Open system approach to the internal dynamics of a model multilevel molecule

TL;DR

This paper models the internal dynamics of a multilevel molecule as an open quantum system using continuous time quantum random walks, revealing power-law relaxation and quantum Zeno effects influenced by collision time distributions.

Contribution

It introduces a novel approach applying quantum random walk theory to model molecular internal dynamics with non-Poissonian collision distributions.

Findings

Populations and coherences relax with inverse power laws.

Asymptotic equilibrium is distribution-independent.

Long-time dynamics can be slowed by heavy-tailed collision distributions.

Abstract

A model multilevel molecule described by two sets of rotational internal energy levels of different parity and degenerate ground states, coupled by a constant interaction, is considered, by assuming that the random collisions in a gas of identical molecules, provoke transitions between adjacent energy levels of the same parity. The prescriptions of the continuous time quantum random walk are applied to the single molecule, interpreted as an open quantum system, and the master equation driving its internal dynamics is built for a general distribution of the waiting times between two consecutive collisions. The coherence terms and the populations of the energy levels relax to the asymptotics with inverse power laws for relevant classes of non-Poissonian distributions of the collision times. The stable asymptotic equilibrium configuration is independent of the distribution. The long time dynamics may be hindered by increasing the tail of the distribution density. This effect may be interpreted as the appearance of the quantum Zeno effect over long time scales.