Condensed Matter Theory

Abstract:

Models of active nematics in biological systems normally require complexity arising from the hydrodynamics involved at the microscopic level as well as the viscoelastic nature of the system. Here we show that a minimal, space-independent, model based on the temporal alignment of active and polymeric particles provides an avenue to predict and study their coupled dynamics within the framework of dynamical systems. In particular, we examine, using analytical and numerical methods, how such a simple model can display self-sustained oscillations in an activity-driven viscoelastic shear flow.

Abstract:

This chapter will provide an overview of how characterising free energy landscapes can provide insights into the biophysical properties of DNA, as well as into the behaviour of the DNA assemblies used in the field of DNA nanotechnology. The landscapes for these complex systems are accessible through the use of accurate coarse-grained descriptions of DNA. Particular foci will be the landscapes associated with DNA self-assembly and mechanical deformation, where the latter can arise from either externally imposed forces or internal stresses.

Abstract:

We construct models hosting classical fractal spin liquids on two realistic three-dimensional (3D) lattices of corner-sharing triangles: trillium and hyperhyperkagome (HHK). Both models involve the same form of three-spin Ising interactions on triangular plaquettes as the Newman-Moore (NM) model on the 2D triangular lattice. However, in contrast to the NM model and its 3D generalizations, their degenerate ground states and low-lying excitations cannot be described in terms of scalar cellular automata (CA), because the corresponding fractal structures lack a simplifying algebraic property, often termed the "freshman's dream."By identifying a link to matrix CAs - that makes essential use of the crystallographic structure - we show that both models exhibit fractal symmetries of a distinct class to the NM-type models. We devise a procedure to explicitly construct low-energy excitations consisting of finite sets of immobile defects or "fractons,"by flipping arbitrarily large self-similar subsets of spins, whose fractal dimensions we compute analytically. We show that these excitations are associated with energetic barriers which increase logarithmically with system size, leading to "fragile"glassy dynamics, whose existence we confirm via classical Monte Carlo simulations. We also discuss consequences for spontaneous fractal symmetry breaking when quantum fluctuations are introduced by a transverse magnetic field, and propose multispin correlation function diagnostics for such transitions. Our findings suggest that matrix CAs may provide a fruitful route to identifying fractal symmetries and fractonlike behavior in lattice models, with possible implications for the study of fracton topological order.