Tom C. Lubensky

Chiral active materials are those that break both time-reversal symmetry and parity microscopically. This is usually a result of the average rotation of the material's complex particles around their center-of-mass (c.m.), which drives the system far from equilibrium. In this paper we show that the nonvanishing spin angular momentum brings about a difference between the c.m. momentum and the total momentum, where the latter accounts for the momentum of all atoms that compose the complex rotating particles. This is in stark contrast to equilibrium fluids where the c.m. stress and the total momentum are essentially equivalent. In fact, we find that generally the c.m. dynamics are insufficient to describe the dynamics of a chiral active material. The total momentum, other than being experimentally accessible in simple rheological experiments, also imposes a constraint-its stress must be allowed to be written in a symmetric way. We find that this requirement imposes a relation between possible central-force interactions and spin-spin interactions, and constraints the amount of odd viscosities in the system to the well-known odd (Hall) viscosity and the odd pressure.

Odd viscosity couples stress to strain rate in a dissipationless way. It has been studied in plasmas under magnetic fields, superfluid He 3 , quantum-Hall fluids, and recently in the context of chiral active matter. In most of these studies, odd terms in the viscosity obey Onsager reciprocal relations. Although this is expected in equilibrium systems, it is not obvious that Onsager relations hold in active materials. By directly coarse-graining the kinetic energy and independently using both the Poisson-bracket formalism and a kinetic theory derivation, we find that the appearance of a nonvanishing angular momentum density, which is a hallmark of chiral active materials, necessarily breaks Onsager reciprocal relations. This leads to a non-Hermitian dynamical matrix for the total hydrodynamic momentum and to the appearance of odd viscosity and other nondissipative contributions to the viscosity. Furthermore, by accounting for both the angular momentum density and interactions that lead to odd viscosity, we find regions in the parameter space in which 3D odd mechanical waves propagate and regions in which they are mechanically unstable. The lines separating these regions are continuous lines of exceptional points, suggesting a possible nonreciprocal phase transition.

Many two-dimensional physical systems ranging from atomic-molecular condensates to low-dimensional superconductors and liquid-crystal films are described by coupled XY models. The interplay of topology and competing interactions in these XY systems drives new kinds of emergent behavior relevant in both quantum and classical settings. Such coupled U(1) systems further introduce rich physics, bringing topology into contact with fractionalization and deconfinement. Motivated by a hidden-order phase transition in isotropic liquid-crystal 54COOBC films, we study the finite-temperature phase diagram of a minimalist hexatic-nematic XY model. We identify a small region of composite Potts order above the vortex-binding transition; this phase is characterized by relative hexatic-nematic ordering though both variables are disordered. We propose that the Potts order results from a confinement of fractional vortices into extended nematic defects and discuss the broader implications of fractional vortices and composite ordering in the wider class of coupled XY condensates.

In common fluids, viscosity is associated with dissipation. However, when time-reversal symmetry is broken a new type of nondissipative “viscosity” emerges. Recent theories and experiments on classical 2D systems with active spinning particles have heightened interest in “odd viscosity,” but a microscopic theory for it in active materials is still absent. Here, we present such first-principles microscopic Hamiltonian theory, valid for both 2D and 3D, showing that odd viscosity is present in any system, even at zero temperature, with globally or locally aligned spinning components. Our work substantially extends the applicability of odd viscosity into 3D fluids, and specifically to internally driven active materials, such as living matter (e.g., actomyosin gels). We find intriguing 3D effects of odd viscosity such as propagation of anisotropic bulk shear waves and breakdown of Bernoulli’s principle.

Nematic elastomers exhibit a rich elastic response to external stresses. Of particular interest is the semisoft response of elastomers with an anisotropy direction (z) frozen in by a double cross-linking process. This response is characterized by a stress-strain curve for stresses along x perpendicular to z that rises initially, exhibits a nearly flat plateau between two critical values of strain, and then rises again. This paper explores elastic response in semisoft elastomers as a function of externally applied strain. It derives general Ward identities for elastic moduli and shows that the elastic modulus measuring response to xz shears vanishes at the boundaries of the semisoft plateau whereas moduli measuring response to shears perpendicular to the xz plane do not. It then calculates all relevant moduli in a simple model of elastomers and verifies the general Ward-identity predictions.