  We investigate the heat conduction properties of molecular junctions
comprising anharmonic interactions. We find that nonlinear interactions can
lead to novel phenomena: it negative differential thermal conductance and heat
rectification. Based on analytically solvable models we derive an expression
for the heat current that clearly reflects the interplay between anharmonic
interactions, strengths of coupling to the thermal reservoirs, and junction
asymmetry. This expression indicates that negative differential thermal
conductance shows up when the molecule is strongly coupled to the thermal
baths, even in the absence of internal molecular nonlinearities. In contrast,
diode like behavior is expected for a highly anharmonic molecule with an
inherent structural asymmetry. Anharmonic interactions are also necessary for
manifesting Fourier type transport. We briefly present an extension of our
model system that can lead to this behavior.
