Dynamics of positive- and negative-mass solitons in optical lattices and inverted traps

We study the dynamics of one-dimensional solitons in the attractive and repulsive Bose-Einstein condensates (BECs) loaded into an optical lattice (OL), which is combined with an external parabolic potential. First, we demonstrate analytically that, in the repulsive BEC, where the soliton is of the gap type, its effective mass is \emph{negative}. This gives rise to a prediction for the experiment: such a soliton cannot be not held by the usual parabolic trap, but it can be captured (performing harmonic oscillations) by an anti-trapping inverted parabolic potential. We also study the motion of the soliton a in long system, concluding that, in the cases of both the positive and negative mass, it moves freely, provided that its amplitude is below a certain critical value; above it, the soliton's velocity decreases due to the interaction with the OL. At a late stage, the damped motion becomes chaotic. We also investigate the evolution of a two-soliton pulse in the attractive model. The pulse generates a persistent breather, if its amplitude is not too large; otherwise, fusion into a single fundamental soliton takes place. Collisions between two solitons captured in the parabolic trap or anti-trap are considered too. Depending on their amplitudes and phase difference, the solitons either perform stable oscillations, colliding indefinitely many times, or merge into a single soliton. Effects reported in this work for BECs can also be formulated for optical solitons in nonlinear photonic crystals. In particular, the capture of the negative-mass soliton in the anti-trap implies that a bright optical soliton in a self-defocusing medium with a periodic structure of the refractive index may be stable in an anti-waveguide.Comment: 22pages, 9 figures, submitted to Journal of Physics

Classical and quantum analysis of chaos in the discrete self-trapping equation

We study the discrete self-trapping model, for three degrees of freedom. The fraction of the energy shell of the phase space that is chaotic is evaluated directly from the classical motion and also from the exact energy levels of the corresponding quantum system. The correspondence between classical and quantum results is discussed

Worthy to Lose Some Money for Better Air Quality: Applications of Bayesian Networks on the Causal Effect of Income and Air Pollution on Life Satisfaction in Switzerland

One important determinant of well-being is the environmental quality. Many countries apply environmental regulations, reforms and policies for its improvement. However, the question is how the people value the environment, including the air quality. This study examines the association between air pollution and life satisfaction using the Swiss Household Panel survey over the years 2000–2013. We follow a Bayesian network (BN) strategy to estimate the causal effect of the income and air pollution on life satisfaction. We look at five main air pollutants: the ground-level ozone (O3), sulphur dioxide (SO2), nitrogen dioxide (NO2), carbon monoxide (CO) and particulate matter of 10 micrometres (PM10). Then, we calculate the individuals’ marginal willingness to pay (MWTP) of reducing air pollution that aims to improve their life satisfaction. Beside the BN model, we take advantage of the panel structure of our data and we follow two approaches as robustness check. This includes the adapted probit fixed effects and the generalised methods of moments system. Our findings show that O3 and PM10 present the highest MWTP values ranging between $8000 and$12,000, followed by the remained air pollutants with MWTP extending between $2000 and$6500. Applying the BNs, we find that the causal effect of income on life satisfaction is substantially increased. We also show the causal effects of air pollutants remain almost the same, leading to lower values of willingness to pay