Chiral pair fluctuations for the inhomogeneous chiral transition

The effects of fluctuations are discussed around the phase boundary of the inhomogeneous chiral transition between the inhomogeneous chiral phase and the chiral-restored phase. The particular roles of thermal and quantum fluctuations are elucidated and a continuity of their effects across the phase boundary is suggested. In addition, it is argued that anomalies in the thermodynamic quantities should have phenomenological implications for the inhomogeneous chiral transition. Some common features for other phase transitions, such as those from the normal to the inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov state in superconductivity, are also emphasized.