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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

The infrared limit of the SRG evolution and Levinson's theorem

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Ruiz Arriola, E. [1, 2] ; Szpigel, S. [3] ; Timoteo, V. S. [4]
Total Authors: 3
[1] Univ Granada, Dept Fis Atom Mol & Nucl, E-18071 Granada - Spain
[2] Univ Granada, Inst Carlos Fis Teor & Computac 1, E-18071 Granada - Spain
[3] Univ Presbiteriana Mackenzie, Escola Engn, Ctr Radioastron & Astrofis Mackenzie, Sao Paulo - Brazil
[4] Univ Estadual Campinas, UNICAMP, Grp Opt & Modelagem Numer GOMNI, Fac Tecnol FT, BR-13081970 Campinas, SP - Brazil
Total Affiliations: 4
Document type: Journal article
Source: Physics Letters B; v. 735, p. 149-156, JUL 30 2014.
Web of Science Citations: 4

On a finite momentum grid with N integration points p(n) and weights w(n) (n = 1,..., N) the Similarity Renormalization Group (SRG) with a given generator G unitarily evolves an initial interaction with a cutoff lambda on energy differences, steadily driving the starting Hamiltonian in momentum space H-n,m(0) = p(n)(2)delta(n,m) + V-n,(m) to a diagonal form in the infrared limit (lambda -> 0), H-n,m(G,lambda -> 0) = E-pi(n) delta(n),(m), where pi(n) is a permutation of the eigenvalues E-n which depends on G. Levinson's theorem establishes a relation between phase-shifts delta(p(n)) and the number of bound-states, n(B), and reads delta(p(1)) - delta(p(N)) = n(B)pi. We show that unitarily equivalent Hamiltonians on the grid generate reaction matrices which are compatible with Levinson's theorem but are phase-inequivalent along the SRG trajectory. An isospectral definition of the phase-shift in terms of an energy-shift is possible but requires in addition a proper ordering of states on a momentum grid such as to fulfill Levinson's theorem. We show how the SRG with different generators G induces different isospectral flows in the presence of bound-states, leading to distinct orderings in the infrared limit. While the Wilson generator induces an ascending ordering incompatible with Levinson's theorem, the Wegner generator provides a much better ordering, although not the optimal one. We illustrate the discussion with the nucleon-nucleon (NN) interaction in the S-1(0) and S-3(1) channels. (C) 2014 The Authors. Published by Elsevier B. V. (AU)

FAPESP's process: 11/18211-2 - The nuclear force and the renormalization group
Grantee:Varese Salvador Timoteo
Support type: Regular Research Grants
FAPESP's process: 14/04975-9 - From two-nucleon forces to light nuclei with the similarity renormalization group
Grantee:Varese Salvador Timoteo
Support type: Regular Research Grants