Particle-like platonic solutions in scalar gravity

We construct globally regular gravitating solutions, which possess only discrete symmetries. These solutions of Yang–Mills-dilaton theory may be viewed as exact (numerical) solutions of scalar gravity, by considering the dilaton as a kind of scalar graviton, or as approximate solutions of Einstein–Yang–Mills theory. We focus on platonic solutions with cubic symmetry, related to a rational map of degree N=4$N=4$. We present the first two solutions of the cubic N=4$N=4$ sequence, and expect this sequence to converge to an extremal Reissner–Nordström solution with magnetic charge P=4$P=4$.     

Manifolds with 1/4-Pinched Flag Curvature

We say that a nonnegatively curved manifold (M, g) has quarter-pinched flag curvature if for any two planes which intersect in a line the ratio of their sectional curvature is bounded above by 4. We show that these manifolds have nonnegative complex sectional curvature. By combining with a theorem of Brendle and Schoen it follows that any positively curved manifold with strictly quarter-pinched flag curvature must be a space form. This in turn generalizes a result of Andrews and Nguyen in dimension 4. For odd-dimensional manifolds we obtain results for the case that the flag curvature is pinched with some constant below one quarter, one of which generalizes a recent work of Petersen and Tao.     

An alternative approach for recording of multidimensional NMR data based on frequency dependent folding mechanism

A new scheme for obtaining HSQC spectra with improved resolution or in a shorter time called SHARC (Shaped Arrayed data aCquisition protocol) is proposed, which uses region selective RF pulses and allows the sweep width to be adjusted individually for each region. It thus bypasses the problems with the Nyquist theorem associated with other method suggested for this purpose. Assignment of the cross-peaks to their respective region is achieved by manipulating the phases of the RF pulses and/or their frequencies. SHARC NMR can be applied without any previous knowledge of the chemical shift distribution, but can be further optimized on the basis of a quick overview spectrum.     

WavePacket: A Matlab package for numerical quantum dynamics. III. Quantum-classical simulations and surface hopping trajectories

WavePacket is an open-source program package for numerical simulations in quantum dynamics. Building on the previous Part I (Schmidt and Lorenz, Comput. Phys. Commun. 2017, 213, 223] and Part II (Schmidt and Hartmann, Comput. Phys. Commun. 2018, 228, 229] which dealt with quantum dynamics of closed and open systems, respectively, the present Part III adds fully classical and mixed quantum-classical propagation techniques to WavePacket. There classical phase-space densities are sampled by trajectories which follow (diabatic or adiabatic) potential energy surfaces. In the vicinity of (genuine or avoided) intersections of those surfaces, trajectories may switch between them. To model these transitions, two classes of stochastic algorithms have been implemented: (1) Tully's fewest switches surface hopping and (2) Landau–Zener-based single switch surface hopping. The latter one offers the advantage of being based on adiabatic energy gaps only, thus not requiring nonadiabatic coupling information any more. The present work describes the MATLAB version of WavePacket 6.1.0, which is essentially an object-oriented rewrite of previous versions, allowing to perform fully classical, quantum-classical and quantum-mechanical simulations on an equal footing, that is, for the same physical system described by the same WavePacket input. The software package is hosted and further developed at the Sourceforge platform, where also extensive Wiki-documentation as well as numerous worked-out demonstration examples with animated graphics are available. © 2019 Wiley Periodicals, Inc.     

Stationary Dyonic regular and black hole solutions

We consider globally regular and black hole solutions in SU(2) Einstein–Yang–Mills–Higgs theory, coupled to a dilaton field. The basic solutions represent magnetic monopoles, monopole–antimonopole systems or black holes with monopole or dipole hair. When the globally regular solutions carry additionally electric charge, an angular momentum density results, except in the simplest spherically symmetric case. We evaluate the global charges of the solutions and their effective action, and analyze their dependence on the gravitational coupling strength. We show, that in the presence of a dilaton field, the black hole solutions satisfy a generalized Smarr type mass formula. B. Kleihaus gratefully acknowledges support by the German Aerospace Center. F. Navarro-Lérida gratefully acknowledges support by the Ministerio de Educación y Ciencia under grant EX2005-0078.