Condensed Matter Theory

Abstract:

We present a computational study of the pairwise interactions between defects in the recently introduced non-reciprocal Cahn-Hilliard model. The evolution of a defect pair exhibits dependence upon their corresponding topological charges, initial separation, and the non-reciprocity coupling constant $α$. We find that the stability of isolated topologically neutral targets significantly affects the pairwise defect interactions. At large separations, defect interactions are negligible and a defect pair is stable. When positioned in relatively close proximity, a pair of oppositely charged spirals or targets merge to form a single target. At low $α$, like-charged spirals form rotating bound pairs, which are however torn apart by spontaneously formed targets at high $α$. Similar preference for charged or neutral solutions is also seen for a spiral target pair where the spiral dominates at low $α$, but concedes to the target at large $α$. Our work sheds light on the complex phenomenology of non-reciprocal active matter systems when their collective dynamics involves topological defects

Abstract:

Double-descent curves in neural networks describe the phenomenon that the generalisation error initially descends with increasing parameters, then grows after reaching an optimal number of parameters which is less than the number of data points, but then descends again in the overparameterized regime. In this paper, we use techniques from random matrix theory to characterize the spectral distribution of the empirical feature covariance matrix as a width-dependent perturbation of the spectrum of the neural network Gaussian process (NNGP) kernel, thus establishing a novel connection between the NNGP literature and the random matrix theory literature in the context of neural networks. Our analytical expressions allow us to explore the generalisation behavior of the corresponding kernel and GP regression. Furthermore, they offer a new interpretation of double-descent in terms of the discrepancy between the width-dependent empirical kernel and the width-independent NNGP kernel.

Abstract:

We introduce oxNA, a new model for the simulation of DNA–RNA hybrids that is based on two previously developed coarse-grained models—oxDNA and oxRNA. The model naturally reproduces the physical properties of hybrid duplexes, including their structure, persistence length, and force-extension characteristics. By parameterizing the DNA–RNA hydrogen bonding interaction, we fit the model’s thermodynamic properties to experimental data using both average-sequence and sequence-dependent parameters. To demonstrate the model’s applicability, we provide three examples of its use—calculating the free energy profiles of hybrid strand displacement reactions, studying the resolution of a short R-loop, and simulating RNA-scaffolded wireframe origami.

Abstract:

It is a matter of current debate whether the gate-tunable superconductivity in twisted bilayer graphene is phonon-mediated or arises from electron-electron interactions. The recent observation of the strong coupling of electrons to so-called K-phonon modes in angle-resolved photoemission spectroscopy experiments has resuscitated early proposals that K-phonons drive superconductivity. We show that the bandwidth-enhancing effect of interactions drastically weakens both the intrinsic susceptibility towards pairing as well as the screening of Coulomb repulsion that is essential for the phonon attraction to dominate at low temperature. This rules out purely K-phonon-mediated superconductivity with the observed transition temperature of ∼1 K. We conclude that the unflattening of bands by Coulomb interactions challenges any purely phonon-driven pairing mechanism, and must be addressed by a successful theory of superconductivity in moiré graphene

Abstract:

The presence of long-lived oscillations in the expectation values of local observables after quantum quenches has recently attracted considerable attention in relation to weak ergodicity breaking. Here, we focus on an alternative mechanism that gives rise to such oscillations in a class of systems that support kinematically protected gapped excitations at zero temperature. An open question in this context is whether such oscillations will ultimately decay. We provide strong support for the decay hypothesis by considering spin models that can be mapped to systems of weakly interacting fermions, which in turn are amenable to an analysis by standard methods based on the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. We find that there is a time scale beyond which the oscillations start to decay that grows as the strength of the quench is made small.