Scaling of free cumulants in closed system-bath setups
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| Format: | Preprint |
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2025
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| _version_ | 1866913111898849280 |
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| author | Füllgraf, Merlin Gemmer, Jochen Wang, Jiaozi |
| author_facet | Füllgraf, Merlin Gemmer, Jochen Wang, Jiaozi |
| contents | The Eigenstate Thermalization Hypothesis (ETH) has been established as a cornerstone for understanding thermalization in quantum many-body systems. Recently, there has been growing interest in the full ETH, which extends the framework of the conventional ETH and postulates a smooth function to describe the multi-point correlations among matrix elements. Within this framework, free cumulants play a central role, and most previous studies have primarily focused on closed systems. In this paper, we extend the analysis to a system-bath setup, considering both an idealized case with a random-matrix bath and a more realistic scenario where the bath is modeled as a defect Ising chain. In both cases, we uncover a universal scaling of the microcanonical free cumulants of observables associated with the central system Hamiltonian with respect to the interaction strength. Furthermore we establish a connection between this scaling behavior and the thermalization dynamics of the thermal free cumulants of corresponding observables. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_11333 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scaling of free cumulants in closed system-bath setups Füllgraf, Merlin Gemmer, Jochen Wang, Jiaozi Statistical Mechanics Quantum Physics The Eigenstate Thermalization Hypothesis (ETH) has been established as a cornerstone for understanding thermalization in quantum many-body systems. Recently, there has been growing interest in the full ETH, which extends the framework of the conventional ETH and postulates a smooth function to describe the multi-point correlations among matrix elements. Within this framework, free cumulants play a central role, and most previous studies have primarily focused on closed systems. In this paper, we extend the analysis to a system-bath setup, considering both an idealized case with a random-matrix bath and a more realistic scenario where the bath is modeled as a defect Ising chain. In both cases, we uncover a universal scaling of the microcanonical free cumulants of observables associated with the central system Hamiltonian with respect to the interaction strength. Furthermore we establish a connection between this scaling behavior and the thermalization dynamics of the thermal free cumulants of corresponding observables. |
| title | Scaling of free cumulants in closed system-bath setups |
| topic | Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2511.11333 |