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Applying the Fermi-Bose equivalence and the boundary state formulation, westudy the hetero-junction of two quantum wires. Two quantum wires are describedby Tomonaga-Luttinger (TL) liquids with different TL parameters and electronstransport between two wires is depicted by a simple hopping interaction. Wecalculate the radiative corrections to the hopping interaction and obtain therenormalization (RG) exponent, making use of the perturbation theory based onthe boundary state formulation. The model exhibits a phase transition at zerotemperature. We discuss the critical line which defines the phase boundary onthe two dimensional parameter space. The model also exhibits the particle-kinkduality, which maps the strong coupling regime of the model onto the weakcoupling regime of the dual model. The strong coupling regime of the model isfound to match exactly the weak coupling regime of the dual model. This modelis also important to study the critical behaviors of the two dimensionaldissipative system with anisotropic friction coefficients.

Hetero-Junction of Two Quantum Wires: Critical Line and Duality