Bose-Einstein condensation in linear sigma model at Hartree and large N approximation

The BEC of charged pions is investigated in the framework of O(4) linear sigma model. By using Cornwall-Jackiw-Tomboulis formalism, we have derived the gap equations for the effective masses of the mesons at finite temperature and finite isospin density. The BEC is discussed in chiral limit and non-chiral limit at Hartree approximation and also at large N approximation.Comment: 11 pages, 9 figure

Periodic solitons for the elliptic-elliptic focussing Davey-Stewartson equations

We consider the elliptic-elliptic, focussing Davey-Stewartson equations, which have an explicit bright line soliton solution. The existence of a family of periodic solitons, which have the profile of the line soliton in the longitudinal spatial direction and are periodic in the transverse spatial direction, is established using dynamical systems arguments. We also show that the line soliton is linearly unstable with respect to perturbations in the transverse direction.Comment: arXiv admin note: text overlap with arXiv:1411.247

Collisional energy loss above the critical temperature in QCD

We compute the collisional energy loss for a heavy quark above the critical temperature in Quantum ChromoDynamics (QCD). We work in the semi Quark-Gluon Plasma, which assumes that this region is dominated by the non-trivial holonomy of the thermal Wilson line. Relative to the result to leading order in perturbation theory, at a fixed value of the coupling constant we generically we find that collisional energy loss is suppressed by powers of the Polyakov loop, l < 1. For small values of the loop, this suppression is linear for the scattering off of light quarks, and quadratic for the scattering off of gluons, or for Compton scattering.Comment: 19 pages, 4 figure

Non-fragile H∞ control with randomly occurring gain variations, distributed delays and channel fadings

This study is concerned with the non-fragile H∞ control problem for a class of discrete-time systems subject to randomly occurring gain variations (ROGVs), channel fadings and infinite-distributed delays. A new stochastic phenomenon (ROGVs), which is governed by a sequence of random variables with a certain probabilistic distribution, is put forward to better reflect the reality of the randomly occurring fluctuation of controller gains implemented in networked environments. A modified stochastic Rice fading model is then exploited to account for both channel fadings and random time-delays in a unified representation. The channel coefficients are a set of mutually independent random variables which abide by any (not necessarily Gaussian) probability density function on [0, 1]. Attention is focused on the analysis and design of a non-fragile H∞ outputfeedback controller such that the closed-loop control system is stochastically stable with a prescribed H∞ performance. Through intensive stochastic analysis, sufficient conditions are established for the desired stochastic stability and H∞ disturbance attenuation, and the addressed non-fragile control problem is then recast as a convex optimisation problem solvable via the semidefinite programme method. An example is finally provided to demonstrate the effectiveness of the proposed design method