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 of 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.
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