Linear response theory and damped modes of stellar clusters
  Because all stars contribute to its gravitational potential, stellar clusters
amplify perturbations collectively. In the limit of small fluctuations, this is
described through linear response theory, via the so-called response matrix.
While the evaluation of this matrix is somewhat straightforward for unstable
modes (i.e. with a positive growth rate), it requires a careful analytic
continuation for damped modes (i.e. with a negative growth rate). We present a
generic method to perform such a calculation in spherically symmetric stellar
clusters. When applied to an isotropic isochrone cluster, we recover the
presence of a low-frequency weakly damped $\ell = 1$ mode. We finally use a set
of direct $N$-body simulations to test explicitly this prediction through the
statistics of the correlated random walk undergone by a cluster's density
centre.
