Complexes of Discrete Distributional Differential Forms and their Homology Theory

Complexes of discrete distributional differential forms are introduced into finite element exterior calculus. Thus we generalize a notion of Braess and Sch\"oberl, originally studied for a posteriori error estimation. We construct isomorphisms between the simplicial homology groups of the triangulation, the discrete harmonic forms of the finite element complex, and the harmonic forms of the distributional finite element complexes. As an application, we prove that the complexes of finite element exterior calculus have cohomology groups isomorphic to the de Rham cohomology, including the case of partial boundary conditions. Poincar\'e-Friedrichs-type inequalities will be studied in a subsequent contribution.Comment: revised preprint, 26 page

Ultrafast separation of photo-doped carriers in Mott antiferromagnets

We use inhomogeneous nonequilibrium dynamical mean-field theory to investigate the spreading of photo-excited carriers in Mott insulating heterostructures with strong internal fields. Antiferromagnetic correlations are found to affect the carrier dynamics in a crucial manner: An antiferromagnetic spin background can absorb energy from photo-excited carriers on an ultrafast timescale, thus enabling fast transport between different layers and the separation of electron and hole-like carriers, whereas in the paramagnetic state, carriers become localized in strong fields. This interplay between charge and spin degrees of freedom can be exploited to control the functionality of devices based on Mott insulating heterostructures with polar layers, e.g., for photovoltaic applications

Field-induced polaron formation in the Holstein-Hubbard model

We study the effect of strong DC and pulsed electric fields on a Mott insulating system with coupling to optical phonons. A DC field of the order of the gap induces a metallic state characterized by polaronic features in the gap region and a partially inverted population. In this quasi-steady state, the field-induced doublon-hole production is balanced by a phonon-enhanced doublon-hole recombination. The photo-excitation of carriers by a pulsed field leads to similar modifications of the electronic structure in the gap region, and an associated reduction of the doublon life-time. We demonstrate that the field-induced localization of electrons effectively enhances the phonon coupling, an effect which should be measureable with time-resolved photoemission spectroscopy

Indirect Evolution versus Strategic Delegation: A Comparison of Two Approaches to Explaining Economic Institutions

Two major methods of explaining economic institutions, namely by strategic choices or through (indirect) evolution, are compared for the case of a homogenous quadratic duopoly market. Sellers either can provide incentives for agents to care for sales, or evolve as sellers who care for sales in addition to profits. The two approaches are conceptually quite different, yet similar in the sense that both allow certain kinds of commitment. We show that when the two models are set up in intuitively comparable ways strategic delegation does not change the market results as compared to the usual duopoly solution, while indirect evolution causes a more competitive behavior. Thus the case at hand underscores the differences between the two approaches in explaining economic institutions.Indirect evolution; strategic delgation; commitment; duopoly markets; agency theory

Dielectric breakdown of Mott insulators in dynamical mean-field theory

Using nonequilibrium dynamical mean-field theory, we compute the time evolution of the current in a Mott insulator after a strong electric field is turned on. We observe the formation of a quasistationary state in which the current is almost time-independent although the system is constantly excited. At moderately strong fields this state is stable for quite long times. The stationary current exhibits a threshold behavior as a function of the field, in which the threshold increases with the Coulomb interaction and vanishes as the metal-insulator transition is approached.Comment: 4 pages, 3 figure