Transparent Dirac potentials in one dimension: the time-dependent case

Abstract

We generalize the original derivation of transparent, static Schroedinger potentials by Kay and Moses, to obtain a large class of time-dependent transparent Dirac potentials in one spatial dimension. They contain all known transparent potentials as special cases and play a key role in the semi-classical solution of 1+1 dimensional, fermionic quantum field theories of Gross-Neveu and Nambu-Jona-Lasinio type.

9 pages, no figure

References in corpus (4)

• Self-consistent multiple complex-kink solutions in Bogoliubov-de Gennes and chiral Gross-Neveu systems
• Time-Dependent Hartree-Fock Solution of Gross-Neveu models: Twisted Kink Constituents of Baryons and Breathers
• Fermionic solutions of chiral Gross-Neveu and Bogoliubov-de Gennes systems in nonlinear Schrödinger hierarchy
• Exact solution of N baryon problem in the Gross-Neveu model

Cited by in corpus (16)

• Super-Klein tunneling of Dirac fermions through electrostatic gratings in graphene
• Moving solitons in a one-dimensional fermionic superfluid
• Transmutations of supersymmetry through soliton scattering, and self-consistent condensates
• Twisted kinks, Dirac transparent systems and Darboux transformations
• Full time-dependent Hartree-Fock solution of large N Gross-Neveu models
• Fermion in a multi-kink-antikink soliton background, and exotic supersymmetry
• Integrable Gross-Neveu models with fermion-fermion and fermion-antifermion pairing
• Bogoliubov-de Gennes Soliton Dynamics in Unconventional Fermi Superfluids
• Exhaustive derivation of static self-consistent multi-soliton solutions in the matrix Bogoliubov-de Gennes systems
• Non-Abelian twisted kinks in chiral Gross-Neveu model with isospin
• Hamiltonian systems, Toda lattices, Solitons, Lax Pairs on weighted Z-graded graphs
• Lorentzian quantum wells in graphene: the role of shape invariance in zero-energy states trapping
• Solitons in lattice field theories via tight-binding supersymmetry
• Dark solitons of the Gross-Neveu model
• SU(N) affine Toda solitons and breathers from transparent Dirac potentials
• The soliton nature of the super-Klein tunneling effect