Quantum thermal conductance of electrons in a one-dimensional wire.

We use an electron thermometer to measure the temperature rise of approximately 2 x 10(5) electrons in a two-dimensional box, due to heat flow into the box through a ballistic one-dimensional (1D) constriction. Using a simple model we deduce the thermal conductance kappa(Vg) of the 1D constriction, which we compare to its electrical conductance characteristics; for the first four 1D subbands the heat carried by the electrons passing through the wire is proportional to its electrical conductance G(Vg). In the vicinity of the 0.7 structure this proportionality breaks down, and a plateau at the quantum of thermal conductance pi(2)k(2/B)T/3h is observed.