We study the motility-induced phase separation of active particles driven through the interconversion of two chemical species controlled by ideal reservoirs (chemiostats). As a consequence, the propulsion speed is non-constant and depends on the actual inter-particle forces, enhancing the positive feedback between increased density and reduced motility that is responsible for the observed inhomogeneous density. For hard discs, we find that this effect is negligible and that the phase separation is controlled by the average propulsion speed. For soft particles and large propulsion speeds, however, we predict an observable impact on the collective behavior. We briefly comment on the reentrant behavior found for soft discs. Finally, we study the influence of non-constant propulsion on the sedimentation profile of non-interacting active particles. arXiv:1811.05746v1 [cond-mat.stat-mech]

No abstract

No abstract

No abstract

Symmetry is usually defined via transformations described by a (higher) group. But a symmetry really corresponds to an algebra of local symmetric operators, which directly constrains the properties of the system. In particular, isomorphic operator algebras correspond to equivalent symmetries. In this paper, we pointed out that the algebra of local symmetry operators actually contains extended string-like, membrane-like, etc operators. The algebra of those extended operators in n-dimensional space gives rise to a non-degenerate braided fusion n-category, which happens to describe a topological order in one higher dimension. This allows us to show that the equivalent classes of finite symmetries actually correspond to topological orders in one higher dimension. Such a holographic theory not only describes (higher) symmetries, it also describes anomalous (higher) symmetries, non-invertible (higher) symmetries (also known as algebraic higher symmetries), and (invertible and non-invertible) gravitational anomalies, in a unified and systematic way. We demonstrate this unified holographic framework via some simple examples of (higher and/or anomalous) symmetries, as well as a symmetry that is neither anomalous nor anomaly-free. We also show the equivalence between Z2 × Z2 symmetry with mixed anomaly and Z4 symmetry, as well as between many other symmetries, in 1-dimensional space. CONTENTS(1) 2 1-symmetry in 2d space D. The equivalence between Z2 0-symmetry and Z(1) 21-symmetry in 2d space IX. 2d non-Abelian symmetry and its dual A. The G 0-symmetry in 2d space B. The Grep 1-symmetry in 2d space X. A review of holographic theory of (algebraic higher) symmetry A. Representation category B. A holographic point view of symmetry C. Transformation category -dual of the representation category D. A simple example 1. Holographic view of 2d Z2 0-symmetry 2. Holographic view of 2d Z2 1-symmetry 3. Symmetry R = 2Rep Z 2 and dual-symmetry R = 2VecZ 2 XI. Equivalent symmetries A. Some known examples B. Equivalence between anomalous and anomaly-free Zn and Zn 1 × Zn 2 symmetries in 1-dimensional space