Influence of relaxation on propagation, storage and retrieving of light pulses in electromagnetically induced transparency medium

By solving the self-consistent system of Maxwell and density matrix equations to the first order with respect to nonadiabaticity, we obtain an analytical solution for the probe pulse propagation. The conditions for efficient storage of light are analyzed. The necessary conditions for optical propagation distance has been obtained.Comment: 7 pages, 7 figure

Steady-state composition of a two-component gas bubble growing in a liquid solution: self-similar approach

The paper presents an analytical description of the growth of a two-component bubble in a binary liquid-gas solution. We obtain asymptotic self-similar time dependence of the bubble radius and analytical expressions for the non-steady profiles of dissolved gases around the bubble. We show that the necessary condition for the self-similar regime of bubble growth is the constant, steady-state composition of the bubble. The equation for the steady-state composition is obtained. We reveal the dependence of the steady-state composition on the solubility laws of the bubble components. Besides, the universal, independent from the solubility laws, expressions for the steady-state composition are obtained for the case of strong supersaturations, which are typical for the homogeneous nucleation of a bubble.Comment: 12 pages, 2 figure

Canonical quantization of the WZW model with defects and Chern-Simons theory

We perform canonical quantization of the WZW model with defects and permutation branes. We establish symplectomorphism between phase space of WZW model with $N$ defects on cylinder and phase space of Chern-Simons theory on annulus times $R$ with $N$ Wilson lines, and between phase space of WZW model with $N$ defects on strip and Chern-Simons theory on disc times $R$ with $N+2$ Wilson lines. We obtained also symplectomorphism between phase space of the $N$-fold product of the WZW model with boundary conditions specified by permutation branes, and phase space of Chern-Simons theory on sphere with $N$ holes and two Wilson lines.Comment: 26 pages, minor corrections don

Gas bubble growth dynamics in a supersaturated solution: Henry's and Sievert's solubility laws

Theoretical description of diffusion growth of a gas bubble after its nucleation in supersaturated liquid solution is presented. We study the influence of Laplace pressure on the bubble growth. We consider two different solubility laws: Henry's law, which is fulfilled for the systems where no gas molecules dissociation takes place and Sievert's law, which is fulfilled for the systems where gas molecules completely dissociate in the solvent into two parts. We show that the difference between Henry's and Sievert's laws for chemical equilibriumconditions causes the difference in bubble growth dynamics. Assuming that diffusion flux of dissolved gas molecules to the bubble is steady we obtain differential equations on bubble radius for both solubility laws. For the case of homogeneous nucleation of a bubble, which takes place at a significant pressure drop bubble dynamics equations for Henry's and Sievert's laws are solved analytically. For both solubility laws three characteristic stages of bubble growth are marked out. Intervals of bubble size change and time intervals of these stages are found. We also obtain conditions of diffusion flux steadiness corresponding to consecutive stages. The fulfillment of these conditions is discussed for the case of nucleation of water vapor bubbles in magmatic melts. For Sievert's law the analytical treatment of the problem of bubble dissolution in a pure solvent is also presented.http://deepblue.lib.umich.edu/bitstream/2027.42/84215/1/CAV2009-final167.pd

Dynamics of gas bubble growth in a supersaturated solution with Sievert's solubility law

This paper presents a theoretical description of diffusion growth of a gas bubble after its nucleation in supersaturated liquid solution. We study systems where gas molecules completely dissociate in the solvent into two parts, thus making Sievert's solubility law valid. We show that the difference between Henry's and Sievert's laws for chemical equilibrium conditions causes the difference in bubble growth dynamics. Assuming that diffusion flux is steady we obtain a differential equation on bubble radius. Bubble dynamics equation is solved analytically for the case of homogeneous nucleation of a bubble, which takes place at a significant pressure drop. We also obtain conditions of diffusion flux steadiness. The fulfillment of these conditions is studied for the case of nucleation of water vapor bubbles in magmatic melts.Comment: 22 pages, 3 figure