On the difference between thermalization in open and isolated quantum systems: A case study, by Archak Purkayastha, Giacomo Guarnieri, Janet Anders, Marco Merkli

SciPost Physics Home Authoring Refereeing Submit a manuscript About On the difference between thermalization in open and isolated quantum systems: A case study Archak Purkayastha, Giacomo Guarnieri, Janet Anders, Marco Merkli SciPost Phys. 19, 136 (2025) · published 25 November 2025 doi: 10.21468/SciPostPhys.19.5.136 pdf BiBTeX RIS Submissions/Reports 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. × TY - JOURPB - SciPost FoundationDO - 10.21468/SciPostPhys.19.5.136TI - On the difference between thermalization in open and isolated quantum systems: A case studyPY - 2025/11/25UR - https://scipost.org/SciPostPhys.19.5.136JF - SciPost PhysicsJA - SciPost Phys.VL - 19IS - 5SP - 136A1 - Purkayastha, ArchakAU - Guarnieri, GiacomoAU - Anders, JanetAU - Merkli, MarcoAB - 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.ER - × @Article{10.21468/SciPostPhys.19.5.136, title={{On the difference between thermalization in open and isolated quantum systems: A case study}}, author={Archak Purkayastha and Giacomo Guarnieri and Janet Anders and Marco Merkli}, journal={SciPost Phys.}, volume={19}, pages={136}, year={2025}, publisher={SciPost}, doi={10.21468/SciPostPhys.19.5.136}, url={https://scipost.org/10.21468/SciPostPhys.19.5.136},} Ontology / Topics See full Ontology or Topics database. Eigenstate thermalization hypothesis (ETH) Open quantum systems Quantum chaos Thermalization Authors / Affiliations: mappings to Contributors and Organizations See all Organizations. 1 Archak Purkayastha, 2 Giacomo Guarnieri, 3 4 Janet Anders, 5 Marco Merkli 1 Indian Institute of Technology Hyderabad [IITH] 2 Università degli Studi di Pavia / University of Pavia [UNIPV] 3 Universität Potsdam / University of Potsdam [UPC] 4 University of Exeter 5 Memorial University of Newfoundland [MUN] Funders for the research work leading to this publication Danmarks Grundforskningsfond / Danish National Research Foundation [DNRF] Deutsche Forschungsgemeinschaft / German Research FoundationDeutsche Forschungsgemeinschaft [DFG] Engineering and Physical Sciences Research Council [EPSRC] Indian Institute of Technology Hyderabad [IITH] Ministero dell'Università e della Ricerca Conseil de Recherches en Sciences Naturelles et en Génie / Natural Sciences and Engineering Research Council [NSERC / CRSNG]