Universal Short-Time Conductance Behavior Emerges between Two Adjacent Reservoirs

When a shutter, which differentiates between two adjacent particles’ reservoirs with a voltage gap, is lifted, a current emerges. In this paper, the temporal dynamics of this emerging current is analyzed. The main results are as follows: (A) the current’s prefactor in the short-time behavior is related to the long-time frequencies, by which the current converges to its equilibrium value (the conductance quantum unit 2e²/h). (B) In the short-time regime, the current is proportional to the square root of the time. (C) The maximum overshoot conductance is bounded by G_max = ζe²/h, where ζ is a universal value which is very close to Euler’s number. (D) Most of these results are valid for a thin wire in 3D, even in the presence of electron–electron interactions.