The Infrared Limit Of The Srg Evolution And Levinson's Theorem

dc.creatorArriola E.R.
dc.creatorSzpigel S.
dc.creatorTimoteo V.S.
dc.date2014
dc.date2015-06-25T18:03:59Z
dc.date2015-11-26T15:06:18Z
dc.date2015-06-25T18:03:59Z
dc.date2015-11-26T15:06:18Z
dc.date.accessioned2018-03-28T22:16:48Z
dc.date.available2018-03-28T22:16:48Z
dc.identifier
dc.identifierPhysics Letters, Section B: Nuclear, Elementary Particle And High-energy Physics. Elsevier, v. 735, n. , p. 149 - 156, 2014.
dc.identifier3702693
dc.identifier10.1016/j.physletb.2014.06.032
dc.identifierhttp://www.scopus.com/inward/record.url?eid=2-s2.0-84902662517&partnerID=40&md5=97ebfbd88582574e66621a0cc7cb692b
dc.identifierhttp://www.repositorio.unicamp.br/handle/REPOSIP/88097
dc.identifierhttp://repositorio.unicamp.br/jspui/handle/REPOSIP/88097
dc.identifier2-s2.0-84902662517
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/1257213
dc.descriptionOn a finite momentum grid with N integration points p n and weights wn (n = 1, ..., N) the Similarity Renormalization Group (SRG) with a given generator G unitarily evolves an initial interaction with a cutoff λ on energy differences, steadily driving the starting Hamiltonian in momentum space Hn,m0=pn2δn,m+Vn,m to a diagonal form in the infrared limit (λ→0), Hn,mG,λ→0=Eπ(n)δn,m, where π(n) is a permutation of the eigenvalues E n which depends on G. Levinson's theorem establishes a relation between phase-shifts δ(p n) and the number of bound-states, n B, and reads δ(p1) - δ(p N) = n Bπ. 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 S01 and S13 channels. © 2014.
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dc.languageen
dc.publisherElsevier
dc.relationPhysics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
dc.rightsaberto
dc.sourceScopus
dc.titleThe Infrared Limit Of The Srg Evolution And Levinson's Theorem
dc.typeArtículos de revistas


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