Full time-dependent Hartree-Fock solution of large N Gross-Neveu models

Abstract

We find the general solution to the time-dependent Hartree-Fock problem for scattering solutions of the Gross-Neveu models, with both discrete (GN_2) and continuous (NJL_2) chiral symmetry. We find new multi-breather solutions both for the GN_2 model, generalizing the Dashen-Hasslacher-Neveu breather solution, and also new twisted breathers for the NJL_2 model. These solutions satisfy the full TDHF consistency conditions, and only in the special cases of GN_2 kink scattering do these conditions reduce to the integrable Sinh-Gordon equation. We also show that all baryons and breathers are composed of constituent twisted kinks of the NJL_2 model. Our solution depends crucially on a general class of transparent, time dependent Dirac potentials found recently by algebraic methods.

24 pages, 12 figures; 1 figure and 11 animations as ancillary files; v2: 6 ancillary files renamed

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Cited by in corpus (18)

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• 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
• Nambu-Jona Lasinio and Nonlinear Sigma Models in Condensed Matter Systems
• Non-Abelian twisted kinks in chiral Gross-Neveu model with isospin
• Gross-Neveu model with O(2)${}_L\times$O(2)${}_R$ chiral symmetry: Duality with Zakharov-Mikhailov model and large $N$ solution
• Beyond integrability: Baryon-baryon backward scattering in the massive Gross-Neveu model
• Twisted kink dynamics in multiflavor chiral Gross-Neveu model
• On instability of ground states in 2D CP(N-1) and O(N) models at large N
• Tsunami Solitons Emerging from Superconducting Gap
• Dark solitons of the Gross-Neveu model
• Supersymmetric construction of self-consistent condensates in large N GN model: solitons on finite-gap potentials
• Detecting inhomogeneous chiral condensation from the bosonic two-point function in the $(1+1)$-dimensional Gross-Neveu model in the mean-field approximation
• The soliton nature of the super-Klein tunneling effect
• SU(N) affine Toda solitons and breathers from transparent Dirac potentials