We present a formalism for an atomic scale study of phononic heat transfer.
The expression of thermal energy current can be cast in the Landauer form
and incorporates the transmission coefficient explicitly. Calculation of th
e thermal conductance of a monoatomic chain of N atoms between two reservoi
rs shows interesting quantum features. The conductance density appears as L
orentzian type resonances at the eigenfrequencies of the chain. At low-temp
erature limit the discrete vibrational frequency spectrum of a "soft" chain
may reflect on the thermal conductance by giving rise to a sudden increase
. At room temperature, the conductance through a 'stiff' chain may oscillat
e with the number of chain atoms. The obtained quantum features are compare
d with similar effects found in the quantized electrical conductance.