The derivation of explicit solutions to Wannier–Stark resonances for electrons on coupled chains

Electrons on infinite coupled chains with nearest neighbour couplings under uniform electric and magnetic fields can be expressed as conditionally solvable systems, which concerns both discrete coordinate and wavenumber representations. We then have to account for multiparameter extra-conditions relying on the single chain phase of the system, which amounts to perform a suitable selection of parameters. The implicit plots provided by such conditions exhibit both regular and irregular patterns. This results in the onset of a finite number of Wannier–Stark resonances, now by performing rescalings needed. However, this time the resonance width is sensitive to the quantum number characterizing the Stark-ladder. Bound-state limits, rescalings and approximations proceeding irrespective of the wavenumber have also been presented.