Conductance from Non-perturbative Methods II

This talk provides a natural continuation of the talk presented by Andreas Fring in this conference. Part I was focused on explaining how the DC conductance for a free Fermion theory in the presence of different kinds of defects can be computed by evaluating the Kubo formula. In this talk I will focus on an alternative method for the computation of the same quantity, that is the evaluation of Landauer formula. Once again, the integrability of the theories under consideration will be exploited, since a thermodynamic Bethe ansatz analysis provides all the input needed in that case, apart from the corresponding reflection and transmition amplitudes of the defect. The basic conclusion of our analysis will be the perfect agreement between the two different theoretical descriptions mentioned. The results I will talk about are contained on a series of papers [1, 2, 3, 4, 5, 6], with emphasis on the first two, resulting mainly from a collaboration with Andreas Fring, who presented the first part of the work. 1. Thermodynamic Bethe ansatz for impurity systems As mentioned in the previous talk, for the evaluation of the Landauer formula [7] one needs to know the density distribution functions involved. I will now present a general method which allows to compute such quantities non-perturbatively, i.e. the thermodynamic Bethe ansatz (TBA) approach, which we generalized in [1] to incorporate the non-trivial effects arising due to the presence of impurities. Besides the aim we have in mind, in general the TBA is a powerful tool for the computation of thermodynamic quantities in 1+1 dimensional integrable systems. Originally formulated by Yang and Yang [8] in the context of the non-relativistic Bose gas, it was thereafter generalized by Zamolodchikov [9] to relativistic quantum field theories which interact by means of factorizable scattering matrices. A TBA-analysis serves to check the consistency of a certain S-matrix proposal, since it allows