Emergent Liouvillian exceptional points from exact principles

Shishir Khandelwal; Gianmichele Blasi

doi:10.22331/q-2025-12-15-1944

Emergent Liouvillian exceptional points from exact principles

Shishir Khandelwal¹ and Gianmichele Blasi²

¹Physics Department and NanoLund, Lund University, Box 118, 22100 Lund, Sweden
²Department of Applied Physics, University of Geneva, 1211 Geneva, Switzerland

Published:	2025-12-15, volume 9, page 1944
Editor:	Thomas Elliott
Eprint:	arXiv:2409.08100v4
Doi:	https://doi.org/10.22331/q-2025-12-15-1944
Citation:	Quantum 9, 1944 (2025).

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Abstract

Recent years have seen a surge of interest in exceptional points in open quantum systems. The natural approach in this area has been the use of Markovian master equations. While the resulting Liouvillian EPs have been seen in a variety of systems and have been associated to numerous exotic effects, it is an open question whether such degeneracies and their peculiarities can persist beyond the validity of master equations. In this work, taking the example of a dissipative double-quantum-dot system, we show that exact Heisenberg equations governing system and bath dynamics exhibit the same EPs as the corresponding master equations. To highlight the importance of this finding, we prove that the paradigmatic property associated to EPs – critical damping, persists well beyond the validity of master equations. Our results demonstrate that Liouvillian EPs can arise from underlying fundamental exact principles, rather than merely as a consequence of approximations involved in deriving master equations.

Popular summary

Exceptional points (EPs) are special mathematical points in an open system’s parameter space that are known to coincide with striking behaviour. Traditionally, EPs in open quantum systems have been identified when the system interacts weakly with its environment. This raises the question: do the associated phenomena truly reflect the underlying physics or merely the assumptions used to describe that regime?

In this work, we consider paradigmatic quantum systems and analyse their evolution using fully exact equations of motion, valid far beyond weak coupling. We find that the same EPs that typically appear only under weak system-environment interaction also arise naturally in the exact description, showing that they are intrinsic features of the dynamics rather than artefacts of approximation. Moreover, the characteristic EP behaviour — in particular, critical damping, where the system reaches its steady state in the fastest possible non-oscillatory way — persists even when the system interacts strongly with its environment.

These results demonstrate that the phenomena linked to exceptional points can have a robust and genuinely physical origin, extending their relevance to a much broader class of open quantum systems than previously believed.

► BibTeX data

@article{Khandelwal2025emergentliouvillian,
  doi = {10.22331/q-2025-12-15-1944},
  url = {https://doi.org/10.22331/q-2025-12-15-1944},
  title = {Emergent {L}iouvillian exceptional points from exact principles},
  author = {Khandelwal, Shishir and Blasi, Gianmichele},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1944},
  month = dec,
  year = {2025}
}

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Cited by

[1] Timofey T. Sergeev, Evgeny S. Andrianov, and Alexander A. Zyablovsky, "Exceptional points of arbitrary high orders induced by non-Markovian dynamics", Physical Review A 113 6, 062212 (2026).

[2] Stefano Longhi, "Non‐Markovian Exceptional Points in Waveguide Quantum Electrodynamics", Advanced Quantum Technologies 9 4, e70277 (2026).

[3] Pitambar Bagui, Arijit Chatterjee, and Bijay Kumar Agarwalla, "Accelerated relaxation and Mpemba-like effect for operators in open quantum systems", Physical Review A 114 1, L010601 (2026).

[4] Jhen-Dong Lin, Po-Chen Kuo, Neill Lambert, Adam Miranowicz, Franco Nori, and Yueh-Nan Chen, "Non-Markovian quantum exceptional points", Nature Communications 16 1, 1289 (2025).

[5] Gianmichele Blasi, Ricard Ravell Rodríguez, Mykhailo Moskalets, Rosa López, and Géraldine Haack, "Quantum Kinetic Uncertainty Relations in Mesoscopic Conductors at Strong Coupling", arXiv:2505.13200, (2025).

[6] Gianmichele Blasi, Shishir Khandelwal, and Géraldine Haack, "Exact finite-time correlation functions for multiterminal setups: Connecting theoretical frameworks for quantum transport and thermodynamics", Physical Review Research 6 4, 043091 (2024).

[7] Jeanne Bourgeois, Gianmichele Blasi, and Géraldine Haack, "Transport Approach to Quantum State Tomography", Physical Review Letters 136 1, 010802 (2026).

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