Accurate Truncations of Chain Mapping Models for Open Quantum Systems

The dynamics of open quantum systems are of great interest in many research fields, such as for the interaction of a quantum emitter with the electromagnetic modes of a nanophotonic structure. A powerful approach for treating such setups in the non-Markovian limit is given by the chain mapping where an arbitrary environment can be transformed to a chain of modes with only nearest-neighbor coupling. However, when long propagation times are desired, the required long chain lengths limit the utility of this approach. We study various approaches for truncating the chains at manageable lengths while still preserving an accurate description of the dynamics. We achieve this by introducing losses to the chain modes in such a way that the effective environment acting on the system remains unchanged, using a number of different strategies. Furthermore, we demonstrate that extending the chain mapping to allow next-nearest neighbor coupling permits the reproduction of an arbitrary environment, and adding longer-range interactions does not further increase the effective number of degrees of freedom in the environment.

Symmetries of Quotient Networks for Doubly Periodic Patterns on the Square Lattice

Patterns of synchrony in networks of coupled dynamical systems can be represented as colorings of the nodes, in which nodes of the same color are synchronous. Balanced colorings, where nodes of the same color have color-isomorphic input sets, correspond to dynamically invariant subspaces, which can have a significant effect on the typical bifurcations of network dynamical systems. Orbit colorings for subgroups of the automorphism (symmetry) group of the network are always balanced, although the converse is false. We compute the automorphism groups of all doubly periodic quotient networks of the square lattice with nearest-neighbor coupling, and classify the “exotic” cases where this quotient network has extra automorphisms not induced by automorphisms of the square lattice. These comprise five isolated exceptions and two infinite families with wreath product symmetry. We also comment briefly on implications for bifurcations to doubly periodic patterns in square lattice models.

Spreading of perturbations in myosin group kinetics along actin filaments

Global changes in the state of spatially distributed systems can often be traced back to perturbations that arise locally. Whether such local perturbations grow into global changes depends on the system geometry and the spatial spreading of these perturbations. Here, we investigate how different spreading behaviors of local perturbations determine their global impact in 1-dimensional systems of different size. Specifically, we assessed sliding arrest events in in vitro motility assays where myosins propel actin, and simulated the underlying mechanochemistry of myosins that bind along the actin filament. We observed spontaneous sliding arrest events that occurred more frequently for shorter actin filaments. This observation could be explained by spontaneous local arrest of myosin kinetics that stabilizes once it spreads throughout an entire actin filament. When we introduced intermediate concentrations of the actin cross-linker filamin, longer actin was arrested more frequently. This observation was reproduced by simulations where filamin binding induces persistent local arrest of myosin kinetics, which subsequently spreads throughout the actin filament. A spin chain model with nearest-neighbor coupling reproduced key features of our experiments and simulations, thus extending to other linear systems with nearest-neighbor coupling the following conclusions: 1) perturbations that are persistent only once they spread throughout the system are more effective in smaller systems, and 2) perturbations that are persistent upon their establishment are more effective in larger systems. Beyond these general conclusions, our work also provides a theoretical model of collective myosin kinetics with a finite range of mechanical coupling along the actin filament.