Lifetimes of impurity states in crossed magnetic and electric fields

We study the quantum dynamics of localized impurity states created by a point interaction for an electron moving in two dimensions under the influence of a perpendicular magnetic field and an in-plane weak electric field. All impurity states are unstable in presence of the electric field. Their lifetimes are computed and shown to grow in a Gaussian way as the electric field tends to zero.Comment: 13 pages, no figures, submitted to J. Math. Phy

The Bose gas beyond mean field

We study a homogeneous Bose gas with purely repulsive forces. Using the Kac scaling of the binary potential we derive analytically the form of the thermodynamic functions of the gas for small but finite values of the scaling parameter in the low density regime. In this way we determine dominant corrections to the mean-field theory. It turns out that repulsive forces increase the pressure at fixed density and decrease the density at given chemical potential (the temperature is kept constant). They also flatten the Bose momentum distribution. However, the present analysis cannot be extended to the region where the mean-field theory predicts the appearence of condensate.Comment: 19 pages, 3 figure

Productivity Spillovers, Terms of Trade and the "Home Market Effect"

This paper analyzes the welfare implications of international spillovers related to productivity gains, changes in market size, or government spending. We introduce trade costs and endogenous varieties in a two-country general-equilibrium model with monopolistic competition, drawing a distinction between productivity gains that enhance manufacturing efficiency, and gains that lower the cost of firms' entry and product differentiation. Our model suggests that countries with lower manufacturing costs have higher GDP but supply a smaller number of goods at a lower international price. Countries with lower entry and differentiation costs also have higher GDP, but supply a larger array of goods at improved terms of trade. The sign of the international welfare spillovers depends on terms of trade, but also on consumers' taste for variety. Higher domestic demand has macroeconomic implications that are similar to those of a reduction in firms' entry costs.

Lorentz's model with dissipative collisions

Propagation of a particle accelerated by an external field through a scattering medium is studied within the generalized Lorentz model allowing inelastic collisions. Energy losses at collisions are proportional to $(1-\alpha^{2})$, where $0\le\alpha\le 1$ is the restitution coefficient. For $\alpha =1$ (elastic collisions) there is no stationary state. It is proved in one dimension that when $\alpha <1$ the stationary state exists . The corresponding velocity distribution changes from a highly asymmetric half-gaussian ($\alpha =0$) to an asymptotically symmetric distribution $\sim {\rm exp}[-(1-\alpha)v^{4}/2]$, for $\alpha\to 1$. The identical scaling behavior in the limit of weak inelasticity is derived in three dimensions by a self-consistent perturbation analysis, in accordance with the behavior of rigorously evaluated moments. The dependence on the external field scales out in any dimension, predicting in particular the stationary current to be proportional to the square root of the external acceleration.Comment: 13 pages, no figures, submitted to Physica