Ginsburg-Landau equation for an interacting quark gas

Publisher Website
Google Scholar
Abstract
A Dyson-equation formalism is used to describe particle-antiparticle pairing in a inhomogeneous quark gas. Explicit correspondence with the Bogoliubov-Valatin variational procedure is demonstrated in the limit of pairing in a homogeneous medium of infinite extent. For a weakly inhomogeneous medium, the analog of the Ginsburg-Landau equation for a superconductor is derived for the quark-pair density function. A solution to this equation may be constructed that corresponds to a localized region of normal vacuum embedded in a condensate of infinite extent, and is reminiscent in form to the soliton field commonly employed in phenomenological σ models. It is shown that the surface thickness λ separating the normal and condensed vacua is related to the inverse of the spread of momenta over which pairing occurs. A value of λ≃2.5 fm is obtained from numerical results of Adler and Davis for a linear confining potential.