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Diagnosing Thermalization Dynamics of Non-Hermitian Quantum Systems via GKSL Master Equations |
| Yiting Mao1, Peigeng Zhong1, Haiqing Lin1,2*, Xiaoqun Wang2*, and Shijie Hu1,3* |
1Beijing Computational Science Research Center, Beijing 100084, China
2School of Physics, Zhejiang University, Hangzhou 310058, China
3Department of Physics, Beijing Normal University, Beijing 100875, China
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| Cite this article: |
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Yiting Mao, Peigeng Zhong, Haiqing Lin et al 2024 Chin. Phys. Lett. 41 070301 |
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Abstract The application of the eigenstate thermalization hypothesis to non-Hermitian quantum systems has become one of the most important topics in dissipative quantum chaos, recently giving rise to intense debates. The process of thermalization is intricate, involving many time-evolution trajectories in the reduced Hilbert space of the system. By considering two different expansion forms of the density matrices adopted in the biorthogonal and right-state time evolutions, we derive two versions of the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) master equations describing the non-Hermitian systems coupled to a bosonic heat bath in thermal equilibrium. By solving the equations, we identify a sufficient condition for thermalization under both time evolutions, resulting in Boltzmann biorthogonal and right-eigenstate statistics, respectively. This finding implies that the recently proposed biorthogonal random matrix theory needs an appropriate revision. Moreover, we exemplify the precise dynamics of thermalization and thermodynamic properties with test models.
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Received: 28 March 2024
Published: 08 July 2024
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| PACS: |
03.65.Yz
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(Decoherence; open systems; quantum statistical methods)
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64.10.+h
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(General theory of equations of state and phase equilibria)
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05.70.-a
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(Thermodynamics)
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05.70.Ce
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(Thermodynamic functions and equations of state)
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