Theory of Lattice and Electronic Fluctuations in Weakly Localized Spin-Peierls Systems

A theoretical approach to the influence of one-dimensional lattice fluctuations on electronic properties in weakly localized spin-Peierls systems is proposed using the renormalization group and the functional integral techniques. The interplay between the renormalization group flow of correlated electrons and one-dimensional lattice fluctuations is taken into account by the one-dimensional functional integral method in the adiabatic limit. Calculations of spin-Peierls precursor effects on response functions are carried out explicitely and the prediction for the temperature dependent magnetic susceptibility and nuclear relaxation is compared with available experimental data for (TMTTF)$_{2}$PF$_{6}$.Comment: 15 pages, 7 Encapsulated Postscript figure

Emergence of nonlinear behavior in the dynamics of ultracold bosons

We study the evolution of a system of interacting ultracold bosons, which presents nonlinear, chaotic, behaviors in the limit of very large number of particles. Using the spectral entropy as an indicator of chaos and three different numerical approaches : Exact diagonalization, truncated Husimi method and mean-field (Gross-Pitaevskii) approximation, we put into evidence the destructive impact of quantum noise on the emergence of the nonlinear dynamics

A mathematical model for the Fermi weak interactions

We consider a mathematical model of the Fermi theory of weak interactions as patterned according to the well-known current-current coupling of quantum electrodynamics. We focuss on the example of the decay of the muons into electrons, positrons and neutrinos but other examples are considered in the same way. We prove that the Hamiltonian describing this model has a ground state in the fermionic Fock space for a sufficiently small coupling constant. Furthermore we determine the absolutely continuous spectrum of the Hamiltonian and by commutator estimates we prove that the spectrum is absolutely continuous away from a small neighborhood of the thresholds of the free Hamiltonian. For all these results we do not use any infrared cutoff or infrared regularization even if fermions with zero mass are involved

Macroscopic limit of a one-dimensional model for aging fluids

We study a one-dimensional equation arising in the multiscale modeling of some non-Newtonian fluids. At a given shear rate, the equation provides the instantaneous mesoscopic response of the fluid, allowing to compute the corresponding stress. In a simple setting, we study the well-posedness of the equation and next the long-time behavior of its solution. In the limit of a response of the fluid much faster than the time variations of the ambient shear rate, we derive some equivalent macroscopic differential equations that relate the shear rate and the stress. Our analytical conclusions are confronted to some numerical experiments. The latter quantitatively confirm our derivations

Mathematical analysis of a one-dimensional model for an aging fluid

We study mathematically a system of partial differential equations arising in the modelling of an aging fluid, a particular class of non Newtonian fluids. We prove well-posedness of the equations in appropriate functional spaces and investigate the longtime behaviour of the solutions

Some complexity and approximation results for coupled-tasks scheduling problem according to topology

We consider the makespan minimization coupled-tasks problem in presence of compatibility constraints with a specified topology. In particular, we focus on stretched coupled-tasks, i.e. coupled-tasks having the same sub-tasks execution time and idle time duration. We study several problems in framework of classic complexity and approximation for which the compatibility graph is bipartite (star, chain,. . .). In such a context, we design some efficient polynomial-time approximation algorithms for an intractable scheduling problem according to some parameters

Kinematics and Mass Modeling of Messier 33: Halpha observations

As part of a long-term project to revisit the kinematics and dynamics of the large disc galaxies of the Local Group, we present the first deep, wide-field (42' x 56') 3D-spectroscopic survey of the ionized gas disc of Messier 33. Fabry-Perot interferometry has been used to map its Ha distribution and kinematics at unprecedented angular resolution (<3'') and resolving power (12600), with the 1.6m telescope at the Observatoire du Mont Megantic. The ionized gas distribution follows a complex, large-scale spiral structure, unsurprisingly coincident with the already-known spiral structures of the neutral and molecular gas discs. The kinematical analysis of the velocity field shows that the rotation center of the Ha disc is distant from the photometric center by 170 pc (sky projected distance) and that the kinematical major-axis position angle and disc inclination are in excellent agreement with photometric values. The Ha rotation curve agrees very well with the HI rotation curves for 0 6.5 kpc. The reason for this discrepancy is not well understood. The velocity dispersion profile is relatively flat around 16 km/s, which is at the low end of velocity dispersions of nearby star-forming galactic discs. A strong relation is also found between the Ha velocity dispersion and the Ha intensity. Mass models were obtained using the Ha rotation curve but, as expected, the dark matter halo's parameters are not very well constrained since the optical rotation curve only extends out to 8 kpc.Comment: 26 pages, 18 figures, accepted for publication in MNRA