Condensed Matter Theory

Abstract:

Attractors such as fixed points, limit cycles and strange attractors arise in nonlinear dynamical systems, however, such attractors may also be used to drive complex dynamics. By using a low-dimensional chaotic dynamical system to model each particle’s internal state space, we present a new class of matter coined “attractor-driven matter”. Through illustrative examples, I will show how attractor-driven particles when combined with particle-particle interactions and environment can give rise to complex dynamical and emergent behaviors reminiscent of active matter. The formalism may be applicable more broadly, to model complex dynamical and emergent behaviors in a variety of contexts.

Abstract:

DNA–RNA hybrid strand displacement underpins the function of many natural and engineered systems. Understanding and controlling factors affecting DNA–RNA strand displacement reactions is necessary to enable control of processes such as CRISPR-Cas9 gene editing. By combining multiscale modeling with strand displacement experiments, we show that the distribution of bases within the displacement domain has a very strong effect on reaction kinetics, a feature unique to DNA–RNA hybrid strand displacement. Merely by redistributing bases within a displacement domain of fixed base composition, we are able to design sequences whose reaction rates span more than four orders of magnitude. We extensively characterize this effect in reactions involving the invasion of dsDNA by an RNA strand, as well as the invasion of a hybrid duplex by a DNA strand. In all-DNA strand displacement reactions, we find a predictable but relatively weak sequence dependence, confirming that DNA–RNA strand displacement permits far more thermodynamic and kinetic control than its all-DNA counterpart. We show that oxNA, a recently introduced coarse-grained model of DNA–RNA hybrids, can reproduce trends in experimentally observed reaction rates. We also develop a simple kinetic model for predicting strand displacement rates. On the basis of these results, we argue that base distribution effects may play an important role in natural R-loop formation and in the function of the guide RNAs that direct CRISPR-Cas systems.

Abstract:

<jats:p> Fusion surface models, as introduced by Inamura and Ohmori, extend the concept of anyon chains to 2+1 dimensions, taking fusion 2-categories as their input. In this work, we construct and analyze fusion surface models on the honeycomb lattice built from braided fusion 1-categories. These models preserve mutually commuting plaquette operators and anomalous 1-form symmetries. Their Hamiltonian is chosen to mimic the structure of Kitaev’s honeycomb model, which is unitarily equivalent to the Ising fusion surface model. In the anisotropic limit, where one coupling constant is dominant, the fusion surface models reduce to Levin-Wen string-nets. In the isotropic limit, they are described by weakly coupled anyon chains and are likely to realize chiral topological order. We focus on three specific examples: (i) Kitaev’s honeycomb model with a perturbation breaking time-reversal symmetry that realizes chiral Ising topological order, (ii) a <jats:inline-formula> <jats:alternatives> <jats:tex-math>\mathbb{Z}_N</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mstyle mathvariant="double-struck"> <mml:mi>ℤ</mml:mi> </mml:mstyle> <mml:mi>N</mml:mi> </mml:msub> </mml:math> </jats:alternatives> </jats:inline-formula> generalization proposed by Barkeshli et al., which potentially realizes chiral parafermion topological order, and (iii) a novel Fibonacci honeycomb model featuring a non-invertible 1-form symmetry. </jats:p>