Control of the quantum path-target state distance: Bistable-like characteristic in a small tight-binding system

The control of the distance between the quantum path and a given target state in the state space of an (N+2) tight-binding isolated system prepared in a non-stationary initial state is studied as a function of an asymmetry introduced by a change in only one of the coupling constants. When N>6, a bistable-like characteristic is found for the variation of the minimum distance between the path and the target as a function of this asymmetry. Optimised systems are proposed to reach the best control of this distance by the asymmetry.