### 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 language | English |
---|---|

Pages (from-to) | 632-637 |

Number of pages | 6 |

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

Volume | 718 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2012 Dec 5 |

### Fingerprint

### 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

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

*718*(2), 632-637. https://doi.org/10.1016/j.physletb.2012.10.058

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

Research output: Contribution to journal › Article

*Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics*, vol. 718, no. 2, pp. 632-637. https://doi.org/10.1016/j.physletb.2012.10.058

}

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 -