of the spectrum. We study the volume dependence of several states below the break-up threshold, spanning one order of magnitude in the binding energy in the infinite volume, for box side lengths L between the two-body scattering length a and L = 0.25a. For example, a state with a three-body energy of -3/(ma2) in the infinite volume has been shifted to -10/(ma2) at L = a. Special emphasis is put on the consequences of the breakdown of spherical symmetry and several ways to perturbatively treat the ensuing partial wave admixtures. We find their contributions to be on the sub-percent level compared to the strong volume dependence of the S-wave component. For shallow bound states, we find a transition to boson-diboson scattering behavior when decreasing the size of the finite volume.