Thermal drag between two coupled quantum wires

In the last two-three decades the study of quantum wires created a lot of interest, in particular for what concerns their transport properties. Different theoretical methods, along with an incredible development of experimental techniques, have provided a lot of information on these peculiar low dimensional systems. In this framework, Coulomb drag effect in coupled systems has been intensively studied recently; drag measurement are now a standard experimental technique to study a quite different variety of physical properties and several different setups were considered so far. In this thesis we study the thermal drag between two coupled quantum wires, with the coupling provided by a Coulombian interaction. This topic is very interesting for both its theoretical and experimental implications: it could help to explain, not only thermal, but also thermoelectric effects in systems exhibiting drag. Furthermore the study of thermal drag will nicely complement the information provided by the ``conventional'' Coulomb drag for electrical transport. It will then provide new and powerful experimental methods to study drag and could have important technological application in reducing the dissipation of heat. In the system we consider, a thermal gradient is applied to the first wire and, thanks to the coupling between the density fluctuations in the two wires, a drag thermal current is induced in the second wire. We derive an expression for the transresistivity (proportionality coefficient between thermal bias and current) valid under general conditions and then we assume to be in a low temperature regime, in order to exploit bosonization formalism and find a Wiedemann-Franz-like law, which allows to connect our result with the much more studied Coulomb drag case. Then we analyse the contribution of forward scattering and backward scattering to the drag, finding out that the first one is dominant. The analythical results obtained using bosonization will be finally complemented by numerical simulations based on the MPS formalism. In the simulations we are able to detect a stationary thermal current dragged by the Coulomb coupling between the wires and reproduce the predicted dependence of the current on the interaction strength, quadratic for small couplings. On extending the simulations range to stronger couplings, we find also the quartic corrections to the thermal drag