On the robustness of democratic electoral processes to computational propaganda.

There is growing evidence of systematic attempts to influence democratic elections by controlled and digitally organized dissemination of fake news. This raises the question of the intrinsic robustness of democratic electoral processes against external influences. Particularly interesting is to identify the social characteristics of a voter population that renders it more resilient against opinion manipulation.

Reconstructing network structures from partial measurements.

The dynamics of systems of interacting agents is determined by the structure of their coupling network. The knowledge of the latter is, therefore, highly desirable, for instance, to develop efficient control schemes, to accurately predict the dynamics, or to better understand inter-agent processes. In many important and interesting situations, the network structure is not known, however, and previous investigations have shown how it may be inferred from complete measurement time series on each and every agent.

Clusterization and phase diagram of the bimodal Kuramoto model with bounded confidence.

Inspired by the Deffuant and Hegselmann-Krause models of opinion dynamics, we extend the Kuramoto model to account for confidence bounds, i.e., vanishing interactions between pairs of oscillators when their phases differ by more than a certain value.

Network desynchronization by non-Gaussian fluctuations.

Many networks must maintain synchrony despite the fact that they operate in noisy environments. Important examples are stochastic inertial oscillators, which are known to exhibit fluctuations with broad tails in many applications, including electric power networks with renewable energy sources. Such non-Gaussian fluctuations can result in rare network desynchronization.

Rate of change of frequency under line contingencies in high voltage electric power networks with uncertainties.

In modern electric power networks with fast evolving operational conditions, assessing the impact of contingencies is becoming more and more crucial. Contingencies of interest can be roughly classified into nodal power disturbances and line faults. Despite their higher relevance, line contingencies have been significantly less investigated analytically than nodal disturbances.

Global robustness versus local vulnerabilities in complex synchronous networks.

In complex network-coupled dynamical systems, two questions of central importance are how to identify the most vulnerable components and how to devise a network making the overall system more robust to external perturbations. To address these two questions, we investigate the response of complex networks of coupled oscillators to local perturbations. We quantify the magnitude of the resulting excursion away from the unperturbed synchronous state through quadratic performance measures in the angle or frequency deviations.

Inertia location and slow network modes determine disturbance propagation in large-scale power grids.

Conventional generators in power grids are steadily substituted with new renewable sources of electric power. The latter are connected to the grid via inverters and as such have little, if any rotational inertia. The resulting reduction of total inertia raises important issues of power grid stability, especially over short-time scales.

The size of the sync basin revisited.

In dynamical systems, the full stability of fixed point solutions is determined by their basins of attraction. Characterizing the structure of these basins is, in general, a complicated task, especially in high dimensionality. Recent works have advocated to quantify the non-linear stability of fixed points of dynamical systems through the relative volumes of the associated basins of attraction [Wiley et al.

Finite-size scaling in the Kuramoto model.

We investigate the scaling properties of the order parameter and the largest nonvanishing Lyapunov exponent for the fully locked state in the Kuramoto model with a finite number N of oscillators. We show that, for any finite value of N, both quantities scale as (K-K_{L})^{1/2} with the coupling strength K sufficiently close to the locking threshold K_{L}. We confirm numerically these predictions for oscillator frequencies evenly spaced in the interval [-1,1] and additionally find that the coupling range δK over which this scaling is valid shrinks like δK∼N^{-α} with α≈1.

Linear stability and the Braess paradox in coupled-oscillator networks and electric power grids.

We investigate the influence that adding a new coupling has on the linear stability of the synchronous state in coupled-oscillator networks. Using a simple model, we show that, depending on its location, the new coupling can lead to enhanced or reduced stability. We extend these results to electric power grids where a new line can lead to four different scenarios corresponding to enhanced or reduced grid stability as well as increased or decreased power flows.

Generation and Detection of Spin Currents in Semiconductor Nanostructures with Strong Spin-Orbit Interaction.

Storing, transmitting, and manipulating information using the electron spin resides at the heart of spintronics. Fundamental for future spintronics applications is the ability to control spin currents in solid state systems. Among the different platforms proposed so far, semiconductors with strong spin-orbit interaction are especially attractive as they promise fast and scalable spin control with all-electrical protocols.

Electric field control of soliton motion and stacking in trilayer graphene.

The crystal structure of a material plays an important role in determining its electronic properties. Changing from one crystal structure to another involves a phase transition that is usually controlled by a state variable such as temperature or pressure. In the case of trilayer graphene, there are two common stacking configurations (Bernal and rhombohedral) that exhibit very different electronic properties.

Scattering theory of nonlinear thermoelectricity in quantum coherent conductors.

We construct a scattering theory of weakly nonlinear thermoelectric transport through sub-micron scale conductors. The theory incorporates the leading nonlinear contributions in temperature and voltage biases to the charge and heat currents. Because of the finite capacitances of sub-micron scale conducting circuits, fundamental conservation laws such as gauge invariance and current conservation require special care to be preserved.

Macroscopic coherent rectification in Andreev interferometers.

We investigate nonlinear transport through quantum coherent metallic conductors contacted to superconducting components. We find that in certain geometries, the presence of superconductivity generates a large, finite-average rectification effect. Specializing to Andreev interferometers, we show that the direction and magnitude of rectification can be controlled by a magnetic flux tuning the superconducting phase difference at two contacts.

Scattering phase of quantum dots: emergence of universal behavior.

We investigate scattering through chaotic ballistic quantum dots in the Coulomb-blockade regime. Focusing on the scattering phase, we show that large universal sequences emerge in the short wavelength limit, where phase lapses of π systematically occur between two consecutive resonances. Our results are corroborated by numerics and are in qualitative agreement with existing experiments.

Spin-to-charge conversion of mesoscopic spin currents.

Recent theoretical investigations have shown that spin currents can be generated by passing electric currents through spin-orbit coupled mesoscopic systems. Measuring these spin currents has, however, not been achieved to date. We show how mesoscopic spin currents in lateral heterostructures can be measured with a single-channel voltage probe.

Scanning tunnelling microscopy and spectroscopy of ultra-flat graphene on hexagonal boron nitride.

Graphene has demonstrated great promise for future electronics technology as well as fundamental physics applications because of its linear energy-momentum dispersion relations which cross at the Dirac point. However, accessing the physics of the low-density region at the Dirac point has been difficult because of disorder that leaves the graphene with local microscopic electron and hole puddles. Efforts have been made to reduce the disorder by suspending graphene, leading to fabrication challenges and delicate devices which make local spectroscopic measurements difficult.

Displacement echoes: classical decay and quantum freeze.

Motivated by neutron scattering experiments, we investigate the decay of the fidelity with which a wave packet is reconstructed by a perfect time-reversal operation performed after a phase-space displacement. In the semiclassical limit, we show that the decay rate is generically given by the Lyapunov exponent of the classical dynamics. For small displacements, we additionally show that, following a short-time Lyapunov decay, the decay freezes well above the ergodic value because of quantum effects.

Chaos, coherence, and the double-slit experiment.

We investigate the influence that classical dynamics has on interference patterns in coherence experiments. We calculate the time-integrated probability current through an absorbing screen and the conductance through a doubly connected ballistic cavity, both in an Aharonov-Bohm geometry with forward scattering only. We show how interference fringes in the probability current generically disappear in the case of a chaotic system with small openings, and how they may persist in the case of an integrable cavity.

Mesoscopic fluctuations of the Loschmidt echo.

We investigate the time-dependent variance of the fidelity with which an initial narrow wave packet is reconstructed after its dynamics is time reversed with a perturbed Hamiltonian. In the semiclassical regime of perturbation, we show that the variance first rises algebraically up to a critical time t(c) , after which it decays. To leading order in the effective Planck's constant Planck's(eff) , this decay is given by the sum of a classical term approximately same as exp [-2lambdat] , a quantum term approximately same as 2Planck's(eff) exp [-Gamma t] , and a mixed term approximately 2 exp [- (Gamma+lambda) t] .

Duality between the weak and strong interaction limits for randomly interacting fermions.

We establish the existence of a duality transformation for generic models of interacting fermions with two-body interactions. The eigenstates at weak and strong interaction U possess similar statistical properties when expressed in the U=0 and U= infinity eigenstates bases, respectively. This implies the existence of a duality point U(d) where the eigenstates have the same spreading in both bases.