The Network Picture of Labor Flow

We construct a data-driven model of flows in graphs that captures the essential elements of the movement of workers between jobs in the companies (firms) of entire economic systems such as countries. The model is based on the observation that certain job transitions between firms are often repeated over time, showing persistent behavior, and suggesting the construction of static graphs to act as the scaffolding for job mobility. Individuals in the job market (the workforce) are modelled by a discrete-time random walk on graphs, where each individual at a node can possess two states: employed or unemployed, and the rates of becoming unemployed and of finding a new job are node dependent parameters. We calculate the steady state solution of the model and compare it to extensive micro-datasets for Mexico and Finland, comprised of hundreds of thousands of firms and individuals. We find that our model possesses the correct behavior for the numbers of employed and unemployed individuals in these countries down to the level of individual firms. Our framework opens the door to a new approach to the analysis of labor mobility at high resolution, with the tantalizing potential for the development of full forecasting methods in the future.Comment: 27 pages, 6 figure

Dynamics and thermalization of Bose-Einstein condensate in Sinai oscillator trap

We study numerically the evolution of Bose-Einstein condensate in the Sinai oscillator trap described by the Gross-Pitaevskii equation in two dimensions. In the absence of interactions this trap mimics the properties of Sinai billiards where the classical dynamics is chaotic and the quantum evolution is described by generic properties of quantum chaos and random matrix theory. We show that, above a certain border, the nonlinear interactions between atoms lead to the emergence of dynamical thermalization which generates the statistical Bose-Einstein distribution over eigenmodes of the system without interactions. Below the thermalization border the evolution remains quasi-integrable. Such a Sinai oscillator trap, formed by the oscillator potential and a repulsive disk located in the vicinity of the center, had been already realized in rst experiments with the Bose-Einstein condensate formation by Ketterle group in 1995 and we argue that it can form a convenient test bed for experimental investigations of dynamical of thermalization. Possible links and implications for Kolmogorov turbulence in absence of noise are also discussed.Comment: 11 pages, 14 figures. Final version. Accepted forpublication at Phys. Rev. A. Additional information available at http://www.quantware.ups-tlse.fr/QWLIB/sinaioscillator