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

N1 - Funding Information:
We would like to thank G. Marmorini and T. Mizushima for useful discussions, and J. Feinberg and M. Thies for valuable comments. This work is supported in part by KAKENHI , Nos. 23740198 (MN) , 23103515 (MN) and 24740276 (ST) .

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

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U2 - 10.1016/j.physletb.2012.10.058

DO - 10.1016/j.physletb.2012.10.058

M3 - Article

AN - SCOPUS:84869886917

SN - 0370-2693

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

IS - 2

ER -