23,565 research outputs found
Complexes of Discrete Distributional Differential Forms and their Homology Theory
Full text linkComplexes 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
Field-induced polaron formation in the Holstein-Hubbard model
Get PDFWe 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
Ultrafast separation of photo-doped carriers in Mott antiferromagnets
Full text linkWe 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
Indirect Evolution versus Strategic Delegation: A Comparison of Two Approaches to Explaining Economic Institutions
Get PDFTwo 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
Thermalization of a pump-excited Mott insulator
Full text linkWe use nonequilibrium dynamical mean-field theory in combination with a
recently implemented strong-coupling impurity solver to investigate the
relaxation of a Mott insulator after a laser excitation with frequency
comparable to the Hubbard gap. The time evolution of the double occupancy
exhibits a crossover from a strongly damped transient at short times towards an
exponential thermalization at long times. In the limit of strong interactions,
the thermalization time is consistent with the exponentially small decay rate
for artificially created doublons, which was measured in ultracold atomic
gases. When the interaction is comparable to the bandwidth, on the other hand,
the double occupancy thermalizes within a few times the inverse bandwidth along
a rapid thermalization path in which the exponential tail is absent. Similar
behavior can be observed in time-resolved photoemission spectroscopy. Our
results show that a simple quasi-equilibrium description of the electronic
state breaks down for pump-excited Mott insulators characterized by strong
interactions.Comment: 8 pages, 4 figure
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