24,572 research outputs found
T-matrix formulation of real-space dynamical mean-field theory and the Friedel sum rule for correlated lattice fermions
We formulate real-space dynamical mean-field theory within scattering theory.
Thereby the Friedel sum rule is derived for interacting lattice fermions at
zero temperature.Comment: 7 pages, no figures, extended and corrected versio
Generalized Opinion Dynamics from Local Optimization Rules
We study generalizations of the Hegselmann-Krause (HK) model for opinion
dynamics, incorporating features and parameters that are natural components of
observed social systems. The first generalization is one where the strength of
influence depends on the distance of the agents' opinions. Under this setup, we
identify conditions under which the opinions converge in finite time, and
provide a qualitative characterization of the equilibrium. We interpret the HK
model opinion update rule as a quadratic cost-minimization rule. This enables a
second generalization: a family of update rules which possess different
equilibrium properties. Subsequently, we investigate models in which a external
force can behave strategically to modulate/influence user updates. We consider
cases where this external force can introduce additional agents and cases where
they can modify the cost structures for other agents. We describe and analyze
some strategies through which such modulation may be possible in an
order-optimal manner. Our simulations demonstrate that generalized dynamics
differ qualitatively and quantitatively from traditional HK dynamics.Comment: 20 pages, under revie
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