Search results for "Function"
showing 10 items of 14432 documents
Bounds on the density of sources of ultra-high energy cosmic rays from the Pierre Auger Observatory
2013
We derive lower bounds on the density of sources of ultra-high energy cosmic rays from the lack of significant clustering in the arrival directions of the highest energy events detected at the Pierre Auger Observatory. The density of uniformly distributed sources of equal intrinsic intensity was found to be larger than similar to (0.06 – 5) x 10(-4) Mpc(-3) at 95% CL, depending on the magnitude of the magnetic defections. Similar bounds, in the range (0.2 – 7) x 10(-4) Mpc(-3), were obtained for sources following the local matter distribution.
Variational Bethe ansatz approach for dipolar one-dimensional bosons
2020
We propose a variational approximation to the ground state energy of a one-dimensional gas of interacting bosons on the continuum based on the Bethe Ansatz ground state wavefunction of the Lieb-Liniger model. We apply our variational approximation to a gas of dipolar bosons in the single mode approximation and obtain its ground state energy per unit length. This allows for the calculation of the Tomonaga-Luttinger exponent as a function of density and the determination of the structure factor at small momenta. Moreover, in the case of attractive dipolar interaction, an instability is predicted at a critical density, which could be accessed in lanthanide atoms.
Polarization angle dependence of the breathing modes in confined one-dimensional dipolar bosons
2021
Probing the radial collective oscillation of a trapped quantum system is an accurate experimental tool to investigate interactions and dimensionality effects. We consider a fully polarized quasi-one dimensional dipolar quantum gas of bosonic dysprosium atoms in a parabolic trap at zero temperature. We model the dipolar gas with an effective quasi-one dimensional Hamiltonian in the single-mode approximation, and derive the equation of state using a variational approximation based on the Lieb-Liniger gas Bethe Ansatz wavefunction or perturbation theory. We calculate the breathing mode frequencies while varying polarization angles by a sum-rule approach, and find them in good agreement with re…
From finite-gap solutions of KdV in terms of theta functions to solitons and positons
2010
We degenerate the finite gap solutions of the KdV equation from the general formulation in terms of abelian functions when the gaps tends to points, to recover solutions of KdV equations in terms of wronskians called solitons or positons. For this we establish a link between Fredholm determinants and Wronskians.
A sum rule approach to total muon capture rates
1986
Abstract The total muon capture rate is expanded in terms of sum rules and the convergence of such an expansion is analyzed. It results that the energy-weighted and the inverse-energy-weighted sum rules provide an accurate estimate for the total rate in agreement with a complete RPA calculation through the response function. The static polarizability of the isovector dipole mode turns out to be the relevant quantity to determine the total muon capture rate, in light and medium nuclei.
A Hirshfeld partitioning of polarizabilities of water clusters
2006
International audience; A new Hirshfeld partitioning of cluster polarizability into intrinsic polarizabilities and charge delocalization contributions is presented. For water clusters, density-functional theory calculations demonstrate that the total polarizability of a water molecule in a cluster depends upon the number and type of hydrogen bonds the molecule makes with its neighbors. The intrinsic contribution to the molecular polarizability is transferable between water molecules displaying the same H-bond scheme in clusters of different sizes, and geometries, while the charge delocalization contribution also depends on the cluster size. These results could be used to improve the existin…
On the analytical expression of the multicompacton and some exact compact solutions of a nonlinear diffusive Burgers’type equation
2018
International audience; We consider the nonlinear diffusive Burgers' equation as a model equation for signals propagation on the nonlinear electrical transmission line with intersite nonlinearities. By applying the extend sine-cosine method and using an appropriate modification of the Double-Exp function method, we successfully derived on one hand the exact analytical solutions of two types of solitary waves with strictly finite extension or compact support: kinks and pulses, and on the other hand the exact solution for two interacting pulse solitary waves with compact support. These analytical results indicate that the speed of the pulse compactons doesn't depends explicitly on the pulse a…
Slow and fast nonlinearities in microfiber resonators
2008
Nonlinear optical properties of microfiber resonators are investigated. First, a miniature optical resonator standing in air is realized out of a silica microfiber, and measurements of the intensity transfer function show a wide variety of hysteresis cycles obtained at low scanning frequency of the input power. The results are satisfactorily interpreted through the action of thermally-induced nonlinear phase shifts. Secondly, we discuss the conditions under which the fast Kerr nonlinearity can be used efficiently in microfiber resonators under pulsed optical operation.
Modèles quantiques à deux états avec croisements de niveaux décrits par les fonctions de Heun
2019
The thesis is devoted to the fundamental problem of excitation and manipulation of quantum systems, having discrete energy spectrum, via external laser fields. We examine the semiclassical time- dependent quantum two-state problem, when the external electromagnetic field is resonant or quasi-resonant for some two of many levels of the system. The focus of the thesis is on the analytic description of the non- adiabatic evolution of quantum systems subject to excitation by level-crossing field configurations. In the present thesis we classify the complete set of the semiclassical time-dependent quantum two-state models solvable in terms of the five function of the Heun class.Main results of t…
High speed cleaving of crystals with ultrafast Bessel beams
2017
International audience; We develop a novel concept for ultra-high speed cleaving of crystalline materials with femtosecond lasers. Using Bessel beams in single shot, fracture planes can be induced nearly all along the Bessel zone in sapphire. For the first time, we show that only for a pulse duration below 650 fs, a single fracture can be induced in sapphire, while above this duration, cracks appear in all crystallographic orientations. We determine the influential parameters which are polarization direction, crystallographic axes and scanning direction. This is applied to cleave sapphire with a spacing as high as 25 μm between laser impacts.