Thermal Transport of Weakly Interacting Electrons in Quantum Wires

We have studied the origin of the electron energy relaxation in clean single channel quantum wires, accounting for the scattering processes that involve threee particule collisions. Thermal transport of Single-channel quantum wires, where a lower value of the thermal conductance than that predicted by the wiedemann-Franz law as observed at the plateau of the electrical conductance. Momeutum resolved tunneling spectroscopy provided direct evidence for the electronic thermalisation in one dimensional systems. Interaction effects are responsible for the observed features. Fabrication of tunable constrictions in high mobility two-dimensional electron gases have allowed precise and sensitive thermal measurements in clean one dimensional systems. We have found that the thermal conductance is reduced by interactions, which is qualitatively consistent with the experimental observation. The three particle collisions are responsible for relaxation and provide an explicit solution of the Boltz-Mann equation. Electrons maintain their integrity during collisions and thus neglects effects of spin-charge separation. The effects of electron-electron collisions on the distribution function depends strongly on the length of the wire. Short wires are traversed by the electrons relatively fast. In the limit of a very long wire we found full equilibration of left and right moving electrons into a single distribution.