Universal scaling in one-dimensional non-reciprocal matter
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908706418982912 |
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| author | Liu, Shuoguang Littlewood, Peter B. Hanai, Ryo |
| author_facet | Liu, Shuoguang Littlewood, Peter B. Hanai, Ryo |
| contents | Unveiling universal non-equilibrium scaling laws has been a central theme in modern statistical physics, with recent attention increasingly directed toward non-equilibrium phases that exhibit rich dynamical phenomena. A striking example arises in non-reciprocal systems, where asymmetric interactions between components lead to inherently dynamic phases and unconventional criticality near a critical exceptional point (CEP), where the criticality arises from the coalescence of collective modes with an existing Nambu-Goldstone mode. However, the universal scaling behavior that emerges in this system with full consideration of many-body effects and stochastic noise remains largely elusive. Here, we establish a dynamical scaling law in a generic one-dimensional (1D) stochastic non-reciprocal $O(2)$-symmetric system. Through large-scale simulations, we uncover a new non-equilibrium scaling in the vicinity of the CEP, distinct from any previously known equilibrium or non-equilibrium universality classes. We report an anomalously large roughening exponent $α_{\rm CEP}=1.35(5)$, which is to be compared with those of simple diffusion $α_{\rm EW}=0.5$. In regimes where the system breaks into domains with opposite chirality and spatiotemporal vortices inevitably emerge, we find that fluctuations are strongly suppressed, leading to a logarithmic scaling as a function of system size $L$ that manifests a short-range correlation. This work elucidates the beyond-mean-field dynamics of non-reciprocal matter, thereby shedding light on the exploration of criticality in non-reciprocal phase transition across diverse physical contexts, from active matter and driven quantum systems to biological pattern formation and non-Hermitian physics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14384 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal scaling in one-dimensional non-reciprocal matter Liu, Shuoguang Littlewood, Peter B. Hanai, Ryo Statistical Mechanics Soft Condensed Matter Strongly Correlated Electrons Unveiling universal non-equilibrium scaling laws has been a central theme in modern statistical physics, with recent attention increasingly directed toward non-equilibrium phases that exhibit rich dynamical phenomena. A striking example arises in non-reciprocal systems, where asymmetric interactions between components lead to inherently dynamic phases and unconventional criticality near a critical exceptional point (CEP), where the criticality arises from the coalescence of collective modes with an existing Nambu-Goldstone mode. However, the universal scaling behavior that emerges in this system with full consideration of many-body effects and stochastic noise remains largely elusive. Here, we establish a dynamical scaling law in a generic one-dimensional (1D) stochastic non-reciprocal $O(2)$-symmetric system. Through large-scale simulations, we uncover a new non-equilibrium scaling in the vicinity of the CEP, distinct from any previously known equilibrium or non-equilibrium universality classes. We report an anomalously large roughening exponent $α_{\rm CEP}=1.35(5)$, which is to be compared with those of simple diffusion $α_{\rm EW}=0.5$. In regimes where the system breaks into domains with opposite chirality and spatiotemporal vortices inevitably emerge, we find that fluctuations are strongly suppressed, leading to a logarithmic scaling as a function of system size $L$ that manifests a short-range correlation. This work elucidates the beyond-mean-field dynamics of non-reciprocal matter, thereby shedding light on the exploration of criticality in non-reciprocal phase transition across diverse physical contexts, from active matter and driven quantum systems to biological pattern formation and non-Hermitian physics. |
| title | Universal scaling in one-dimensional non-reciprocal matter |
| topic | Statistical Mechanics Soft Condensed Matter Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2503.14384 |