Non-commutative dynamics and roton-like spectra in bosonic and fermionic condensates

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.