  We show that the linearized phase space flow around a discrete breather
solution is not capable of generating persistent energy flow away from the
breather even in the case of instabilities of extended states. This holds both
for the classical and quantized description of the flow. The main reason for
that is the parametric driving the breather provides to the flow. Corresponding
scaling arguments are derived for both classical and quantum cases. Numerical
simulations of the classical flow support our findings.
