6,821 research outputs found
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
, where is the restitution coefficient. For
(elastic collisions) there is no stationary state. It is proved in
one dimension that when the stationary state exists . The
corresponding velocity distribution changes from a highly asymmetric
half-gaussian () to an asymptotically symmetric distribution , for . 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
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