  The relation between symmetry breaking in non-commutative cut-off field
theories and transitions to inhomogeneous phases in condensed matter is
discussed. The non-commutative dynamics can be regarded as an effective
description of the mechanisms which lead to inhomogeneous phase transitions and
their relation to the roton-like excitation spectrum. The typical
infrared-ultraviolet mixing in non-commutative theories contains the peculiar
ingredients to describe the interplay between short and long distance particle
interactions which is responsible for the non-uniform background and the roton
spectrum both in bosonic and fermionic condensates.
