We study a conjecture by Fendley, Ludwig and Saleur for the nonlinear conductance in the boundary sine-Gordon model. They have calculated the perturbative series of twisted partition functions, which require particular (unphysical) imaginary values o
f the bias, by applying the tools of Jack symmetric functions to the log-sine Coulomb gas on a circle. We have analyzed the conjectured relation between the analytically continued free energy and the nonlinear conductance in various limits. We confirm the conjecture for weak and strong tunneling, in the classical regime, and in the zero temperature limit. We also shed light on this special variant of the ${rm Im} F$-method and compare it with the real-time Keldysh approach. In addition, we address the issue of quantum statistical fluctuations.
We review recent advances in the field of full counting statistics (FCS) of charge transfer through impurities imbedded into strongly correlated one-dimensional metallic systems, modelled by Tomonaga-Luttinger liquids (TLLs). We concentrate on the ex
act analytic solutions for the cumulant generating function (CGF), which became available recently and apply these methods in order to obtain the FCS of a non-trivial contact between two crossed TLL.
