Disordered hyperuniformity is a state of matter which has isotropic liquid like properties while simultaneously having crystalline like properties such as little variation in the density fluctuations over long distances. Such states arise for the packing of photoreceptor cells in chicken eyes, jammed particle assemblies, and in nonequilibrium systems. An open question is what possible applications could utilize properties of hyperuniformity. One of the major issues for applications of type-II superconductors is how to achieve high critical currents by preventing the motion or depinning of vortices, so there is great interest in understanding which pinning site geometries will lead to the optimal pinning of vortices. Here, using large scale computational simulations, we show that vortices in a type-II superconductor with a hyperuniform pinning arrangement exhibit enhanced pinning compared to an equal number of pinning sites with a purely random arrangement, and that the enhancement is robust over a wide range of parameters. The stronger pinning arises in the hyperuniform arrays due to the suppression of pinning density fluctuations, permitting higher pin occupancy and the reduction of weak links that lead to easy flow channeling. We also show that in general, in amorphous vortex states in the presence of either random or hyperuniform pinning arrays, the vortices themselves exhibit disordered hyperuniformity due to the repulsive nature of the vortex-vortex interactions.

We develop a new approach for calculating the spin-independent two-neutrino exchange potential (2NEP) between nonrelativistic fermions which places emphasis on the neutrino vacuum state, an area of theoretical interest in recent years. The 2NEP is a natural probe of fundamental issues of neutrino physics such as neutrino masses, flavor mixing, the number of neutrino flavors, neutrino nature (Dirac or Majorana), CP -violation, and the neutrino vacuum state. We explore the dependence of the 2NEP on the mixing of neutrino mass states assuming normal and inverted mass ordering for nucleon-nucleon, nucleon-lepton, and lepton-lepton interactions, and the CP -violation phase in the neutrino mixing matrix.

We examine the statics and dynamics of vortices in the presence of a periodic quasi-one dimensional substrate, focusing on the limit where the vortex lattice constant is smaller than the substrate lattice period. As a function of the substrate strength and filling factor, within the pinned state we observe a series of order-disorder transitions associated with buckling phenomena in which the number of vortex rows that fit between neighboring substrate maxima increases. These transitions coincide with steps in the depinning threshold, jumps in the density of topological defects, and changes in the structure factor. At the buckling transition the vortices are disordered, while between the buckling transitions the vortices form a variety of crystalline and partially ordered states. In the weak substrate limit, the buckling transitions are absent and the vortices form an ordered hexagonal lattice that undergoes changes in its orientation with respect to the substrate as a function of vortex density. At intermediate substrate strength, certain ordered states appear that are correlated with peaks in the depinning force. Under an applied drive the system exhibits a rich variety of distinct dynamical phases, including plastic flow, a density-modulated moving crystal, and moving floating solid phases. We also find a dynamic smectic-to-smectic transition in which the smectic ordering changes from being aligned with the substrate to being aligned with the external drive. The different dynamical phases can be characterized using velocity histograms and the structure factor. We discuss how these results are related to recent experiments on vortex ordering in thin films with periodic thickness modulations. Our results should also be relevant for other types of systems such as ions, colloids, or Wigner crystals interacting with periodic quasi-one-dimensional substrates.