Anisotropic symmetrization and Sobolev inequalities on Finsler manifolds with nonnegative Ricci curvature

By using a sharp isoperimetric inequality and an anisotropic symmetrization argument, we establish Morrey-Sobolev and Hardy-Sobolev inequalities on $n$-dimensional Finsler manifolds having nonnegative $n$-Ricci curvature; in some cases we also discuss the sharpness of these functional inequalities. As applications, by using variational arguments, we guarantee the existence/multiplicity of solutions for certain eigenvalue problems and elliptic PDEs involving the Finsler-Laplace operator. Our results are also new in the Riemannian setting.Comment: 17 page

Mass loss and longevity of gravitationally bound oscillating scalar lumps (oscillatons) in D-dimensions

Spherically symmetric oscillatons (also referred to as oscillating soliton stars) i.e. gravitationally bound oscillating scalar lumps are considered in theories containing a massive self-interacting real scalar field coupled to Einstein's gravity in 1+D dimensional spacetimes. Oscillations are known to decay by emitting scalar radiation with a characteristic time scale which is, however, extremely long, it can be comparable even to the lifetime of our universe. In the limit when the central density (or amplitude) of the oscillaton tends to zero (small-amplitude limit) a method is introduced to compute the transcendentally small amplitude of the outgoing waves. The results are illustrated in detail on the simplest case, a single massive free scalar field coupled to gravity.Comment: 23 pages, 2 figures, references on oscillons added, version to appear in Phys. Rev.

Computation of the radiation amplitude of oscillons

The radiation loss of small amplitude oscillons (very long-living, spatially localized, time dependent solutions) in one dimensional scalar field theories is computed in the small-amplitude expansion analytically using matched asymptotic series expansions and Borel summation. The amplitude of the radiation is beyond all orders in perturbation theory and the method used has been developed by Segur and Kruskal in Phys. Rev. Lett. 58, 747 (1987). Our results are in good agreement with those of long time numerical simulations of oscillons.Comment: 22 pages, 9 figure

Interrelations Between the Neutron's Magnetic Interactions and the Magnetic Aharonov-Bohm Effect

It is proved that the phase shift of a polarized neutron interacting with a spatially uniform time-dependent magnetic field, demonstrates the same physical principles as the magnetic Aharonov-Bohm effect. The crucial role of inert objects is explained, thereby proving the quantum mechanical nature of the effect. It is also proved that the nonsimply connectedness of the field-free region is not a profound property of the system and that it cannot be regarded as a sufficient condition for a nonzero phase shift.Comment: 18 pages, 1 postscript figure, Late

Boson stars and oscillatons in an inflationary universe

Spherically symmetric gravitationally bound, oscillating scalar lumps (boson stars and oscillatons) are considered in Einstein's gravity coupled to massive scalar fields in 1+D dimensional de Sitter-type inflationary space-times. We show that due to inflation bosons stars and oscillatons lose mass through scalar radiation, but at a rate that is exponentially small when the expansion rate is slow.Comment: 19 pages, 5 figure

Non exponential relaxation in fully frustrated models

We study the dynamical properties of the fully frustrated Ising model. Due to the absence of disorder the model, contrary to spin glass, does not exhibit any Griffiths phase, which has been associated to non-exponential relaxation dynamics. Nevertheless we find numerically that the model exhibits a stretched exponential behavior below a temperature T_p corresponding to the percolation transition of the Kasteleyn-Fortuin clusters. We have also found that the critical behavior of this clusters for a fully frustrated q-state spin model at the percolation threshold is strongly affected by frustration. In fact while in absence of frustration the q=1 limit gives random percolation, in presence of frustration the critical behavior is in the same universality class of the ferromagnetic q=1/2-state Potts model.Comment: 7 pages, RevTeX, 11 figs, to appear on Physical Review

Oscillons in dilaton-scalar theories

It is shown by both analytical methods and numerical simulations that extremely long living spherically symmetric oscillons appear in virtually any real scalar field theory coupled to a massless dilaton (DS theories). In fact such "dilatonic" oscillons are already present in the simplest non-trivial DS theory -- a free massive scalar field coupled to the dilaton. It is shown that in analogy to the previously considered cases with a single nonlinear scalar field, in DS theories there are also time periodic quasibreathers (QB) associated to small amplitude oscillons. Exploiting the QB picture the radiation law of the small amplitude dilatonic oscillons is determined analytically.Comment: extended discussion on stability, to appear in JHEP, 29 pages, 7 figure

Theory of the Fano Resonance in the STM Tunneling Density of States due to a Single Kondo Impurity

The conduction electron density of states nearby single magnetic impurities, as measured recently by scanning tunneling microscopy (STM), is calculated, taking into account tunneling into conduction electron states only. The Kondo effect induces a narrow Fano resonance in the conduction electron density of states, while scattering off the d-level generates a weakly energy dependent Friedel oscillation. The line shape varies with the distance between STM tip and impurity, in qualitative agreement with experiments, but is very sensitive to details of the band structure. For a Co impurity the experimentally observed width and shift of the Kondo resonance are in accordance with those obtained from a combination of band structure and strongly correlated calculations.Comment: 4 pages, ReVTeX + 4 figures (Encapsulated Postscript), submitted to PR

Electron density errors and density-driven exchange-correlation energy errors in approximate density functional calculations

Since its formal introduction, density functional theory has achieved many successes in the fields of molecular and solid-state chemistry. According to its central theorems, the ground state of a many-electron system is fully described by its electron density, and the exact functional minimizes the energy at the exact electron density. For many years of density functional development, it was assumed that the improvements in the energy are accompanied by the improvements in the density, and the approximations approach the exact functional. In a recent analysis (Medvedev et al. Science 2017, 355, 49−52.), it has been pointed out for 14 first row (Be–Ne) atoms and cations with 2, 4, or 10 electrons that the nowadays popular flexible but physically less rigorous approximate density functionals may provide large errors in the calculated electron densities despite the accurate energies. Although far-reaching conclusions have been drawn in this work, the methodology used by the authors may need improvements. Most importantly, their benchmark set was biased toward small atomic cations with compressed, high electron densities. In our paper, we construct a molecular test set with chemically relevant densities and analyze the performance of several density functional approximations including the less-investigated double hybrids. We apply an intensive error measure for the density, its gradient, and its Laplacian and examine how the errors in the density propagate into the semilocal exchange-correlation energy. While we have confirmed the broad conclusions of Medvedev et al., our different way of analyzing the data has led to conclusions that differ in detail. Finally, seeking for a rationale behind the global hybrid or double hybrid methods from the density’s point of view, we also analyze the role of the exact exchange and second-order perturbative correlation mixing in PBE-based global hybrid and double hybrid functional forms