Simple wealth distribution model causing inequality-induced crisis without external shocks

We address the issue of the dynamics of wealth accumulation and economic crisis triggered by extreme inequality, attempting to stick to most possibly intrinsic assumptions. Our general framework is that of pure or modified multiplicative processes, basically geometric Brownian motions. In contrast with the usual approach of injecting into such stochastic agent models either specific, idiosyncratic internal nonlinear interaction patterns, or macroscopic disruptive features, we propose a dynamic inequality model where the attainment of a sizable fraction of the total wealth by very few agents induces a crisis regime with strong intermittency, the explicit coupling between the richest and the rest being a mere normalization mechanism, hence with minimal extrinsic assumptions. The model thus harnesses the recognized lack of ergodicity of geometric Brownian motions. It also provides a statistical intuition to the consequences of Thomas Piketty's recent "$r>g$" (return rate $>$ growth rate) paradigmatic analysis of very-long-term wealth trends. We suggest that the "water-divide" of wealth flow may define effective classes, making an objective entry point to calibrate the model. Consistently, we check that a tax mechanism associated to a few percent relative bias on elementary daily transactions is able to slow or stop the build-up of large wealth. When extreme fluctuations are tamed down to a stationary regime with sizable but steadier inequalities, it should still offer opportunities to study the dynamics of crisis and the inner effective classes induced through external or internal factors.Comment: 15 pages, 11 figures. Work initiated from discussion on Aristotle's status revisited by Paul Jorion in the many cases where the law of supply and demand fails. Accepted for publication in Physical Review E on April 19, 201

Compact and fault-tolerant photonic crystal add drop filter

International audienceWe propose an add-drop filter consisting of two adjacent waveguides carved into a two-dimensional photonic crystal that is etched through a standard guiding structure. This filter is based on distributed energy transfer via the frequency-selective intermediate conversion of the fundamental guided mode to a high-order low-group-velocity mode. This geometry circumvents the fabrication sensitivity on the single-hole scale of previous cavity-based designs. Combining distributed energy transfer and reduced group velocity preserves compactness. The design is analytically optimized with a coupled-mode approach

Restoring robust binary switching operation and exceptional point using long-period grating-assisted parity-time symmetric couplers

International audienceThe impact of imbalance in waveguides propagation constants among Parity-Time symmetric coupled waveguides and/or of a complex-valued coupling coefficient is assessed. The narrow tolerance found implies that attempts to tightly control waveguides parameters appear as elusive because of fabrication technology limitations, calling for more feasible mitigation avenues. It is shown that a grating-assisted Parity-Time symmetric coupler design restores both technologically robust binary switching operation and exceptional point. In addition the proposed design is compatible with birefringence compensation techniques providing polarization-independent operation as well as coupling and/or gain-loss profile modulation techniques that extend the control of switching operation in the Parity-Time symmetric phase. Using wavelength as an additional tuning parameter near exceptional points opens promising avenues for manipulating the trajectory on Riemann sheets in topological photonics applications

2D label-free imaging of resonant grating biochips in ultraviolet

International audience2D images of label-free biochips exploiting resonant waveguide grating (RWG) are presented. They indicate sensitivities on the order of 1 pg/mm2 for proteins in air, and hence 10 pg/mm2 in water can be safely expected. A 320×256 pixels Aluminum-Gallium-Nitride-based sensor array is used, with an intrinsic narrow spectral window centered at 280 nm. The additional role of characteristic biological layer absorption at this wavelength is calculated, and regimes revealing its impact are discussed. Experimentally, the resonance of a chip coated with protein is revealed and the sensitivity evaluated through angular spectroscopy and imaging. In addition to a sensitivity similar to surface plasmon resonance (SPR), the RWGs resonance can be flexibly tailored to gain spatial, biochemical, or spectral sensitivity

Spontaneous emission enhancement at a photonic wire miniband edge

International audienceIn a multimode photonic-crystal waveguide, we observe strong enhancement of the photoluminescence of embedded quantum dots at the edges of the so-called mini-stopband that were opened by Bragg diffraction between two guided modes. Taking into account light collection, we relate this observation to the singular photon density of states that is characteristic of a one-dimensional photon system. Furthermore, we quantify by how much the radiation losses smooth the divergence. For the first time to our knowledge, a clear account of the control of spontaneous emission in a one-dimensional system is thus demonstrated

Stability mapping of bipartite tight-binding graphs with losses and gain: PT−{\cal PT}-symmetry and beyond

We consider bipartite tight-binding graphs composed by $N$ nodes split into two sets of equal size: one set containing nodes with on-site loss, the other set having nodes with on-site gain. The nodes are connected randomly with probability $p$. We give a rationale for the relevance of such "throttle/brake" coupled systems (physically open systems) to grasp the stability issues of complex networks in areas such as biochemistry, neurons or economy, for which their modelling in terms of non-hermitian Hamiltonians is still in infancy. Specifically, we measure the connectivity between the two sets with the parameter $\alpha$, which is the ratio of current adjacent pairs over the total number of possible adjacent pairs between the sets. For general undirected-graph setups, the non-hermitian Hamiltonian $H(\gamma,\alpha,N)$ of this model presents pseudo-Hermiticity, where $\gamma$ is the loss/gain strength. However, we show that for a given graph setup $H(\gamma,\alpha,N)$ becomes ${\cal PT}-$symmetric. In both scenarios (pseudo-Hermiticity and ${\cal PT}-$symmetric), depending on the parameter combination, the spectra of $H(\gamma,\alpha,N)$ can be real even when it is non-hermitian. Thus, we numerically characterize the average fractions of real and imaginary eigenvalues of $H(\gamma,\alpha,N)$ as a function of the parameter set $\{\gamma,\alpha,N\}$. We demonstrate, for both setups, that there is a well defined sector of the $\gamma\alpha-$plane (which grows with $N$) where the spectrum of $H(\gamma,\alpha,N)$ is predominantly real.Comment: 10 pages, 9 figure