Fermionic solutions of chiral Gross-Neveu and Bogoliubov-de Gennes systems in nonlinear Schrödinger hierarchy

Daisuke A. Takahashi, Shunji Tsuchiya, Ryosuke Yoshii, Muneto Nitta

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

The chiral Gross-Neveu model or equivalently the linearized Bogoliubov-de Gennes equation has been mapped to the nonlinear Schrödinger (NLS) hierarchy in the Ablowitz-Kaup-Newell-Segur formalism by Correa, Dunne and Plyushchay. We derive the general expression for exact fermionic solutions for all gap functions in the arbitrary order of the NLS hierarchy. We also find that the energy spectrum of the n-th NLS hierarchy generally has n+. 1 gaps. As an illustration, we present the self-consistent two-complex-kink solution with four real parameters and two fermion bound states. The two kinks can be placed at any position and have phase shifts. When the two kinks are well separated, the fermion bound states are localized around each kink in most parameter region. When two kinks with phase shifts close to each other are placed at distance as short as possible, the both fermion bound states have two peaks at the two kinks, i.e., the delocalization of the bound states occurs.

Original languageEnglish
Pages (from-to)632-637
Number of pages6
JournalPhysics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Volume718
Issue number2
DOIs
Publication statusPublished - 2012 Dec 5

Fingerprint

hierarchies
fermions
phase shift
energy spectra
formalism

Keywords

  • AKNS formalism
  • Bogoliubov-de Gennes equation
  • Chiral Gross-Neveu model
  • Nonlinear Schrödinger hierarchy

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Cite this

Fermionic solutions of chiral Gross-Neveu and Bogoliubov-de Gennes systems in nonlinear Schrödinger hierarchy. / Takahashi, Daisuke A.; Tsuchiya, Shunji; Yoshii, Ryosuke; Nitta, Muneto.

In: Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, Vol. 718, No. 2, 05.12.2012, p. 632-637.

Research output: Contribution to journalArticle

@article{7973f065fb884823823fc356cb6c8538,
title = "Fermionic solutions of chiral Gross-Neveu and Bogoliubov-de Gennes systems in nonlinear Schr{\"o}dinger hierarchy",
abstract = "The chiral Gross-Neveu model or equivalently the linearized Bogoliubov-de Gennes equation has been mapped to the nonlinear Schr{\"o}dinger (NLS) hierarchy in the Ablowitz-Kaup-Newell-Segur formalism by Correa, Dunne and Plyushchay. We derive the general expression for exact fermionic solutions for all gap functions in the arbitrary order of the NLS hierarchy. We also find that the energy spectrum of the n-th NLS hierarchy generally has n+. 1 gaps. As an illustration, we present the self-consistent two-complex-kink solution with four real parameters and two fermion bound states. The two kinks can be placed at any position and have phase shifts. When the two kinks are well separated, the fermion bound states are localized around each kink in most parameter region. When two kinks with phase shifts close to each other are placed at distance as short as possible, the both fermion bound states have two peaks at the two kinks, i.e., the delocalization of the bound states occurs.",
keywords = "AKNS formalism, Bogoliubov-de Gennes equation, Chiral Gross-Neveu model, Nonlinear Schr{\"o}dinger hierarchy",
author = "Takahashi, {Daisuke A.} and Shunji Tsuchiya and Ryosuke Yoshii and Muneto Nitta",
year = "2012",
month = "12",
day = "5",
doi = "10.1016/j.physletb.2012.10.058",
language = "English",
volume = "718",
pages = "632--637",
journal = "Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics",
issn = "0370-2693",
publisher = "Elsevier",
number = "2",

}

TY - JOUR

T1 - Fermionic solutions of chiral Gross-Neveu and Bogoliubov-de Gennes systems in nonlinear Schrödinger hierarchy

AU - Takahashi, Daisuke A.

AU - Tsuchiya, Shunji

AU - Yoshii, Ryosuke

AU - Nitta, Muneto

PY - 2012/12/5

Y1 - 2012/12/5

N2 - The chiral Gross-Neveu model or equivalently the linearized Bogoliubov-de Gennes equation has been mapped to the nonlinear Schrödinger (NLS) hierarchy in the Ablowitz-Kaup-Newell-Segur formalism by Correa, Dunne and Plyushchay. We derive the general expression for exact fermionic solutions for all gap functions in the arbitrary order of the NLS hierarchy. We also find that the energy spectrum of the n-th NLS hierarchy generally has n+. 1 gaps. As an illustration, we present the self-consistent two-complex-kink solution with four real parameters and two fermion bound states. The two kinks can be placed at any position and have phase shifts. When the two kinks are well separated, the fermion bound states are localized around each kink in most parameter region. When two kinks with phase shifts close to each other are placed at distance as short as possible, the both fermion bound states have two peaks at the two kinks, i.e., the delocalization of the bound states occurs.

AB - The chiral Gross-Neveu model or equivalently the linearized Bogoliubov-de Gennes equation has been mapped to the nonlinear Schrödinger (NLS) hierarchy in the Ablowitz-Kaup-Newell-Segur formalism by Correa, Dunne and Plyushchay. We derive the general expression for exact fermionic solutions for all gap functions in the arbitrary order of the NLS hierarchy. We also find that the energy spectrum of the n-th NLS hierarchy generally has n+. 1 gaps. As an illustration, we present the self-consistent two-complex-kink solution with four real parameters and two fermion bound states. The two kinks can be placed at any position and have phase shifts. When the two kinks are well separated, the fermion bound states are localized around each kink in most parameter region. When two kinks with phase shifts close to each other are placed at distance as short as possible, the both fermion bound states have two peaks at the two kinks, i.e., the delocalization of the bound states occurs.

KW - AKNS formalism

KW - Bogoliubov-de Gennes equation

KW - Chiral Gross-Neveu model

KW - Nonlinear Schrödinger hierarchy

UR - http://www.scopus.com/inward/record.url?scp=84869886917&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84869886917&partnerID=8YFLogxK

U2 - 10.1016/j.physletb.2012.10.058

DO - 10.1016/j.physletb.2012.10.058

M3 - Article

AN - SCOPUS:84869886917

VL - 718

SP - 632

EP - 637

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

IS - 2

ER -