2017/04/30 by Sebastian M. Dawid, R. Gonsior, Rafał Gonsior +4
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Cutoff #Eigenvalues and eigenvectors #Fixed point #Gaussian #Hamiltonian (control theory) #Infrared fixed point #Mathematical analysis #Mathematical physics #Mathematics #Momentum (technical analysis) #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum electrodynamics #Quantum mechanics #Renormalization #Renormalization group #Singularity #Triviality #Universality (dynamical systems) #quant-ph
paper · pdf · doi:10.1016/j.physletb.2017.12.028
published as Physics Letters B 777 (2018) 260 · 6 pages, 3 figures
openalex publication_date 2017/12/14 · arxiv created 2017/12/21 · arxiv updated 2017/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Schrödinger equation with potential −g/r2 exhibits a limit cycle, described in the literature in a broad range of contexts using various regularizations of the singularity at r=0. Instead, we use the renormalization group transformation based on Gaussian elimination, from the Hamiltonian eigenvalue problem, of high momentum modes above a finite, floating cutoff scale. The procedure identifies a richer structure than the one we found in the literature. Namely, it directly yields an equation that determines the renormalized Hamiltonians as functions of the floating cutoff: solutions to this equation exhibit, in addition to the limit-cycle, also the asymptotic-freedom, triviality, and fixed-point behaviors, the latter in vicinity of infinitely many separate pairs of fixed points in different partial waves for different values of g.