Interaction of a polaron with a trap. Influence of adiabaticity

A lattice model of the interaction of a polaron with a stationary trap is considered in this work. For estimation of an electron-phonon interaction we used the Su–Schrieffer–Heeger approximation, which is more typical for DNA. The trap is localized at a lattice site with energy $U<0$. Depending on the depth of the trap, there are two mechanisms for the interaction of the polaron with the trap. For a shallow trap, the interaction is adiabatic, and the trap does not capture the wave function. For a deeper trap, the dynamics of the interaction of the charge with the trap is determined by the nonadiabaticity of the process with the participation of excited electronic states. In a narrow range of values of the trap depth $-0.6\le U\le -0.4$, a polaron is completely captured by the trap, and a stationary polaron is formed on the trap. For deeper traps, for $U< -0.6$, the polaron is not captured by the trap, and the wave function either tunnels through the trap or is reflected from it. The phase of the wave function provides useful information about the mechanism of interaction between the polaron and the trap.