Pub Date : 2026-01-02DOI: 10.1146/annurev-conmatphys-031324-031350
José Alvarado, Erin G. Teich, David A. Sivak, John Bechhoefer
Soft and active condensed matter represent a class of fascinating materials that we encounter in our everyday lives—and constitute life itself. Control signals interact with the dynamics of these systems, and this influence is formalized in control theory and optimal control. Recent advances have employed various control-theoretical methods to design desired dynamics, properties, and functionality. Here, we provide an introduction to optimal control aimed at physicists working with soft and active matter. We describe two main categories of control, feedforward control and feedback control, and their corresponding optimal control methods. We emphasize their parallels to Lagrangian and Hamiltonian mechanics and provide a worked example problem. Finally, we review recent studies of control in soft, active, and related systems. Applying control theory to soft, active, and living systems will lead to an improved understanding of the signal processing, information flows, and actuation that underlie the physics of life.
{"title":"Optimal Control in Soft and Active Matter","authors":"José Alvarado, Erin G. Teich, David A. Sivak, John Bechhoefer","doi":"10.1146/annurev-conmatphys-031324-031350","DOIUrl":"https://doi.org/10.1146/annurev-conmatphys-031324-031350","url":null,"abstract":"Soft and active condensed matter represent a class of fascinating materials that we encounter in our everyday lives—and constitute life itself. Control signals interact with the dynamics of these systems, and this influence is formalized in control theory and optimal control. Recent advances have employed various control-theoretical methods to design desired dynamics, properties, and functionality. Here, we provide an introduction to optimal control aimed at physicists working with soft and active matter. We describe two main categories of control, feedforward control and feedback control, and their corresponding optimal control methods. We emphasize their parallels to Lagrangian and Hamiltonian mechanics and provide a worked example problem. Finally, we review recent studies of control in soft, active, and related systems. Applying control theory to soft, active, and living systems will lead to an improved understanding of the signal processing, information flows, and actuation that underlie the physics of life.","PeriodicalId":7925,"journal":{"name":"Annual Review of Condensed Matter Physics","volume":"183 1","pages":""},"PeriodicalIF":22.6,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145908293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-02DOI: 10.1146/annurev-conmatphys-031424-125004
Anthony R. Thornton, Kimberly Hill, Lu Jing, Benjy Marks, Deepak R. Tunuguntla
In this review, we introduce granular materials as a condensed matter system and briefly discuss their general properties. We then focus on particle segregation in rapid, dense granular flows, a phenomenon that occurs more readily in granular materials than in other condensed matter systems. Our primary emphasis is on the development of continuum models to describe segregation in these systems. Over the years, numerous approaches have been proposed, each offering different perspectives on how to construct such models. Rather than providing an exhaustive review of any single approach, we compare and contrast various modeling strategies, highlighting their commonalities and respective advantages. By doing so, we aim to establish a clearer connection between different approaches, facilitating closer comparisons and potential synergies between them. We believe that bridging these approaches is essential for advancing our understanding and improving predictive capabilities in granular segregation modeling in the future.
{"title":"Modeling Granular Segregation: Insights from Four Decades of Research","authors":"Anthony R. Thornton, Kimberly Hill, Lu Jing, Benjy Marks, Deepak R. Tunuguntla","doi":"10.1146/annurev-conmatphys-031424-125004","DOIUrl":"https://doi.org/10.1146/annurev-conmatphys-031424-125004","url":null,"abstract":"In this review, we introduce granular materials as a condensed matter system and briefly discuss their general properties. We then focus on particle segregation in rapid, dense granular flows, a phenomenon that occurs more readily in granular materials than in other condensed matter systems. Our primary emphasis is on the development of continuum models to describe segregation in these systems. Over the years, numerous approaches have been proposed, each offering different perspectives on how to construct such models. Rather than providing an exhaustive review of any single approach, we compare and contrast various modeling strategies, highlighting their commonalities and respective advantages. By doing so, we aim to establish a clearer connection between different approaches, facilitating closer comparisons and potential synergies between them. We believe that bridging these approaches is essential for advancing our understanding and improving predictive capabilities in granular segregation modeling in the future.","PeriodicalId":7925,"journal":{"name":"Annual Review of Condensed Matter Physics","volume":"23 1","pages":""},"PeriodicalIF":22.6,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145908294","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-22DOI: 10.1146/annurev-conmatphys-032922-100843
Jonathan Michel, Itai Cohen, Lawrence J. Bonassar, Moumita Das
Articular cartilage is a load-bearing, hierarchically organized tissue composed of a network of type II collagen embedded in an aggrecan-rich polyelectrolyte gel. Its ability to resist deformation and dissipate energy arises from spatially varying matrix composition and architecture. Here, we review experimental and theoretical advances that elucidate the mechanistic basis of cartilage shear mechanics. Recent studies have shown that the tissue operates near a rigidity transition, in which small changes in collagen density, cross-linking, or osmotic stress can produce large, nonlinear changes in shear stiffness. We discuss how this behavior is captured by models rooted in rigidity percolation, continuum elasticity, and micromechanics, and how these frameworks connect depth-dependent composition to macroscale mechanical response. Throughout, we emphasize physical principles that describe observations across native, degraded, and engineered tissues, and we highlight emerging strategies for designing cartilage-inspired materials with tunable, anisotropic mechanics, with applications in soft robotics, synthetic gels, and load-bearing biomaterials.
{"title":"Shear Mechanics of Articular Cartilage and Cartilage-Inspired Materials","authors":"Jonathan Michel, Itai Cohen, Lawrence J. Bonassar, Moumita Das","doi":"10.1146/annurev-conmatphys-032922-100843","DOIUrl":"https://doi.org/10.1146/annurev-conmatphys-032922-100843","url":null,"abstract":"Articular cartilage is a load-bearing, hierarchically organized tissue composed of a network of type II collagen embedded in an aggrecan-rich polyelectrolyte gel. Its ability to resist deformation and dissipate energy arises from spatially varying matrix composition and architecture. Here, we review experimental and theoretical advances that elucidate the mechanistic basis of cartilage shear mechanics. Recent studies have shown that the tissue operates near a rigidity transition, in which small changes in collagen density, cross-linking, or osmotic stress can produce large, nonlinear changes in shear stiffness. We discuss how this behavior is captured by models rooted in rigidity percolation, continuum elasticity, and micromechanics, and how these frameworks connect depth-dependent composition to macroscale mechanical response. Throughout, we emphasize physical principles that describe observations across native, degraded, and engineered tissues, and we highlight emerging strategies for designing cartilage-inspired materials with tunable, anisotropic mechanics, with applications in soft robotics, synthetic gels, and load-bearing biomaterials.","PeriodicalId":7925,"journal":{"name":"Annual Review of Condensed Matter Physics","volume":"16 1","pages":""},"PeriodicalIF":22.6,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145908296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-22DOI: 10.1146/annurev-conmatphys-031524-071133
Ting Cao, Liang Fu, Long Ju, Di Xiao, Xiaodong Xu
The realization of the fractional quantum anomalous Hall effect (FQAHE) in a zero-field fractional Chern insulator is a new advancement in condensed matter physics, resulting from the interplay among strong correlations, topology, and spontaneous time-reversal symmetry breaking in lattice systems. In this review, we highlight the experimental and theoretical progress toward achieving FQAHE in two material platforms: twisted bilayer MoTe 2 and rhombohedral-stacked multilayer graphene. These systems host narrow topological bands with nontrivial Chern numbers, enabling interaction-driven fractionalized states analogous to the fractional quantum Hall effect, but without external magnetic fields. We discuss how spontaneous ferromagnetism, moiré lattice reconstruction, and band topological effects underpin the emergence of FQAHE in twisted MoTe 2 . We describe experimental discoveries of zero-field fractional Chern insulators in both transport and optical experiments, as well as signatures of composite Fermi liquids and higher-energy Chern band, which may shed light on engineering nonabelian states. In rhombohedral graphene/hexagonal boron nitride moiré superlattices, we review the recent observations of fractionally quantized Hall resistance, connections between FQAHE and extended quantum anomalous Hall phases, and the coexistence of superconductivity and FQAHE. These discoveries not only deepen our understanding of strongly correlated topological matter but also open new frontiers for exploring nonabelian anyons, fault-tolerant quantum computation, and topological opto-spintronics free of magnetic fields.
{"title":"Fractional Quantum Anomalous Hall Effect","authors":"Ting Cao, Liang Fu, Long Ju, Di Xiao, Xiaodong Xu","doi":"10.1146/annurev-conmatphys-031524-071133","DOIUrl":"https://doi.org/10.1146/annurev-conmatphys-031524-071133","url":null,"abstract":"The realization of the fractional quantum anomalous Hall effect (FQAHE) in a zero-field fractional Chern insulator is a new advancement in condensed matter physics, resulting from the interplay among strong correlations, topology, and spontaneous time-reversal symmetry breaking in lattice systems. In this review, we highlight the experimental and theoretical progress toward achieving FQAHE in two material platforms: twisted bilayer MoTe <jats:sub>2</jats:sub> and rhombohedral-stacked multilayer graphene. These systems host narrow topological bands with nontrivial Chern numbers, enabling interaction-driven fractionalized states analogous to the fractional quantum Hall effect, but without external magnetic fields. We discuss how spontaneous ferromagnetism, moiré lattice reconstruction, and band topological effects underpin the emergence of FQAHE in twisted MoTe <jats:sub>2</jats:sub> . We describe experimental discoveries of zero-field fractional Chern insulators in both transport and optical experiments, as well as signatures of composite Fermi liquids and higher-energy Chern band, which may shed light on engineering nonabelian states. In rhombohedral graphene/hexagonal boron nitride moiré superlattices, we review the recent observations of fractionally quantized Hall resistance, connections between FQAHE and extended quantum anomalous Hall phases, and the coexistence of superconductivity and FQAHE. These discoveries not only deepen our understanding of strongly correlated topological matter but also open new frontiers for exploring nonabelian anyons, fault-tolerant quantum computation, and topological opto-spintronics free of magnetic fields.","PeriodicalId":7925,"journal":{"name":"Annual Review of Condensed Matter Physics","volume":"14 1","pages":""},"PeriodicalIF":22.6,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145908295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-19DOI: 10.1146/annurev-conmatphys-061225-105656
Amir Pahlavan, Michael Murrell
Active wetting extends classical wetting physics to living systems, in which cells and tissues spread by generating internal forces rather than relying solely on passive interfacial tensions. Unlike passive systems, which evolve toward thermodynamic and mechanical equilibrium by minimizing free energy, active systems remain far from equilibrium due to continuous energy input and dissipation. Their dynamics are sustained, adaptive, and responsive to chemical and mechanical cues in ways that depart fundamentally from passive behavior. In addition, active systems lack a unified energetic or variational principle to describe their evolution. What insights can be drawn from passive models, and how these models might be generalized to account for activity, remain open questions. Studying active wetting may thus reveal new principles of nonequilibrium dynamics at soft and living interfaces, and offer deeper understanding of key biological processes such as wound healing, cancer invasion, and biofilm growth.
{"title":"Active Wetting: Statics and Dynamics","authors":"Amir Pahlavan, Michael Murrell","doi":"10.1146/annurev-conmatphys-061225-105656","DOIUrl":"https://doi.org/10.1146/annurev-conmatphys-061225-105656","url":null,"abstract":"Active wetting extends classical wetting physics to living systems, in which cells and tissues spread by generating internal forces rather than relying solely on passive interfacial tensions. Unlike passive systems, which evolve toward thermodynamic and mechanical equilibrium by minimizing free energy, active systems remain far from equilibrium due to continuous energy input and dissipation. Their dynamics are sustained, adaptive, and responsive to chemical and mechanical cues in ways that depart fundamentally from passive behavior. In addition, active systems lack a unified energetic or variational principle to describe their evolution. What insights can be drawn from passive models, and how these models might be generalized to account for activity, remain open questions. Studying active wetting may thus reveal new principles of nonequilibrium dynamics at soft and living interfaces, and offer deeper understanding of key biological processes such as wound healing, cancer invasion, and biofilm growth.","PeriodicalId":7925,"journal":{"name":"Annual Review of Condensed Matter Physics","volume":"29 1","pages":""},"PeriodicalIF":22.6,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145908390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-19DOI: 10.1146/annurev-conmatphys-031620-105420
Luiza Angheluta, Anna Lång, Emma Lång, Stig Ove Bøe
Polar active matter—including animal herds, aggregates of motile cells, and active colloids—often forms coordinated migration patterns, such as flocking. This orderly motion can be disrupted by full-integer topological defects representing localized disturbances in which directional alignment is lost. Such polar defects can serve as key organizing centers across scales, sustaining collective behavior such as swirling motion and other large-scale coherent states. Although significant progress has been made in understanding active matter principles in recent years, a quantitative understanding of how topological defects influence active polar matter is still needed. We present a brief overview of recent experimental observations in synthetic active colloids and various biological systems. We describe how polar defects mediate dynamical transitions and contribute to the spontaneous emergence of large-scale coherent states. We also discuss theoretical advances in the physical modeling of coupled processes involving polar defects and collective behavior in active polar matter.
{"title":"Full-Integer Topological Defects in Polar Active Matter: From Collective Migration to Tissue Patterning","authors":"Luiza Angheluta, Anna Lång, Emma Lång, Stig Ove Bøe","doi":"10.1146/annurev-conmatphys-031620-105420","DOIUrl":"https://doi.org/10.1146/annurev-conmatphys-031620-105420","url":null,"abstract":"Polar active matter—including animal herds, aggregates of motile cells, and active colloids—often forms coordinated migration patterns, such as flocking. This orderly motion can be disrupted by full-integer topological defects representing localized disturbances in which directional alignment is lost. Such polar defects can serve as key organizing centers across scales, sustaining collective behavior such as swirling motion and other large-scale coherent states. Although significant progress has been made in understanding active matter principles in recent years, a quantitative understanding of how topological defects influence active polar matter is still needed. We present a brief overview of recent experimental observations in synthetic active colloids and various biological systems. We describe how polar defects mediate dynamical transitions and contribute to the spontaneous emergence of large-scale coherent states. We also discuss theoretical advances in the physical modeling of coupled processes involving polar defects and collective behavior in active polar matter.","PeriodicalId":7925,"journal":{"name":"Annual Review of Condensed Matter Physics","volume":"29 1","pages":""},"PeriodicalIF":22.6,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145908297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-19DOI: 10.1146/annurev-conmatphys-071125-054711
Sayantani Kayal, Anh Q. Nguyen, Dapeng Bi
Biological tissue rheology investigates the mechanical behavior of tissues, emphasizing their viscoelastic and plastic properties that enable both solid-like elasticity and fluid-like viscosity under mechanical stress. These mechanical characteristics are pivotal in various physiological processes, such as embryonic development, tissue remodeling, wound healing, and pathological conditions including cancer metastasis. The mechanical responses of tissues, shaped by cellular forces and extracellular matrix dynamics, are crucial for maintaining tissue integrity and functionality. Rheological behaviors such as viscoelasticity, plasticity, and active mechanical responses underlie critical biological functions, enabling tissues to adapt structurally and functionally to internal and external stimuli. Recent theoretical and experimental advances have illuminated the complex interplay among cellular mechanics, biochemical signaling, and tissue-level forces, highlighting their roles in governing tissue morphogenesis, repair, and disease progression. This review synthesizes current knowledge, identifies key challenges, and discusses future directions for research in biological tissue rheology.
{"title":"The Rheology of Living Tissues: From Cells to Organismal Mechanics","authors":"Sayantani Kayal, Anh Q. Nguyen, Dapeng Bi","doi":"10.1146/annurev-conmatphys-071125-054711","DOIUrl":"https://doi.org/10.1146/annurev-conmatphys-071125-054711","url":null,"abstract":"Biological tissue rheology investigates the mechanical behavior of tissues, emphasizing their viscoelastic and plastic properties that enable both solid-like elasticity and fluid-like viscosity under mechanical stress. These mechanical characteristics are pivotal in various physiological processes, such as embryonic development, tissue remodeling, wound healing, and pathological conditions including cancer metastasis. The mechanical responses of tissues, shaped by cellular forces and extracellular matrix dynamics, are crucial for maintaining tissue integrity and functionality. Rheological behaviors such as viscoelasticity, plasticity, and active mechanical responses underlie critical biological functions, enabling tissues to adapt structurally and functionally to internal and external stimuli. Recent theoretical and experimental advances have illuminated the complex interplay among cellular mechanics, biochemical signaling, and tissue-level forces, highlighting their roles in governing tissue morphogenesis, repair, and disease progression. This review synthesizes current knowledge, identifies key challenges, and discusses future directions for research in biological tissue rheology.","PeriodicalId":7925,"journal":{"name":"Annual Review of Condensed Matter Physics","volume":"94 1","pages":""},"PeriodicalIF":22.6,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145908298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-18DOI: 10.1146/annurev-conmatphys-082225-051908
Muhittin Mungan, Eric Clément, Damien Vandembroucq, Srikanth Sastry
Disordered systems subject to a fluctuating environment can self-organize into a complex history-dependent response, retaining a memory of the driving. In sheared amorphous solids, self-organization is established by the emergence of a persistent system of mechanical instabilities that can repeatedly be triggered by the driving, leading to a state of high mechanical reversibility. As a result of self-organization, the response of the system becomes correlated with the dynamics of its environment, which can be viewed as a sensing mechanism of the system's environment. Such phenomena emerge across a wide variety of soft matter systems, suggesting that they are generic and, hence, may depend very little on the underlying specifics. We review self-organization in driven amorphous solids, concluding with a discussion of what self-organization in driven disordered systems can teach us about how simple organisms sense and adapt to their changing environments.
{"title":"Self-Organization, Memory, and Learning: From Driven Disordered Systems to Living Matter","authors":"Muhittin Mungan, Eric Clément, Damien Vandembroucq, Srikanth Sastry","doi":"10.1146/annurev-conmatphys-082225-051908","DOIUrl":"https://doi.org/10.1146/annurev-conmatphys-082225-051908","url":null,"abstract":"Disordered systems subject to a fluctuating environment can self-organize into a complex history-dependent response, retaining a memory of the driving. In sheared amorphous solids, self-organization is established by the emergence of a persistent system of mechanical instabilities that can repeatedly be triggered by the driving, leading to a state of high mechanical reversibility. As a result of self-organization, the response of the system becomes correlated with the dynamics of its environment, which can be viewed as a sensing mechanism of the system's environment. Such phenomena emerge across a wide variety of soft matter systems, suggesting that they are generic and, hence, may depend very little on the underlying specifics. We review self-organization in driven amorphous solids, concluding with a discussion of what self-organization in driven disordered systems can teach us about how simple organisms sense and adapt to their changing environments.","PeriodicalId":7925,"journal":{"name":"Annual Review of Condensed Matter Physics","volume":"32 1","pages":""},"PeriodicalIF":22.6,"publicationDate":"2025-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145908299","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-17DOI: 10.1146/annurev-conmatphys-031424-011954
Oleg D. Lavrentovich
Ground states of materials with orientational order ranging from solid ferromagnets and ferroelectrics to liquid crystals often contain spatially varying vector-like order parameter caused by inner factors such as the shape of building units or by the geometry of confinement. This review presents examples of how the shapes, chirality, and polarity of molecules and spatial confinement induce deformed equilibrium and polydomain states with parity breaking, splay, bend, and twist-bend deformations of the order parameter in paraelectric and ferroelectric nematic liquid crystals. Parity breaking results either from chirality of the constituent molecules, as a replacement of energetically costly splay and bend in paraelectric nematics, or in response to a depolarization field in the ferroelectric nematic. Both paraelectric and ferroelectric nematics exhibit a splay cancellation effect, in which the elastic and electrostatic energies of splay along one direction are reduced by an additional splay along orthogonal directions.
{"title":"Deformed States in Paraelectric and Ferroelectric Nematic Liquid Crystals","authors":"Oleg D. Lavrentovich","doi":"10.1146/annurev-conmatphys-031424-011954","DOIUrl":"https://doi.org/10.1146/annurev-conmatphys-031424-011954","url":null,"abstract":"Ground states of materials with orientational order ranging from solid ferromagnets and ferroelectrics to liquid crystals often contain spatially varying vector-like order parameter caused by inner factors such as the shape of building units or by the geometry of confinement. This review presents examples of how the shapes, chirality, and polarity of molecules and spatial confinement induce deformed equilibrium and polydomain states with parity breaking, splay, bend, and twist-bend deformations of the order parameter in paraelectric and ferroelectric nematic liquid crystals. Parity breaking results either from chirality of the constituent molecules, as a replacement of energetically costly splay and bend in paraelectric nematics, or in response to a depolarization field in the ferroelectric nematic. Both paraelectric and ferroelectric nematics exhibit a splay cancellation effect, in which the elastic and electrostatic energies of splay along one direction are reduced by an additional splay along orthogonal directions.","PeriodicalId":7925,"journal":{"name":"Annual Review of Condensed Matter Physics","volume":"43 1","pages":""},"PeriodicalIF":22.6,"publicationDate":"2025-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145908301","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-17DOI: 10.1146/annurev-conmatphys-071125-063050
Paul M. Goldbart
A rich variety of amorphous solids are found throughout nature, science, and technology, including those formed via the vulcanization of long, flexible polymer molecules. A special class—those featuring a wide separation between the very long timescales on which constraining bonds release and the much shorter timescales on which unconstrained degrees of freedom relax—exhibit equilibrium states and are therefore amenable to equilibrium statistical mechanics. A review is given of the least detailed (and thus most general) approach to equilibrium amorphous solids: statistical field theory. The field at the center of this theory is motivated by the aim of characterizing the amorphous solid state. This field, and the theory that governs it, turn out to be rather unusual in essential ways. What the statistical field theory approach predicts—and can predict—is discussed, including the following: the emergence of the solid and its intrinsic heterogeneity; fluctuations and connections with percolation; symmetry breaking and elasticity; and correlations and the information they furnish. Emphasis is placed on the idea, particular to amorphous solids, that such solids are naturally characterized in terms of distributions that describe the spatial heterogeneity of the thermal motions of their constituents. This information is subtly encoded in the wave vector dependencies of the average field and its correlations. The review concludes with some reflections on the applicability—or otherwise—of the ideas and results it explores to a variety of amorphous solids and related systems.
{"title":"Statistical Field Theory of Equilibrium Amorphous Solids and the Intrinsic Heterogeneity Distributions that Characterize Them","authors":"Paul M. Goldbart","doi":"10.1146/annurev-conmatphys-071125-063050","DOIUrl":"https://doi.org/10.1146/annurev-conmatphys-071125-063050","url":null,"abstract":"A rich variety of amorphous solids are found throughout nature, science, and technology, including those formed via the vulcanization of long, flexible polymer molecules. A special class—those featuring a wide separation between the very long timescales on which constraining bonds release and the much shorter timescales on which unconstrained degrees of freedom relax—exhibit equilibrium states and are therefore amenable to equilibrium statistical mechanics. A review is given of the least detailed (and thus most general) approach to equilibrium amorphous solids: statistical field theory. The field at the center of this theory is motivated by the aim of characterizing the amorphous solid state. This field, and the theory that governs it, turn out to be rather unusual in essential ways. What the statistical field theory approach predicts—and can predict—is discussed, including the following: the emergence of the solid and its intrinsic heterogeneity; fluctuations and connections with percolation; symmetry breaking and elasticity; and correlations and the information they furnish. Emphasis is placed on the idea, particular to amorphous solids, that such solids are naturally characterized in terms of distributions that describe the spatial heterogeneity of the thermal motions of their constituents. This information is subtly encoded in the wave vector dependencies of the average field and its correlations. The review concludes with some reflections on the applicability—or otherwise—of the ideas and results it explores to a variety of amorphous solids and related systems.","PeriodicalId":7925,"journal":{"name":"Annual Review of Condensed Matter Physics","volume":"13 1","pages":""},"PeriodicalIF":22.6,"publicationDate":"2025-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145908300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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