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

TL;DR

This paper explores how non-commutative field theories can effectively model inhomogeneous phase transitions and roton-like spectra in both bosonic and fermionic condensates, linking symmetry breaking to complex excitation behaviors.

Contribution

It introduces a framework connecting non-commutative dynamics with inhomogeneous phases and roton spectra in condensed matter systems.

Findings

Non-commutative theories describe inhomogeneous phase transitions.

Infrared-ultraviolet mixing explains roton-like excitations.

The approach applies to both bosonic and fermionic condensates.

Abstract

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.