Self-consistent multiple complex-kink solutions in Bogoliubov-de Gennes and chiral Gross-Neveu systems

TL;DR

This paper systematically finds all exact complex fermionic condensate solutions in 1+1D Bogoliubov-de Gennes and chiral Gross-Neveu models, revealing multi-kink configurations with quantized phase shifts.

Contribution

It provides a complete classification of self-consistent complex kink solutions, including their parameterization and phase quantization conditions.

Findings

Derived $n$ complex kink solutions with $2n$ parameters.

Established phase shift quantization by $rac{ ext{pi}}{N}$ for $N$ flavors.

Demonstrated arbitrary placement of solitons while maintaining self-consistency.

Abstract

We exhaust all exact self-consistent solutions of complex-valued fermionic condensates in the 1+1 dimensional Bogoliubov-de Gennes and chiral Gross-Neveu systems under uniform boundary conditions. We obtain $n$ complex (twisted) kinks, or grey solitons, with $2n$ parameters corresponding to their positions and phase shifts. Each soliton can be placed at an arbitrary position while the self-consistency requires its phase shift to be quantized by $\pi/N$ for $N$ flavors.