  We consider an infinite chain of coupled harmonic oscillators with a Langevin
thermostat attached at the origin and energy, momentum and volume conserving
noise that models the collisions between atoms. The noise is rarefied in the
limit, {that corresponds to the hypothesis} that in the macroscopic unit time
only a finite number of collisions takes place (Boltzmann-Grad limit). We prove
that, after the hyperbolic space-time rescaling, the Wigner distribution,
describing the energy density of phonons in space-frequency domain, converges
to a positive energy density function $W(t, y, k)$ that evolves according to a
linear kinetic equation, with the interface condition at $y=0$ that corresponds
to reflection, transmission and absorption of phonons. The paper extends the
results of [3], where a thermostatted harmonic chain (with no inter-particle
scattering) has been considered.
