We discuss the linear response conductance of electrons in a
Luttinger liquid with arbitrary interaction g2, and subject
to a potential barrier of arbitrary strength, as a function of
temperature [1]. Our result agrees with known limiting cases.
We first map the Hamiltonian in the basis of scattering states
into an effective low energy Hamiltonian in current algebra form.
Analyzing the perturbation theory in the fermionic representation
the principal diagrams contributing to the renormalization group(RG)
beta-function are identified and summed to all orders in g2.
The RG-equation for the temperature dependent conductance is
solved analytically. For the case of weak interaction results
for a time-dendent barrier are prrsented as well.
[1] D. Aristov and P. Wölfle, cond-mat/0709.1562