  We review various connections between condensed matter systems with the
Nambu-Jona Lasinio model and nonlinear sigma models. The field theoretical
description of interacting systems offers a systematic framework to describe
the dynamical generation of condensates. Resent findings of a duality between
the Nambu-Jona Lasinio model and the nonlinear sigma model enables us to
investigate various properties underlying both theories. In this review we
mainly focus on inhomogeneous condensations in static situations. The various
methods developed in the Nambu-Jona Lasinio model reveal the inhomogeneous
phase structures and also yield new inhomogeneous solutions in the nonlinear
sigma model owing to the duality. The recent progress on interacting systems in
finite systems is also reviewed.

Superconductivity;High Energy Physics - Theory