The Bogoliubov/de Gennes system, the AKNS hierarchy, and nonlinear quantum mechanical supersymmetry

Abstract

We show that the Ginzburg-Landau expansion of the grand potential for the Bogoliubov-de Gennes Hamiltonian is determined by the integrable nonlinear equations of the AKNS hierarchy, and that this provides the natural mathematical framework for a hidden nonlinear quantum mechanical supersymmetry underlying the dynamics.

25 pages, 4 figures; published version

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• Spectral singularities in PT-symmetric periodic finite-gap systems
• Inhomogeneous charged pion condensation phenomenon in the NJL${}_2$ model with quark number and isospin chemical potentials
• Self-consistent multiple complex-kink solutions in Bogoliubov-de Gennes and chiral Gross-Neveu systems
• Symmetry Protected Topological Superfluid ${}^3$He-B
• Classical torus conformal block, N=2* twisted superpotential and the accessory parameter of Lame equation
• Chiral density waves in the NJL${}_2$ model with quark number and isospin chemical potentials
• Effect of scalings and translations on the supersymmetric quantum mechanical structure of soliton systems
• Exotic supersymmetry of the kink-antikink crystal, and the infinite period limit
• The origin of the hidden supersymmetry
• Klein tunneling in carbon nanostructures: a free particle dynamics in disguise
• Self-isospectrality, mirror symmetry, and exotic nonlinear supersymmetry
• Super-Klein tunneling of Dirac fermions through electrostatic gratings in graphene
• Properties of the massive Gross-Neveu model with nonzero baryon and isospin chemical potentials
• Spectrally isomorphic Dirac systems: graphene in electromagnetic field
• Supersymmetric twisting of carbon nanotubes
• Chiral asymmetry in propagation of soliton defects in crystalline backgrounds
• Fermionic solutions of chiral Gross-Neveu and Bogoliubov-de Gennes systems in nonlinear Schrödinger hierarchy
• Moving solitons in a one-dimensional fermionic superfluid
• Integrable model for density-modulated quantum condensates: solitons passing through a soliton lattice
• Transmutations of supersymmetry through soliton scattering, and self-consistent condensates
• Twisted kinks, Dirac transparent systems and Darboux transformations
• Higgs algebraic symmetry in the two-dimensional Dirac equation
• Multifaceted properties of Andreev bound states: Interplay of symmetry and topology
• Soliton defects in one-gap periodic system and exotic supersymmetry
• Full time-dependent Hartree-Fock solution of large N Gross-Neveu models
• Self-Consistent Large-$N$ Analytical Solutions of Inhomogneous Condensates in Quantum $\mathbb{C}{P}^{N-1}$ Model
• Gross-Neveu Models, Nonlinear Dirac Equations, Surfaces and Strings
• Generic matrix superpotentials
• Hidden superconformal symmetry of spinless Aharonov-Bohm system
• Schwarzian derivative treatment of the quantum second-order supersymmetry anomaly, and coupling-constant metamorphosis
• Carbon nanotubes in almost homogeneous transverse magnetic field: exactly solvable model
• Bogoliubov-de Gennes Soliton Dynamics in Unconventional Fermi Superfluids
• Nambu-Jona Lasinio and Nonlinear Sigma Models in Condensed Matter Systems
• Exhaustive derivation of static self-consistent multi-soliton solutions in the matrix Bogoliubov-de Gennes systems
• Reflectionless PT-symmetric potentials in the one-dimensional Dirac equation
• Matrix Superpotential Linear in Variable Parameter
• An Effective Field Theory Model for One-Dimensional $\mathrm{CH}$ Chains: Effects at Finite Chemical Potential, Temperature and External Zeeman Magnetic Field
• Finite-gap twists of carbon nanotubes and an emergent hidden supersymmetry
• Self-consistent Analytic Solutions in Twisted $\mathbb{C}{P}^{N-1}$ Model in the Large-$N$ Limit
• Suppression of superconductivity by inhomogeneous chiral condensation in the NJL${}_2$ model
• Nonlinear supersymmetry as a hidden symmetry
• Kink Crystalline Condensate and Multi-kink Solution in Holographic Superconductor
• Newton's equation of motion with quadratic drag force and Toda's potential as a solvable one
• Two-dimensional Dirac fermion in presence of an asymmetric vector potential
• Exotic nonlinear supersymmetry and integrable systems
• Tsunami Solitons Emerging from Superconducting Gap
• Aspects of coherent states of nonlinear algebras
• Coupled system of Dirac fermions with different Fermi velocities via composites of SUSY operators
• Solitons in lattice field theories via tight-binding supersymmetry
• Supersymmetric construction of self-consistent condensates in large N GN model: solitons on finite-gap potentials