  The dynamic response of asymmetric nuclear matter is studied by using a
Time-Dependent Local Isospin Density (TDLIDA) approximation approach.
Calculations are based on a local density energy functional derived by an
Auxiliary Field Diffusion Monte Carlo (AFDMC) calculation of bulk nuclear
matter. Three types of excited states emerge: collective states, a continuum of
quasi-particle-quasi-hole excitations and unstable solutions. These states are
analyzed and discussed for different values of the nuclear density $\rho$ and
isospin asymmetry $\xi=(N-Z)/A$. An analytical expression of the
compressibility as a function of $\rho$ and $\xi$ is derived which show
explicitly an instability of the neutron matter around $\rho\simeq 0.09
fm^{-3}$ when a small fraction of protons is added to the system.
