| Contents |
| $N$-body long-range interacting systems get trapped in long-living out-of-equilibrium states,
called quasi-stationary states (QSS), whose lifetime diverges algebraically with system size $N$.
We have studied the influence of a small external perturbation acting on a stationary stable QSS.
In the large $N$ limit, the time evolution of a QSS is well described by the Vlasov equation,
which has an infinite number of stationary solutions that can be either homogeneous or
inhomogeneous in space. We have developed a linear response theory for homogeneous QSS
using the Fourier-Laplace techniques usually applied in the theory of linear Landau damping.
The theory allows us to compute the time evolution of a generic observable
when a small perturbing field is added to the Hamiltonian of the system. We have also
developed an "approximate" linear response theory for inhomogeneous states, for which
the standard Fourier-Laplace approach cannot work because of the coupling between
different mean-field Fourier modes and the presence of an infinite number of conserved quantities, the
Casimirs of the Vlasov equation. The theory is applied the Hamiltonian Mean Field (HMF) model,
which describes the motion of particles on a unitary circle which interact all-to-all, and is
tested against numerical simulations. |
|