On the difference between thermalization in open and isolated quantum systems: a case study

TL;DR

This paper investigates the fundamental differences between thermalization in open and isolated quantum systems, demonstrating how the order of limits affects observed physics through numerical analysis of a double quantum dot model.

Contribution

It clarifies the connection between open and isolated quantum system thermalization by analyzing a specific model and showing how the order of limits influences the dynamics and observed thermalization.

Findings

Isolated thermalization occurs only in free DQD, not in interacting DQD.

Open thermalization is observed in both free and interacting DQD.

Thermalization in the two paradigms occurs at different time scales, depending on the order of limits.

Abstract

Thermalization of isolated and open quantum systems has been studied extensively. However, being the subject of investigation by different scientific communities and being analysed using different mathematical tools, the connection between the isolated (IQS) and open (OQS) approaches to thermalization has remained opaque. Here we demonstrate that the fundamental difference between the two paradigms is the order in which the long time and the thermodynamic limits are taken. This difference implies that they describe physics on widely different time and length scales. Our analysis is carried out numerically for the case of a double quantum dot (DQD) coupled to a fermionic lead, also known as the interacting resonant level model in quantum impurity physics. We show how both OQS and IQS thermalization can be explored in this model on equal footing, allowing a fair comparison between the two. We find that while the quadratically coupled (free) DQD experiences no isolated thermalization, it of course does experience open thermalization. For the non-linearly interacting DQD coupled to a fermionic lead, the many-body interaction in the DQD breaks the integrability of the whole system. We find that this system shows strong evidence of both OQS and IQS thermalization in the same dynamics, but at widely different time scales, consistent with reversing the order of the long time and the thermodynamic limits.