Impurity Scattering of Wave Packets on a Lattice

TL;DR

This paper explores quantum transport and impurity scattering of wave packets on a one-dimensional lattice, highlighting differences from continuum media, and investigates spin-flip interactions in a spin chain system.

Contribution

It introduces three formulations for quantum scattering on a lattice and demonstrates real-time wave packet propagation, phase shifts, and spin-flip effects in a unified framework.

Findings

Resonant transmission characteristics in lattice transport

Wave packet phase shifts due to impurities

Spin evolution resulting from spin-flip interactions

Abstract

Quantum transport in a lattice is distinct from its counterpart in continuum media. Even a free wave packet travels differently in a lattice than in the continuum. We describe quantum scattering in a one dimensional lattice using three different formulations and illustrate characteristics of quantum transport such as resonant transmission. We demonstrate the real time propagation of a wave packet and its phase shift due to impurity configurations. Spin-flip scattering is also taken into account in a spin chain system. We show how individual spins in the chain evolve as a result of a spin-flip interaction between an incoming electron and a spin chain.