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Hyperuniformity, the suppression of density fluctuations at large length scales, is observed across a wide variety of domains, from cosmology to condensed matter and biological systems. Although the standard definition of hyperuniformity…

Statistical Mechanics · Physics 2024-05-07 Marco Salvalaglio , Dominic J. Skinner , Jörn Dunkel , Axel Voigt

We demonstrate that the complex spatiotemporal structure in active fluids can feature characteristics of hyperuniformity. Using a hydrodynamic model, we show that the transition from hyperuniformity to non-hyperuniformity and…

Soft Condensed Matter · Physics 2023-11-28 Rainer Backofen , Abdelrahman Y. A. Altawil , Marco Salvalaglio , Axel Voigt

Extending hyperuniformity from classical to quantum fluctuations in electron systems yields a framework that identifies quantum phase transitions and reveals underlying gap structures through the quantum weight. We study long-wavelength…

Strongly Correlated Electrons · Physics 2026-01-27 Junmo Jeon , Shiro Sakai

Nonequilibrium hyperuniformity can arise either as a steady-state property of driven active fluids or as a critical signature at continuous absorbing transition points in two and three dimensions. Whether analogous structural order exists…

Soft Condensed Matter · Physics 2026-05-28 Yusheng Lei , Ran Ni

We present a brief survey of fluctuations and large deviations of particle systems with subextensive growth of the variance. These are called hyperuniform (or superhomogeneous) systems. We then discuss the relation between hyperuniformity…

Probability · Mathematics 2016-12-07 Subhro Ghosh , Joel L. Lebowitz

We characterize steady-state static and dynamic properties in a broad class of mass transport processes on a periodic hypercubic lattice of volume $L^d$, where both mass and {\it center-of-mass} (CoM) remain conserved and detailed balance…

Statistical Mechanics · Physics 2025-03-31 Animesh Hazra , Anirban Mukherjee , Punyabrata Pradhan

Hyperuniformity, whereby the static structure factor (or density correlator) obeys $S(q)\sim q^{\varsigma}$ with $\varsigma> 0$, emerges at criticality in systems having multiple absorbing states, such as periodically sheared suspensions.…

Statistical Mechanics · Physics 2023-10-27 Xiao Ma , Johannes Pausch , Michael E. Cates

Understanding the non-equilibrium dynamics of quantum many-body systems remains one of the grand challenges of modern physics. In particular, increasing attention has been devoted to the emergence of non-equilibrium universality classes…

Quantum Physics · Physics 2025-12-22 Wenbo Zhou , Yuke Zhang , Pengfei Zhang

Disordered hyperuniform structures are locally random while uniform like crystals at large length scales. Recently, an exotic hyperuniform fluid state was found in several non-equilibrium systems, while the underlying physics remains…

Soft Condensed Matter · Physics 2019-11-14 Qunli Lei , Ran Ni

Employing a two-species Cahn-Hilliard model with nonreciprocal interactions we show that the interplay of nonreciprocity and conservation laws results in the robust coexistence of uniform stationary and oscillatory phases as well as of…

Pattern Formation and Solitons · Physics 2025-08-27 Daniel Greve , Giorgio Lovato , Tobias Frohoff-Hülsmann , Uwe Thiele

We investigate the role of generalized symmetries in driving non-equilibrium and non-linear phenomena, specifically focusing on turbulent systems. While conventional turbulence studies have revealed inverse cascades driven by conserved…

High Energy Physics - Theory · Physics 2026-02-18 Yuji Hirono , Kohei Kamada , Naoki Yamamoto , Ryo Yokokura

Systems driven far from equilibrium may exhibit anomalous density fluctuations: active matter with orientational order display giant density fluctuations at large scale, while systems of interacting particles close to an absorbing phase…

Statistical Mechanics · Physics 2026-03-23 Sara Dal Cengio , Romain Mari , Eric Bertin

In harsh environments, organisms may self-organize into spatially patterned systems in various ways. So far, studies of ecosystem spatial self-organization have primarily focused on apparent orders reflected by regular patterns. However,…

Populations and Evolution · Quantitative Biology 2023-11-15 Wensi Hu , Quan-Xing Liu , Bo Wang , Nuo Xu , Lijuan Cui , Chi Xu

When driven out of equilibrium by a temperature gradient, fluids respond by developing a nontrivial, inhomogeneous structure according to the governing macroscopic laws. Here we show that such structure obeys strikingly simple scaling laws…

Statistical Mechanics · Physics 2015-03-26 J. J. del Pozo , P. L. Garrido , P. I. Hurtado

We explore the emergence of nonequilibrium collective motion in disordered non-thermal active matter when persistent motion and crowding effects compete, using simulations of a two-dimensional model of size polydisperse self-propelled…

Soft Condensed Matter · Physics 2022-07-27 Yann-Edwin Keta , Robert L. Jack , Ludovic Berthier

Hyperuniform point patterns are characterized by vanishing infinite wavelength density fluctuations and encompass all crystal structures, certain quasi-periodic systems, and special disordered point patterns. This article generalizes the…

Statistical Mechanics · Physics 2015-05-14 Chase E. Zachary , Salvatore Torquato

We construct infinite families of new universality classes of fracton hydrodynamics with momentum conservation, both with multipole conservation laws and/or subsystem symmetry. We explore the effects of broken inversion and/or time-reversal…

Statistical Mechanics · Physics 2022-02-01 Andrew Osborne , Andrew Lucas

In statistical physics, it is well established that the liquid-gas (LG) phase transition with divergent critical fluctuations belongs to the Ising universality class. Whether non-equilibrium effects can alter this universal behavior remains…

Statistical Mechanics · Physics 2026-04-07 Shang Gao , Hao Shang , Hao Hu , Yu-Qiang Ma , Qun-Li Lei

We study diffusion in systems of classical particles whose dynamics conserves the total center of mass. This conservation law leads to several interesting consequences. In finite systems, it allows for equilibrium distributions that are…

Statistical Mechanics · Physics 2024-01-04 Jung Hoon Han , Ethan Lake , Sunghan Ro

Hyperuniformity characterizes a state of matter for which density fluctuations diminish towards zero at the largest length scales. However, the task of determining whether or not an experimental system is hyperuniform is experimentally…

Soft Condensed Matter · Physics 2015-06-22 Remi Dreyfus , Ye Xu , Tim Still , Lawrence A. Hough , A. G. Yodh , Salvatore Torquato