Density susceptibility (${\chi }_{\rho }(q)=\delta {\rho }_q/\delta {\mu }_q$)

The static density susceptibility is the linear density response to a chemical-potential perturbation. In the quadratic uniform contact Bose gas, ${\chi }_{\rho }(q)=[g+q^2/(4m{\rho }_0){]}^{-1}$. Its inverse is a density stiffness. At zero wavevector $\partial \rho /\partial \mu =1/g$ at mean field, while the isothermal compressibility includes the additional factor $1/{\rho }^2$.