We explore the consequences of Replica Symmetry Breaking at zero temperature.
We introduce a repulsive coupling between a system and its unperturbed ground
state. In the Replica Symmetry Breaking scenario a finite coupling induces a
non trivial overlap probability distribution among the unperturbed ground state
and the one in presence of the coupling. We find a closed formula for this
probability for arbitrary ultrametric trees, in terms of the parameters
defining the tree. The same probability is computed in numerical simulations of
a simple model with many ground states, but no ultrametricity: polymers in
random media in 1+1 dimension. This gives us an idea of what violation of our
formula can be expected in cases when ultrametricity does not hold.Comment: 9 pages, 8 figures; 3 references added, address correcte
