Interacting many-body non-Hermitian systems as Markov chains
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915482900103168 |
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| author | Hao, Zichang Chan, Wei Jie Lee, Ching Hua |
| author_facet | Hao, Zichang Chan, Wei Jie Lee, Ching Hua |
| contents | Rich phenomenology emerges at the intersection of non-Hermiticity and many-body dynamics, yet physically realizable implementations remain challenging. In this work, we propose a general formalism that maps non-Hermitian many-body Hamiltonians to the Laplacians of Markov chains, such that wavefunction amplitudes are re-interpreted as stochastic many-body configuration probabilities. Despite explicitly preserving all state transition processes and inheriting analogous non-Hermitian localization and state-space fragmentation, our Markov chain processes exhibit distinct steady-state behavior independently of energetic considerations that govern quantum evolution. We demonstrate our framework with two contrasting representative scenarios, one involving asymmetric (biased) propagation with exclusion interactions, and the other involving flipping pairs of adjacent spins (agents). These results reveal robust and distinctive signatures of non-Hermitian phenomena in classical stochastic settings such as ecological and social networks, and provide a versatile framework for studying non-reciprocal many-body dynamics across and beyond physics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_05411 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Interacting many-body non-Hermitian systems as Markov chains Hao, Zichang Chan, Wei Jie Lee, Ching Hua Other Condensed Matter Statistical Mechanics Quantum Physics Rich phenomenology emerges at the intersection of non-Hermiticity and many-body dynamics, yet physically realizable implementations remain challenging. In this work, we propose a general formalism that maps non-Hermitian many-body Hamiltonians to the Laplacians of Markov chains, such that wavefunction amplitudes are re-interpreted as stochastic many-body configuration probabilities. Despite explicitly preserving all state transition processes and inheriting analogous non-Hermitian localization and state-space fragmentation, our Markov chain processes exhibit distinct steady-state behavior independently of energetic considerations that govern quantum evolution. We demonstrate our framework with two contrasting representative scenarios, one involving asymmetric (biased) propagation with exclusion interactions, and the other involving flipping pairs of adjacent spins (agents). These results reveal robust and distinctive signatures of non-Hermitian phenomena in classical stochastic settings such as ecological and social networks, and provide a versatile framework for studying non-reciprocal many-body dynamics across and beyond physics. |
| title | Interacting many-body non-Hermitian systems as Markov chains |
| topic | Other Condensed Matter Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2509.05411 |