Introducing Unobserved Heterogeneity in Earnings Mobility

This paper introduces and describes unobserved heterogeneity in earnings quintiles transition matrices in the US. Unobserved heterogeneity is found to play a crucial role in earnings mobility. Each individual is attracted, given his characteristics, towards a specific zone of the distribution. At the stationnary equilibrium, the earnings quintiles distribution is thus segmented. Interestingly, while the level of earnings mobility has remained quite stable since 1970, the width of these zones has decreased, such that this segmentation was more pronounced in the 80's and the 90's than in the 70's, especially in the middle of the quintiles distribution.earnings mobility; unobserved heterogeneity; segmentation; state dependence; dynamic multinomial logit

One dimensional Fokker-Planck reduced dynamics of decision making models in Computational Neuroscience

We study a Fokker-Planck equation modelling the firing rates of two interacting populations of neurons. This model arises in computational neuroscience when considering, for example, bistable visual perception problems and is based on a stochastic Wilson-Cowan system of differential equations. In a previous work, the slow-fast behavior of the solution of the Fokker-Planck equation has been highlighted. Our aim is to demonstrate that the complexity of the model can be drastically reduced using this slow-fast structure. In fact, we can derive a one-dimensional Fokker-Planck equation that describes the evolution of the solution along the so-called slow manifold. This permits to have a direct efficient determination of the equilibrium state and its effective potential, and thus to investigate its dependencies with respect to various parameters of the model. It also allows to obtain information about the time escaping behavior. The results obtained for the reduced 1D equation are validated with those of the original 2D equation both for equilibrium and transient behavior

Non-linear oscillatory rheological properties of a generic continuum foam model: comparison with experiments and shear-banding predictions

The occurence of shear bands in a complex fluid is generally understood as resulting from a structural evolution of the material under shear, which leads (from a theoretical perspective) to a non-monotonic stationnary flow curve related to the coexistence of different states of the material under shear. In this paper we present a scenario for shear-banding in a particular class of complex fluids, namely foams and concentrated emulsions, which differs from other scenarii in two important ways. First, the appearance of shear bands is shown to be possible both without any intrinsic physical evolution of the material (e.g. via a parameter coupled to the flow such as concentration or entanglements) and without any finite critical shear rate below which the flow does not remain stationary and homogeneous. Secondly, the appearance of shear bands depends on the initial conditions, i.e., the preparation of the material. In other words, it is history dependent. This behaviour relies on the tensorial character of the underlying model (2D or 3D) and is triggered by an initially inhomogeneous strain distribution in the material. The shear rate displays a discontinuity at the band boundary, whose amplitude is history dependent and thus depends on the sample preparation.Comment: 18 pages - 17 figure

Classification of Dark States in Multi-level Dissipative Systems

Dark states are eigenstates or steady-states of a system that are decoupled from the radiation. Their use, along with associated techniques such as Stimulated Raman Adiabatic Passage, has extended from atomic physics where it is an essential cooling mechanism, to more recent versions in condensed phase where it can increase the coherence times of qubits. These states are often discussed in the context of unitary evolution and found with elegant methods exploiting symmetries, or via the Bruce-Shore transformation. However, the link with dissipative systems is not always transparent, and distinctions between classes of CPT are not always clear. We present a detailed overview of the arguments to find stationary dark states in dissipative systems, and examine their dependence on the Hamiltonian parameters, their multiplicity and purity. We find a class of dark states that depends not only on the detunings of the lasers but also on their relative intensities. We illustrate the criteria with the more complex physical system of the hyperfine transitions of $^{87}$Rb and show how a knowledge of the dark state manifold can inform the preparation of pure states.Comment: additional example