The SP formula for the dephasing rate Γ Γ φ φ of a particle that moves in a fluctuating environment unifies various results that have been obtained, notably in condensed matter physics, with regard to the motion of electrons in a metal. The general case requires to take into account not only the temporal correlations but also the spatial correlations of the environmental fluctuations. These can be characterized by the spectral form factor S ~ ~ ( q , ω ω ) , while the motion of the particle is characterized by its power spectrum P ~ ~ ( q , ω ω ) . Consequently, at finite temperature the expression for the dephasing rate takes the following form that involves S and P functions: