Open Harmonic Chain Study Reveals Non-Divergent Energy Flow Due to Rotating Wave Approximation

The behaviour of energy and particle transport within open quantum systems presents a significant challenge to physicists, and recent work by Melika Babakan and Laleh Memarzadeh of Sharif University of Technology, alongside Fabio Benatti of the University of Trieste, sheds new light on this complex area. The researchers investigate a chain of three harmonic oscillators connected to thermal reservoirs at differing temperatures, meticulously comparing the exact quantum dynamics with commonly used approximations. Their analysis reveals that while simplified models often predict a standard flow of probability, energy transport exhibits a more nuanced behaviour, with approximations introducing artificial energy sinks and sources not present in the full quantum description. This discovery highlights the critical importance of carefully selecting approximation methods when modelling open quantum systems, and offers a pathway towards more accurate descriptions of energy flow in a wide range of physical scenarios.

It details the theoretical foundations for understanding how quantum systems interact with their environment, leading to effects like decoherence and dissipation. The core challenge lies in accurately modelling these interactions, as real quantum systems are never truly isolated. The document explores key concepts including master equations, which track the evolution of a quantum system’s state, and the distinction between Markovian and non-Markovian dynamics. Markovian dynamics simplify calculations by assuming the system’s future depends only on its present state, while non-Markovian dynamics account for the influence of the system’s past.

It also details the Lindblad master equation, a widely used approach that ensures the validity of quantum states, and the mathematical framework of dynamical semigroups. Researchers utilize approximations like the weak coupling limit and secular approximation to simplify calculations. The document highlights ongoing debates regarding the accuracy of local versus global master equations, and the importance of correctly calculating currents to ensure consistency with thermodynamic laws. Techniques like coarse-graining are also explored to reduce the complexity of modelling these systems.

Energy and Particle Transport Divergences Explained

This research systematically investigates particle and energy transport within an open quantum system, specifically a chain of three harmonic oscillators coupled to thermal baths at differing temperatures. By comparing exact dynamics with local and global Markovian approximations, scientists demonstrated a consistent divergence-like continuity equation for probability current across all approaches. However, significant differences emerged in the description of energy transport, with the global approximation introducing non-divergence sink and source terms into the energy continuity equation. The team further showed that these anomalous terms persist even when circumventing the rotating wave approximation through a time-coarse-graining method, suggesting they reflect inherent complexities in modelling energy transport.

The findings emphasize the crucial role of approximation choices and highlight how collective effects can significantly influence transport properties, even in weakly interacting systems. This research contributes to the ongoing discussion regarding the reliability of local versus global open reduced dynamics, underscoring the importance of considering physical time-scales when approximating the evolution of open quantum systems. The authors acknowledge that their analysis focused on a relatively small system, and future work could extend this investigation to larger systems where the interplay between interactions and dissipation may reveal even richer phenomena.