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Institute
We discuss a formalism that allows for the calculation of a higher-harmonic-current response to a strong applied electric field for disordered superconducting systems described on the basis of tight-binding models with on- and/or intersite interactions. The theory is based on an expansion of the density matrix in powers of the field amplitudes, where we solve the equation of motion for the individual components. This allows the evaluation of higher-order response functions on significantly larger lattices than one can achieve with a previously used approach, which is based on a direct temporal integration of the equation of motion for the complete density matrix. In the case of small lattices, where both methods can be applied by including also the contribution of collective modes, we demonstrate the agreement of the corresponding results.
Within the time-dependent Gutzwiller approximation applied to the negative-U Hubbard model, we investigate the dynamics of a superconductor after an interaction quench for different values of the final interaction from weak to strong coupling. The equilibrium BCS-BEC crossover becomes a sharp transition in the out-of-equilibrium dynamics between weak- and strong-coupling dynamical phases. Two different frequencies (ΩJ<ΩU) dominate the order parameter dynamics. In the weak coupling phase, ΩJ follows twice the asymptotic average value of the gap (ΩJ≈2Δ∞) and ΩU is much larger but hardy visible in the anomalous density. At long times the BCS dynamics is recovered but surprisingly differences remain during the transient phase. In the strong coupling phase, the dynamics decouples from the asymptotic value of the order parameter except at exactly half filling and close to the dynamical transition where ΩU≈2Δ∞. The out-of-equilibrium transient spectral density and optical conductivity are presented and discussed in relation to pump probe experiments. Both ΩJ and ΩU give rise to a complex structure of self-driven slow Rabi oscillations which are visible in the nonequilibrium optical conductivity where also sidebands appear due to the modulation of the double occupancy by superconducting amplitude oscillations. Analogous results apply to CDW and SDW systems. Our results show that in systems with long coherence times, pump-probe experiments allow us to characterize the regime (BCS vs preformed pairs) through very specific out-of-equilibrium fingerprints.
We calculate the dynamics of tax evasion within a multi-agent econophysics model which is adopted from the theory of magnetism and previously has been shown to capture the main characteristics from agent-based based models which build on the standard Allingham and Sandmo approach. In particular, we implement a feedback of public goods provision on the decision-making of selfish agents which aim to pursue their self interest. Our results imply that such a feedback enhances the moral attitude of selfish agents thus reducing the percentage of tax evasion. Two parameters govern the behavior of selfish agents,
(i) the rate of adaption to changes in public goods provision and (ii) the threshold of perception of public goods provision. Furtheron we analyze the tax evasion
dynamics for different agent compositions and under the feedback of public goods provision. We conclude that policymakers may enhance tax compliance behavior via the threshold of perception by means of targeted public relations.
We investigate an inhomogeneous Ising model in the context of tax evasion dynamics where different types of agents are parameterized via local temperatures and magnetic fields. In particular, we analyze the impact of lapse of time effects (i.e. backauditing) and endogenously determined penalty rates on tax compliance. Both features contribute to a microfoundation of agent-based econophysics models of tax evasion.
Electronic Inhomogeneities and Pairing from Unscreened Interactions in High-Tc Superconductors
(2007)