Revisiting Thouless conductance formula

It was shown using perturbation theory[1] that Thouless energy Ec for a quantum system scales linearly with the conductance of the system. We derive in an alternate way in 1-D that Ec scales with the conductance in a very different way. We physically show the difference between our approach and that of ref. 1 to expect our results to hold in higher dimensions also. We verify our results with exact numerical calculations.