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

G3-homogeneous gravitational instantons

We provide an exhaustive classification of self-dual four-dimensional gravitational instantons foliated with three-dimensional homogeneous spaces, i.e. homogeneous self-dual metrics on four-dimensional Euclidean spaces admitting a Bianchi simply transitive isometry group. The classification pattern is based on the algebra homomorphisms relating the Bianchi group and the duality group SO(3). New and general solutions are found for Bianchi III.Comment: 24 pages, few correction

Ricci flows and expansion in axion-dilaton cosmology

We study renormalization-group flows by deforming a class of conformal sigma-models. We consider overall scale factor perturbation of Einstein spaces as well as more general anisotropic deformations of three-spheres. At leading order in alpha, renormalization-group equations turn out to be Ricci flows. In the three-sphere background, the latter is the Halphen system, which is exactly solvable in terms of modular forms. We also analyze time-dependent deformations of these systems supplemented with an extra time coordinate and time-dependent dilaton. In some regimes time evolution is identified with renormalization-group flow and time coordinate can appear as Liouville field. The resulting space-time interpretation is that of a homogeneous isotropic Friedmann-Robertson-Walker universe in axion-dilaton cosmology. We find as general behaviour the superposition of a big-bang (polynomial) expansion with a finite number of oscillations at early times. Any initial anisotropy disappears during the evolution.Comment: 22 page

Dispersion-shifted all-solid high index-contrast microstructured optical fiber for nonlinear applications at 1.55µm

We report the fabrication of an all-solid highly nonlinear microstructured optical fiber. The structured preform was made by glass extrusion using two types of commercial lead silicate glasses that provide high index-contrast. Effectively single-moded guidance was observed in the fiber at 1.55µm. The effective nonlinearity and the propagation loss at this wavelength were measured to be 120W/km respectively at 1.55µm. These predictions are consistent with the experimentally determined dispersion of +12.5ps/nm/km at 1.55µm. Tunable and efficient four-wave-mixing based wavelength conversion was demonstrated at wavelengths around 1.55µm using a 1.5m length of the fiber

Multichannel wavelength conversion of 40 Gbit/s NRZ DPSK signals in a highly nonlinear dispersion flattened lead silicate fibre

We experimentally demonstrate the wavelength conversion of three wavelength multiplexed 40 Gbit/s Differential Phase Shift Keyed (DPSK) signals in a 2.2m length of highly nonlinear, dispersion tailored W-type lead-silicate optical fibre

From the WZWN Model to the Liouville Equation: Exact String Dynamics in Conformally Invariant AdS Background

It has been known for some time that the SL(2,R) WZWN model reduces to Liouville theory. Here we give a direct and physical derivation of this result based on the classical string equations of motion and the proper string size. This allows us to extract precisely the physical effects of the metric and antisymmetric tensor, respectively, on the {\it exact} string dynamics in the SL(2,R) background. The general solution to the proper string size is also found. We show that the antisymmetric tensor (corresponding to conformal invariance) generally gives rise to repulsion, and it precisely cancels the dominant attractive term arising from the metric. Both the sinh-Gordon and the cosh-Gordon sectors of the string dynamics in non-conformally invariant AdS spacetime reduce here to the Liouville equation (with different signs of the potential), while the original Liouville sector reduces to the free wave equation. Only the very large classical string size is affected by the torsion. Medium and small size string behaviours are unchanged. We also find illustrative classes of string solutions in the SL(2,R) background: dynamical closed as well as stationary open spiralling strings, for which the effect of torsion is somewhat like the effect of rotation in the metric. Similarly, the string solutions in the 2+1 BH-AdS background with torsion and angular momentum are fully analyzed.Comment: 24 pages including 4 postscript figures. Enlarged version including a section on string solutions in 2+1 black hole background. To be published in Phys. Rev. D., December 199

Improved shaping approach to the preliminary design of low-thrust trajectories

This paper presents a general framework for the development of shape-based approaches to low-thrust trajectory design. A novel shaping method, based on a three-dimensional description of the trajectory in spherical coordinates, is developed within this general framework. Both the exponential sinusoid and the inverse polynomial shaping are demonstrated to be particular two-dimensional cases of the spherical one. The pseudoequinoctial shaping is revisited within the new framework, and the nonosculating nature of the pseudoequinoctial elements is analyzed. A two step approach is introduced to solve the time of flight constraint, related to the design of low-thrust arcs with boundary constraints for both spherical and pseudoequinoctial shaping. The solution derived from the shaping approach is improved with a feedback linear-quadratic controller and compared against a direct collocation method based on finite elements in time. The new shaping approach and the combination of shaping and linear-quadratic controller are tested on three case studies: a mission to Mars, a mission to asteroid 1989ML, a mission to comet Tempel-1, and a mission to Neptune

The O(N) Model at Finite Temperature: Renormalization of the Gap Equations in Hartree and Large-N Approximation

The temperature dependence of the sigma meson and pion masses is studied in the framework of the O(N) model. The Cornwall-Jackiw-Tomboulis formalism is applied to derive gap equations for the masses in the Hartree and large-N approximations. Renormalization of the gap equations is carried out within the cut-off and counter-term renormalization schemes. A consistent renormalization of the gap equations within the cut-off scheme is found to be possible only in the large-N approximation and for a finite value of the cut-off. On the other hand, the counter-term scheme allows for a consistent renormalization of both the large-N and Hartree approximations. In these approximations, the meson masses at a given nonzero temperature depend in general on the choice of the cut-off or renormalization scale. As an application, we also discuss the in-medium on-shell decay widths for sigma mesons and pions at rest.Comment: 21 pages, 6 figures, typos corrected and refs. added, accepted in Journal of Physics

Bose-Einstein condensation and chiral phase transition in linear sigma model

With the linear sigma model, we have studied Bose-Einstein condensation and the chiral phase transition in the chiral limit for an interacting pion system. A $\mu-T$ phase diagram including these two phenomena is presented. It is found that the phase plane has been divided into three areas: the Bose-Einstein condensation area, the chiral symmetry broken phase area and the chiral symmetry restored phase area. Bose-Einstein condensation can happen either from the chiral symmetry broken phase or from the restored phase. We show that the onset of the chiral phase transition is restricted in the area where there is no Bose-Einstein condensation.Comment: 13 pages, 7 figure