Time-dependent Ginzburg-Landau Equation in the Nambu--Jona-Lasinio Model

TL;DR

This paper derives time-dependent Ginzburg-Landau equations for the chiral order parameter within the Nambu--Jona-Lasinio model using the closed time-path Green function formalism, connecting microscopic parameters to macroscopic dynamics.

Contribution

It introduces a novel derivation of the Ginzburg-Landau and time-dependent Ginzburg-Landau equations directly from the NJL model without additional parameters.

Findings

Derived the gap equation for quark condensate in stationary systems.

Obtained the Ginzburg-Landau and TDGL equations for inhomogeneous systems.

No extra parameters introduced beyond the original NJL model.

Abstract

We apply the closed time-path Green function formalism in the Nambu--Jona-Lasinio model. First of all, we use this formalism to obtain the well-known gap equation for the quark condensate in a stationary homogeneous system. We have also used this formalism to obtain the Ginzburg-Landau (GL) equation and the time-dependent Ginzburg-Landau (TDGL) equation for the chiral order parameter in an inhomogeneous system. In our derived GL and TDGL equations, there is no other parameters except for those in the original NJL model.