The importance of the weak: Interaction modifiers in artificial spin ices

The modification of geometry and interactions in two-dimensional magnetic nanosystems has enabled a range of studies addressing the magnetic order, collective low-energy dynamics, and emergent magnetic properties, in e.g. artificial spin ice structures. The common denominator of all these investigations is the use of Ising-like mesospins as building blocks, in the form of elongated magnetic islands. Here we introduce a new approach: single interaction modifiers, using slave-mesospins in the form of discs, within which the mesospin is free to rotate in the disc plane. We show that by placing these on the vertices of square artificial spin ice arrays and varying their diameter, it is possible to tailor the strength and the ratio of the interaction energies. We demonstrate the existence of degenerate ice-rule obeying states in square artificial spin ice structures, enabling the exploration of thermal dynamics in a spin liquid manifold. Furthermore, we even observe the emergence of flux lattices on larger length-scales, when the energy landscape of the vertices is reversed. The work highlights the potential of a design strategy for two-dimensional magnetic nano-architectures, through which mixed dimensionality of mesospins can be used to promote thermally emergent mesoscale magnetic states.Comment: 17 pages, including methods, 4 figures. Supplementary information contains 16 pages and 15 figure

HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations

Explicit answer is given for the HOMFLY polynomial of the figure eight knot $4_1$ in arbitrary symmetric representation R=[p]. It generalizes the old answers for p=1 and 2 and the recently derived results for p=3,4, which are fully consistent with the Ooguri-Vafa conjecture. The answer can be considered as a quantization of the \sigma_R = \sigma_{[1]}^{|R|} identity for the "special" polynomials (they define the leading asymptotics of HOMFLY at q=1), and arises in a form, convenient for comparison with the representation of the Jones polynomials as sums of dilogarithm ratios. In particular, we construct a difference equation ("non-commutative A-polynomial") in the representation variable p. Simple symmetry transformation provides also a formula for arbitrary antisymmetric (fundamental) representation R=[1^p], which also passes some obvious checks. Also straightforward is a deformation from HOMFLY to superpolynomials. Further generalizations seem possible to arbitrary Young diagrams R, but these expressions are harder to test because of the lack of alternative results, even partial.Comment: 14 page

Noisy Splicing Drives mRNA Isoform Diversity in Human Cells

While the majority of multiexonic human genes show some evidence of alternative splicing, it is unclear what fraction of observed splice forms is functionally relevant. In this study, we examine the extent of alternative splicing in human cells using deep RNA sequencing and de novo identification of splice junctions. We demonstrate the existence of a large class of low abundance isoforms, encompassing approximately 150,000 previously unannotated splice junctions in our data. Newly-identified splice sites show little evidence of evolutionary conservation, suggesting that the majority are due to erroneous splice site choice. We show that sequence motifs involved in the recognition of exons are enriched in the vicinity of unconserved splice sites. We estimate that the average intron has a splicing error rate of approximately 0.7% and show that introns in highly expressed genes are spliced more accurately, likely due to their shorter length. These results implicate noisy splicing as an important property of genome evolution

Dynamically generated flat-band phases in optical kagome lattices

Motivated by recent advances in the realization of complex two-dimensional optical lattices, we investigate theoretically the quantum transport of ultracold fermions in an optical kagome lattice. In particular, we focus on its extensively degenerate localized states (flat band). By loading fermions in a partial region of the lattice and depleting the mobile atoms at the far boundary of the initially unoccupied region, we find a dynamically generated flat-band insulator, which is also a population-inverted state. We further show that inclusion of weak repulsion leads to a dynamical stripe phase for two-component fermions in a similar setup. Finally, by preparing a topological insulating state in a partially occupied kagome lattice, we find that the topological chiral current decays but exhibits an interesting oscillating dynamics during the nonequilibrium transport. Given the broad variety of lattice geometries supporting localized or topological states, our work suggests new possibilities for using geometrical effects and their dynamics in atomtronic devices. © 2014 American Physical Society

Coherent phonons, nanoseismology and THz radiation in InGaN/GaN heterostructures

The ultrafast optical photoexcitation of hot electrons and holes in semiconductors by femtosecond laser pulses can trigger coherent phonon oscillations. We discuss the huge coherent acoustic phonons which have been generated in InGaN/GaN heterostructures and epilayers and how they might be used in imaging of surfaces and interfaces in nanostructures. We also discuss the THz radiation emitted from these phonons