Clustering of spectra and fractals of regular graphs

We exhibit a characteristic structure of the class of all regular graphs of degree d that stems from the spectra of their adjacency matrices. The structure has a fractal threadlike appearance. Points with coordinates given by the mean and variance of the exponentials of graph eigenvalues cluster around a line segment that we call a filar. Zooming-in reveals that this cluster splits into smaller segments (filars) labeled by the number of triangles in graphs. Further zooming-in shows that the smaller filars split into subfilars labelled by the number of quadrangles in graphs, etc. We call this fractal structure, discovered in a numerical experiment, a multifilar structure. We also provide a mathematical explanation of this phenomenon based on the Ihara-Selberg trace formula, and compute the coordinates and slopes of all filars in terms of Bessel functions of the first kind.Comment: 10 pages, 5 figure

Generation of bipartite spin entanglement via spin-independent scattering

We consider the bipartite spin entanglement between two identical fermions generated in spin-independent scattering. We show how the spatial degrees of freedom act as ancillas for the creation of entanglement to a degree that depends on the scattering angle, $\theta$. The number of Slater determinants generated in the process is greater than 1, corresponding to genuine quantum correlations between the identical fermions. The maximal entanglement attainable of 1 ebit is reached at $\theta=\pi/2$. We also analyze a simple $\theta$ dependent Bell's inequality, which is violated for $\pi/4<\theta\leq\pi/2$. This phenomenon is unrelated to the symmetrization postulate but does not appear for unequal particles.Comment: 5 pages and 3 figures. Accepted in PR

Emergence of long-range order in BaTiO3 from local symmetry-breaking distortions

By using a symmetry motivated basis to evaluate local distortions against pair distribution function data (PDF), we show without prior bias, that the off-centre Ti displacements in the archetypal ferroelectric BaTiO3 are zone centred and rhombohedral-like in nature across its known ferroelectric and paraelectric phases. With our newly-gained insight we construct a simple Monte Carlo (MC) model which captures our main experimental findings and demonstrate how the rich crystallographic phase diagram of BaTiO3 emerges from correlations of local symmetry-breaking distortions alone. Our results strongly support the order-disorder picture for these phase transitions, but can also be reconciled with the soft-mode theory of BaTiO3 that is supported by some spectroscopic techniques.Comment: 5 pages, 3 figure

Earth-like sand fluxes on Mars

Strong and sustained winds on Mars have been considered rare, on the basis of surface meteorology measurements and global circulation models, raising the question of whether the abundant dunes and evidence for wind erosion seen on the planet are a current process. Recent studies showed sand activity, but could not determine whether entire dunes were moving—implying large sand fluxes—or whether more localized and surficial changes had occurred. Here we present measurements of the migration rate of sand ripples and dune lee fronts at the Nili Patera dune field. We show that the dunes are near steady state, with their entire volumes composed of mobile sand. The dunes have unexpectedly high sand fluxes, similar, for example, to those in Victoria Valley, Antarctica, implying that rates of landscape modification on Mars and Earth are similar

Adiabatic Electron-Phonon Interaction and High-Temperature Thermodynamics of A15 Compounds

Inelastic neutron scattering was used to measure the phonon densities of states of the A15 compounds V_3Si, V_3Ge, and V_3Co at temperatures from 10 to 1273 K. It was found that phonons in V_3Si and V_3Ge, which are superconducting at low temperatures, exhibit an anomalous stiffening with increasing temperature, whereas phonons in V_3Co have a normal softening behavior. First-principles calculations show that this anomalous increase in phonon frequencies at high temperatures originates with an adiabatic electron-phonon coupling mechanism. The anomaly is caused by the thermally induced broadening of sharp peaks in the electronic density of states of V_3Si and V_3Ge, which tends to decrease the electronic density at the Fermi level. These results show that the adiabatic electron-phonon coupling can influence the phonon thermodynamics at temperatures exceeding 1000 K