Bahnpropagation

Bahnpropagation is a theoretical and experimental concept describing the directed propagation of excitations along a predefined network of pathways within a material or engineered structure. The term leverages the German 'Bahn' meaning path or track, emphasizing channelized transport rather than isotropic diffusion. In Bahnpropagation, the geometry of the path and the coupling between adjacent sites govern how an excitation travels from one end of the network to the other.

The standard description models the system as a graph or lattice with nodes connected by edges. The evolution of the excitation follows a Hamiltonian that includes hopping terms between connected sites. Propagation is analyzed through transfer matrices or Green's functions and is associated with a characteristic group velocity along the channel. Coherence and interference can yield ballistic transport along the designed route, while disorder or junctions cause scattering, dephasing, or localization.

Experimental realizations include photonic waveguide arrays that guide light along one-dimensional channels, cold atoms in engineered optical lattices forming network geometries, electronic nanowire networks, and exciton-polariton circuits. Measurements focus on time-resolved transmission, channel conductance, and the sensitivity of the propagation to perturbations. Bahnpropagation has potential applications in nanoscale information routing, on-chip signal processing, and quantum simulation where directional transport is advantageous.

Relation to related concepts such as ballistic transport and quantum walks highlights its emphasis on geometry-driven, directed transport. Key questions address the effects of strong disorder, interactions, and how to optimize network designs for robust propagation under realistic conditions.