The pair-coupling model

Chen, H.; Song, Ting-Ting; Rowe, D.J.

doi:10.1016/0375-9474(94)00472-y

Cited by 23 publications

(22 citation statements)

References 27 publications

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“…In particular, an investigation of the U(n 1 + n 2 )/[U(n 1 ) ⊗ U(n 2 )] geometry of the models is necessary. While the coherent state analysis has been pursued extensively for the s-b models [2,16,38,39,56], only preliminary use of coherent states has so far been made for the generic pairing models [57].…”

Section: Discussionmentioning

confidence: 99%

Excited state quantum phase transitions in many-body systems

2008

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Phenomena analogous to ground state quantum phase transitions have recently been noted to occur among states throughout the excitation spectra of certain many-body models. These excited state phase transitions are manifested as simultaneous singularities in the eigenvalue spectrum (including the gap or level density), order parameters, and wave function properties. In this article, the characteristics of excited state quantum phase transitions are investigated. The finite-size scaling behavior is determined at the mean field level. It is found that excited state quantum phase transitions are universal to two-level bosonic and fermionic models with pairing interactions.

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Section: Discussionmentioning

confidence: 99%

Excited state quantum phase transitions in many-body systems

2008

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“…It turns out, as shown in refs. [1,2] that the function Φ s n is well-known in the theory of symmetric polynomials [15] as a Schur function (or S-function); such functions are the characters of fully antisymmetric irreps of the unitary groups and easy to derive. The definition…”

Section: Vcs Wave Functions Of Number-projected Statesmentioning

confidence: 99%

“…[1,2], this recursion relation is solved by making a change of variables from {z j } to the symmetric power functions…”

Section: Vcs Wave Functions Of Number-projected Statesmentioning

confidence: 99%

“…[1,2,15]. It follows from Claim 1 that the VCS wave function for a one quasi-particle state u j α † jm |x has values given by…”

Section: Vcs Wave Functions Of Number-projected Statesmentioning

confidence: 99%

“…However, it can be restored with relative ease in a coherent-state representation [1,2] in a manner that preserves much of the elegance and simplicity of the models.…”

Section: Introductionmentioning

confidence: 99%

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Restoration of particle number as a good quantum number in BCS theory

Rowe

2001

Nuclear Physics A

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As shown in previous work, number projection can be carried out analytically for states defined in a quasi-particle scheme when the states are expressed in a coherent state representation. The wave functions of number-projected states are well-known in the theory of orthogonal polynomials as Schur functions. Moreover, the functions needed in pairing theory are a particularly simple class of Schur functions that are easily constructed by means of recursion relations. It is shown that complete sets of states can be projected from corresponding quasi-particle states and that such states retain many of the properties of the quasi-particle states from which they derive. It is also shown that number projection can be used to construct a complete set of orthogonal states classified by generalized seniority for any nucleus.

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Dynamical symmetries of nuclear collective models

Rowe

1996

Progress in Particle and Nuclear Physics

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The pair-coupling model

Cited by 23 publications

References 27 publications

Excited state quantum phase transitions in many-body systems

Excited state quantum phase transitions in many-body systems

Restoration of particle number as a good quantum number in BCS theory

Dynamical symmetries of nuclear collective models

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