d-dimensional Lüscher's formula and the near-threshold three-body states in a finite volume

2019/05/13 by Shangguo Zhu, Zhu, Shangguo, Shina Tan +1
Physics and Astronomy · #Atomic Physics (physics.atom-ph) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Nuclear Theory (nucl-th) #Quantum Gases (cond-mat.quant-gas) #Quantum and electron transport phenomena #Quantum, superfluid, helium dynamics

paper · pdf · doi:10.48550/arxiv.1905.05117

openalex publication_date 2019/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study two particles colliding in a d-dimensional finite volume and generalize Lüscher's formula to arbitrary d spatial dimensions. We obtain the s- and p-wave approximations of the generalized Lüscher's formula. For resonant s- or p-wave interactions, we analytically determine the energies of the low-lying states at large box size L. At s-wave resonance, we discover two low-lying states with nearly opposite energies, which are proportional to ± 1/L^d/2 for d≥ 5, or ± 1/L²√(ln L) for d=4. This provides important insights into the near-threshold states of three bosons at a three-body resonance in a 2- or higher-dimensional finite volume.

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