  Recently the authors developed a scattering approach that allows for a
complete description of the steady-state physics of quantum-impurities in and
out of equilibrium. Quantum impurities are described using scattering
eigenstates defined ab initio on the open, infinite line with asymptotic
boundary conditions imposed by the leads. The scattering states on the open
line are constructed for integrable quantum-impurity models by means of a
significant generalization of the Bethe-Ansatz which we call the Scattering
Bethe-Ansatz (SBA). The purpose of the paper is to present in detail the
scattering approach to quantum-impurity models and the SBA and show that they
reproduce well-known thermodynamic results for several widely studied models:
the Resonance Level model, Interacting Resonance Level model and the Kondo
model. Though the SBA is more complex than the traditional Thermodynamic Bethe
Ansatz (TBA) when applied to thermodynamical questions, the scattering approach
(SBA) allows access to an array of new questions that cannot be addressed
otherwise, ranging from scattering of electrons off magnetic impurities to
nonequilibrium dynamics.
