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Control of the Liouvillian gap in the finite open quantum system |
| Kai-Li Li(李凯丽), Yan-Sheng Liu(刘延盛), and Xi-Zheng Zhang(张禧征)† |
| College of Physics and Materials Science, Tianjin Normal University, Tianjin 300387, China |
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Abstract Relaxation processes in quantum systems coupled to external environments represent one of the most fundamental nonequilibrium phenomena in condensed matter physics. The Lindblad master equation provides a powerful framework for characterizing such open quantum dynamics. In this work, we systematically investigate how different types of quantum jump operators and system geometries influence the Liouvillian gap and the properties of the nonequilibrium steady state (NESS) in finite-size systems. We demonstrate that, due to the intricate structure of the Liouvillian superoperator, multiple NESSs with unphysical characteristics can emerge. The physically meaningful steady state must instead be understood as a superposition of these NESSs that collectively satisfy the required physical constraints. Furthermore, we find that the Liouvillian gap does not necessarily increase monotonically with the system-environment coupling strength. Instead, it can exhibit a nontrivial peak structure, corresponding to a minimum in the relaxation time. The magnitude of this peak is closely related to the symmetry properties of the system. Our results provide a deeper understanding of nonequilibrium behavior in finite quantum systems and offer new insights into the design and control of open quantum dynamics.
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Received: 10 May 2025
Revised: 20 June 2025
Accepted manuscript online: 03 July 2025
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PACS:
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03.65.Yz
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(Decoherence; open systems; quantum statistical methods)
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03.65.-w
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(Quantum mechanics)
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03.65.Aa
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(Quantum systems with finite Hilbert space)
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| Fund: This project was supported by the National Natural Science Foundation of China (Grant Nos. 12275193 and 11975166). |
Corresponding Authors:
Xi-Zheng Zhang
E-mail: zhangxz@tjnu.edu.cn
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Cite this article:
Kai-Li Li(李凯丽), Yan-Sheng Liu(刘延盛), and Xi-Zheng Zhang(张禧征) Control of the Liouvillian gap in the finite open quantum system 2026 Chin. Phys. B 35 010306
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