Topology protects chiral edge currents in stochastic systems

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   Thermodynamic origins of topological protection in nonequilibrium stochastic systems

   Pankaj Mehta, Jason W. Rocks · 2022 · cited 2 times · Not summarized yet

   Abstract

   Topological protection has emerged as an organizing principle for understanding and engineering robust collective behavior in electronic and material systems. Recent work suggests that topology may also play a role in organizing stochastic processes relevant to biology and self-assembly. Here, we show that topological protection in chemical networks can be understood entirely in terms of nonequilibrium thermodynamics. We illustrate these ideas using simple examples inspired by the literature.

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   Designing topological edge states in bacterial active matter

   Yoshi Uchida, Daiki Nishiguchi, Kazumasa A. Takeuchi · 2026 · cited 6 times · Not summarized yet

   Abstract

   Topology provides a unifying framework for understanding robust transport through protected edge states arising from nontrivial wavenumber topology. Extending these concepts to active matter, however, remains largely unexplored experimentally, with realizations limited to systems composed of chiral active particles. Here, we realize topological edge states in dense bacterial suspension, which represents a prototypical active matter system, using microfabricated geometrical structures with nontrivial wavenumber topology. Inspired by previous theoretical studies, we constructed a directional kagome network composed of ratchet-shaped channels that induce unidirectional bacterial flow. In this n…

3. Very close Cites this paper Not relevant

   An interdimensional funnel enhances topologically protected oscillations in high-dimensional stochastic systems

   Varsha Traynor, J. Agudo-Canalejo · 2026 · Not summarized yet

   Abstract

   Biochemical systems such as protein complexes often occupy configuration spaces whose dimensionality grows with the number of molecular components. Although usually viewed as an obstacle to coherent dynamics, here we show that high dimensionality can enhance topologically protected oscillations. In the topological regime, a stochastic system with a $D$-dimensional configuration space develops a steady-state current confined to a one-dimensional edge cycle. The intervening boundary faces between the $D$-dimensional bulk and the one-dimensional cycle form an interdimensional funnel, sequentially pushing the system towards lower dimensional faces, down to the one-dimensional cycle. As a consequ…

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   Topologically protected edge oscillations in nonlinear dynamical units.

   Sayantan Nag Chowdhury, H. Meyer-Ortmanns · 2025 · Physical Review E · cited 6 times · Not summarized yet

   Abstract

   Many examples from quantum and classical physics are known where topological protection is responsible for the robustness of the dynamics. Less explored is the role of topological protection in the context of classical oscillatory systems. As on-site dynamics, we consider prototypical oscillator models with possible applications in biochemical systems. However, our choice of coupling geometry is inspired by models from condensed matter physics which-in isolation-guarantee nontrivial topology in momentum space. We choose directed couplings between units on a two-dimensional grid, alternating between weak and strong values, such that oscillations become localized at the edges of the grid while…

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   Classification of topological phases of matter in stochastic systems

   De-Xin Li, Evelyn Tang · 2026 · Not summarized yet

   Abstract

   Topological phases of matter support edge states protected from random perturbations, and the identification of the discrete non-spatial symmetries and dimensions that support such phases was systematically developed for quantum systems and analogous platforms. While topological phases were also discovered in stochastic systems and posited as mechanisms for key biochemical processes, a classification consistent with their Markovian constraints remains lacking, impeding generalization to new scenarios. To address this, we develop new methods including a new homotopy approach, real-space invariants and a redefinition of the point gap to classify both transient and steady states. We find robust…

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   Microscopic Nonreciprocity-Governed Topological Boundary Flows in Active Matter

   Tong Zhu, Zhi-Gang Zheng · 2026 · Not summarized yet

   Abstract

   We connect microscopic nonreciprocity to chiral boundary transport in a minimal frustrated Vicsek--Kuramoto model. Unlike field-level constructions, a low-angular-harmonic closure of particle dynamics yields the non-Hermitian operator. Direction-independent polar projector limits permit wave-number compactification, and the Sakaguchi phase lag reverses the polar spin weights, producing $C=\pm2$ where the closure is nonsingular and the projector remains globally isolated. Strip edge-mode propagation agrees with particle circulation. Crucially, chirality and defect tolerance are distinct: before pattern onset, boundary streams retain chirality on regular convex boundaries but are vulnerable to…

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   Topological localization in out-of-equilibrium dissipative systems

   K. Dasbiswas, K. Mandadapu, Suriyanarayanan Vaikuntanathan · 2017 · Proceedings of the National Academy of Sciences of the United States of America · cited 74 times · Not summarized yet

   Abstract

   Significance Topological insulators and their analogs in mechanical materials support conducting states only on their surface. We show that such topologically protected edge modes can also occur as the steady states of classical systems driven out of equilibrium. As proof of principle of the generic applicability of such notions, we show the existence of topologically localized states in a collection of interacting particles described by a hydrodynamic theory and discuss a general procedure to establish them in stochastic networks. In both cases, dissipative processes that break time-reversal symmetry are key to topological protection. Our results provide design principles for robust edge mo…

8. Very close Cites this paper Not relevant

   Topological chiral random walker

   Saeed Osat, Ellen Meyberg, Jakob Metson et al. · 2026 · cited 2 times · Not summarized yet

   Abstract

   Understanding how biological and synthetic systems achieve robust function in noisy environments remains a fundamental challenge across the physical and life sciences. To connect robust behavior with non-trivial topological features present already in the dynamics of individual units, here we introduce the topological chiral random walker (TCRW) model. While exploring the system, a TCRW locates edges and boundaries in the system and develops topologically protected edge currents even in the presence of defects and disorder. Drawing on the bulk-boundary correspondence found in hard condensed matter systems allows us to rationalize the emergence of robust edge currents through topological feat…

Prior work it builds on

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   The effects of retardation on the topological plasmonic chain: plasmonic edge states beyond the quasistatic limit

   Simon R. Pocock, P. Huidobro, V. Giannini · 2017 · cited 73 times · Not summarized yet

   Abstract

   We study a one-dimensional plasmonic system with non-trivial topology: a chain of metallic nanoparticles with alternating spacing, which is the plasmonic analogue to the Su-Schreiffer-Heeger model. We extend previous efforts by including long range hopping with retardation and radiative damping, which leads to a non-Hermitian Hamiltonian with frequency dependence. We calculate band structures numerically and show that topological features such as quantised Zak phase persist due to chiral symmetry. This predicts parameters leading to topologically protected edge modes, which allows for positioning of disorder-robust hotspots at topological interfaces, opening up novel nanophotonics applications…

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   Topological Band Theory for Non-Hermitian Hamiltonians.

   Huitao Shen, B. Zhen, L. Fu · 2017 · Physical Review Letters · cited 976 times · Not summarized yet

   Abstract

   We develop the topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex. After generalizing the notion of gapped band structures to the non-Hermitian case, we classify "gapped" bands in one and two dimensions by explicitly finding their topological invariants. We find nontrivial generalizations of the Chern number in two dimensions, and a new classification in one dimension, whose topology is determined by the energy dispersion rather than the energy eigenstates. We then study the bulk-edge correspondence and the topological phase transition in two dimensions. Different from the Hermitian case, the transition generically involves…

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   Topological active matter

   Suraj Shankar, A. Souslov, M. Bowick et al. · 2020 · Nature Reviews Physics · cited 377 times · Not summarized yet

   Abstract

   In active matter systems, individual constituents convert energy into non-conservative forces or motion at the microscale, leading to morphological features and transport properties that do not occur in equilibrium and that are robust against certain perturbations. In recent years, a fruitful method for analysing these features has been to use tools from topology. In this Review, we focus on topological defects and topologically protected edge modes, with an emphasis on the distinctive properties they acquire in active media. These paradigmatic examples represent two physically distinct classes of phenomena that are robust thanks to a common mathematical origin: the presence of topological i…

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   Anomalous Topological Active Matter.

   K. Sone, Y. Ashida · 2019 · Physical Review Letters · cited 48 times · Not summarized yet

   Abstract

   Active systems exhibit spontaneous flows induced by self-propulsion of microscopic constituents and can reach a nonequilibrium steady state without an external drive. Constructing the analogy between the quantum anomalous Hall insulators and active matter with spontaneous flows, we show that topologically protected sound modes can arise in a steady-state active system in continuum space. We point out that the net vorticity of the steady-state flow, which acts as a counterpart of the gauge field in condensed-matter settings, must vanish under realistic conditions for active systems. The quantum anomalous Hall effect thus provides design principles for realizing topological metamaterials. We p…

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   Topological phases in the non-Hermitian Su-Schrieffer-Heeger model

   S. Lieu · 2017 · Physical Review B · cited 426 times · Not summarized yet

   Abstract

   We address the conditions required for a $\mathbb{Z}$ topological classification in the most general form of the non-Hermitian Su-Schrieffer-Heeger (SSH) model. Any chirally symmetric SSH model will possess a ``conjugated-pseudo-Hermiticity'' which we show is responsible for a quantized ``complex'' Berry phase. Consequently, we provide an example where the complex Berry phase of a band is used as a quantized invariant to predict the existence of gapless edge modes in a non-Hermitian model. The chirally broken, $PT$-symmetric model is studied; we suggest an explanation for why the topological invariant is a global property of the Hamiltonian. A geometrical picture is provided by examining eig…

Papers that cite it

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   Persistent homology of convection cycles in network flows

   M. Le, D. Taylor · 2021 · Physical Review E · cited 4 times · Not summarized yet

   Abstract

   Convection is a well-studied topic in fluid dynamics, yet it is less understood in the context of network flows. Here, we incorporate techniques from topological data analysis (namely, persistent homology) to automate the detection and characterization of convective flows (also called cyclic or chiral flows) over networks, particularly those that arise for irreversible Markov chains. As two applications, we study convection cycles arising under the PageRank algorithm and we investigate chiral edge flows for a stochastic model of a bimonomer's configuration dynamics. Our experiments highlight how system parameters-e.g., the teleportation rate for PageRank and the transition rates of external …

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   Topological edge flows drive macroscopic reorganization in magnetic colloids

   Aleksandra Nelson, Dana M Lobmeyer, S. Biswal et al. · 2024 · Physical Review Research · cited 4 times · Not summarized yet

   Abstract

   Magnetic colloids can be driven with time-varying fields to form clusters and voids that re-organize over vastly different timescales. However, the driving force behind these nonequilibrium dynamics is not well-understood. Here, we introduce a topological framework that predicts protected edge flows despite strong thermal motion. Notably, these edge flows produce shear stress that creates global rotation of clusters but not of voids. We verify this theory experimentally using micrometer-sized superparamagnetic colloids to demonstrate these emergent physical predictions and show how they drive system reorganization differentially at long timescales. Our results elucidate fundamental principle…

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   Analytical topological invariants for 2D non-Hermitian phases using Morse theory

   C. Gibson, Evelyn Tang · 2026 · cited 1 time · Not summarized yet

   Abstract

   As energy dissipation and gain are ubiquitous in the real world, such phenomena demand the generalization of Hermitian methods such as the analysis of topological properties for non-Hermitian systems. However, as non-Hermitian systems typically contain more degrees of freedom, this poses a challenge for analytical approaches to understand their topology and invariants. In this work, we analytically calculate the 2D Zak phase for a 2D non-Hermitian SSH-type Hamiltonian that supports a rich structure and edge currents. Closed-form expressions for eigenstates and divisions of the phase diagram are obtained, including for regions in the phase diagram where different types of exceptional points e…

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   Topological Nature of Edge States for One-Dimensional Systems without Symmetry Protection.

   Janet Zhong, Heming Wang, A. Poddubny et al. · 2024 · Physical Review Letters · cited 11 times · Not summarized yet

   Abstract

   We numerically verify and analytically prove a winding number invariant that correctly predicts the number of edge states in one-dimensional, nearest-neighbor (between unit cells), two-band models with any complex couplings and open boundaries. Our winding number uses analytical continuation of the wave-vector into the complex plane and involves two special points on the full Riemann surface band structure that correspond to bulk eigenvector degeneracies. Our winding number is invariant under unitary or similarity transforms. We emphasize that the topological criteria we propose here differ from what is traditionally defined as a topological or trivial phase in symmetry-protected classificat…

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   Topological invariant and anomalous edge modes of strongly nonlinear systems

   Di Zhou, D. Rocklin, M. Leamy et al. · 2020 · Nature Communications · cited 44 times · Not summarized yet

   Abstract

   Despite the extensive studies of topological states, their characterization in strongly nonlinear classical systems has been lacking. In this work, we identify the proper definition of Berry phase for nonlinear bulk waves and characterize topological phases in one-dimensional (1D) generalized nonlinear Schrödinger equations in the strongly nonlinear regime, where the general nonlinearities are beyond Kerr-like interactions. Without utilizing linear analysis, we develop an analytic strategy to demonstrate the quantization of nonlinear Berry phase due to reflection symmetry. Mode amplitude itself plays a key role in nonlinear modes and controls topological phase transitions. We then show bulk-…