Interacting many-body non-Hermitian systems as Markov chains

Fuente: arXiv
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Main Authors: Hao, Zichang, Chan, Wei Jie, Lee, Ching Hua
Format: Preprint
Published: 2025
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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
id 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