Exact wave-packet decoherence dynamics in a discrete spectrum environment

TL;DR

This paper provides an exact analytical solution for wave-packet decoherence in a discrete spectrum environment, revealing how intrinsic energy scales influence decoherence dynamics and non-Markovian effects.

Contribution

It introduces an exact solution for wave-packet decoherence influenced by discrete environment modes and a new decoherence measure based on wave packet delocalization.

Findings

Exact solution characterizes decoherence dynamics.

Decoherence measure captures off-diagonal density matrix evolution.

Non-Markovian effects arise from wave packet diffusion.

Abstract

We find an exact analytical solution of the reduced density matrix from the Feynman-Vernon influence functional theory for a wave packet influenced by an environment containing a few discrete modes. We obtain two intrinsic energy scales relating to the time scales of the system and the environment. Different relationship between these two scales alters the overall form of the solution of the system. We also introduce a decoherence measure for a single wave packet which is defined as the ratio of Schr\"odinger uncertainty over the delocalization extension of the wave packet and characterizes the time-evolution behavior of the off-diagonal reduced density matrix element. We utilize the exact solution and the docherence measure to study the wave packet decoherence dynamics. We further demonstrate how the dynamical diffusion of the wave packet leads to non-Markovian decoherence in such a microscopic environment.