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A quantum impurity attached to an interacting quantum wire gives rise to anarray of of new phenomena. Using Bethe Ansatz we solve exactly modelsdescribing two geometries of a quantum dot coupled to an interacting quantumwire: a quantum dot that is (i) side-coupled and (ii) embedded in a Luttingerliquid. We find the eigenstates and determine the spectrum through the BetheAnsatz equations. Using this we derive exact expressions for the ground statedot occupation. The thermodynamics are then studied using the thermodynamicsBethe Ansatz equations. It is shown that at low energies the dot becomes fullyhybridized and acts as a backscattering impurity or tunnel junction dependingon the geometry and furthermore that the two geometries are related by changingthe sign of the interactions. Although remaining strongly coupled for allvalues of the interaction in the wire, there exists competition between thetunneling and backscattering leading to a suppression or enhancement of the dotoccupation depending on the sign of the bulk interactions.

Quantum Dot in Interacting Environments