"Ping-pong" electron transfer. II. Multiple reflections of the Loschmidt echo and the wave function trapping by an acceptor

TL;DR

This paper investigates quantum wave function dynamics on a lattice, focusing on multiple reflections, wave trapping by defects, and their implications for efficient charge transfer in biological molecules.

Contribution

It introduces analytical and numerical analysis of wave function reflections and trapping, explaining high charge transfer efficiency in biological systems.

Findings

Wave function concentration occurs after multiple reflections.

Analytical solutions match numerical simulations.

Results explain efficient charge transport in biological molecules.

Abstract

This paper continues the preceding paper on the problem of quantum dynamics on the lattice. Firstly we consider the multiple reflections of the wave function (Loschmidt echo). The phenomenon of wave function concentration on the impurity site after reflections is found. The solution representing the total amplitude $a(t)$ is obtained as the series in terms of partial amplitudes $a_k(t)$. The contribution of $k$th partial amplitude becomes dominant only after $k$th reflection from the lattice end. An excellent agreement between analytical and accurate numerical results is obtained. Next problem, -- wave packet trapping by defects, is solved by numerical simulation. Analytical expressions are derived in few cases allowing to estimate the quantum efficiency of charge transfer. Obtained results can qualitatively explain recent experiments on the highly efficient charge transport in olygonucleotides and polypeptides.