Fermion in a multi-kink-antikink soliton background, and exotic supersymmetry

Abstract

We construct a fermion system in a multi-kink-antikink soliton background, and present in an explicit form all its trapped configurations (bound state solutions) as well as scattering states. This is achieved by exploiting an exotic N=4 centrally extended nonlinear supersymmetry of completely isospectral pairs of reflectionless Schrodinger systems with potentials to be n-soliton solutions for the Korteweg-de Vries equation. The obtained reflectionless Dirac system with a position-dependent mass is shown to possess its own exotic nonlinear supersymmetry associated with the matrix Lax-Novikov operator being a Darboux-dressed momentum. In the process, we get an algebraic recursive representation for the multi-kink-antikink backgrounds, and establish their relation to the the modified Korteweg-de Vries equation. We also indicate how the results can be related to the physics of self-consistent condensates based on the Bogoliubov-de Gennes equations.

26 pages, 3 figures; acknowledgement added

References in corpus (11)

• Self-consistent crystalline condensate in chiral Gross-Neveu and Bogoliubov-de Gennes systems
• Self-isospectrality, special supersymmetry, and their effect on the band structure
• Aharonov-Bohm effect on AdS_2 and nonlinear supersymmetry of reflectionless Poschl-Teller system
• Finite-gap systems, tri-supersymmetry and self-isospectrality
• Remarks on bell-shaped lumps: stability and fermionic modes
• Self-consistent multiple complex-kink solutions in Bogoliubov-de Gennes and chiral Gross-Neveu systems
• Effect of scalings and translations on the supersymmetric quantum mechanical structure of soliton systems
• Time-Dependent Hartree-Fock Solution of Gross-Neveu models: Twisted Kink Constituents of Baryons and Breathers
• Transparent Dirac potentials in one dimension: the time-dependent case
• Gross-Neveu Models, Nonlinear Dirac Equations, Surfaces and Strings
• Stretching the electron as far as it will go

Cited by in corpus (16)

• $PT$-symmetric invisible defects and confluent Darboux-Crum transformations
• Chiral asymmetry in propagation of soliton defects in crystalline backgrounds
• Transmutations of supersymmetry through soliton scattering, and self-consistent condensates
• Perfectly invisible $\mathcal{P}\mathcal{T}$-symmetric zero-gap systems, conformal field theoretical kinks, and exotic nonlinear supersymmetry
• Twisted kinks, Dirac transparent systems and Darboux transformations
• Soliton defects in one-gap periodic system and exotic supersymmetry
• Rational deformations of conformal mechanics
• Particle in a self-dual dyon background: hidden free nature, and exotic superconformal symmetry
• Conformal bridge transformation and PT symmetry
• Pöschl-Teller Hamiltonian: Gazeau-Klauder type coherent states, related statistics and geometry
• Nonlinear supersymmetry as a hidden symmetry
• An exactly soluble model of a shallow double well
• A Relation Between $Z_3$-Graded Symmetry and Shape Invariant Supersymmetric Systems
• Localized Fermions on Superconducting Domain Walls and Extended Supersymmetry with non-trivial Topological Charges
• Fermions in a Reissner-Nordström-anti-de Sitter Black Hole Background and $N=4$ Supersymmetry with non-trivial Topological Charges
• Supersymmetric construction of self-consistent condensates in large N GN model: solitons on finite-gap potentials