Search results for "Integrable system"
showing 10 items of 354 documents
Some new results on integration for multifunction
2018
It has been proven in previous papers that each Henstock-Kurzweil-Pettis integrable multifunction with weakly compact values can be represented as a sum of one of its selections and a Pettis integrable multifunction. We prove here that if the initial multifunction is also Bochner measurable and has absolutely continuous variational measure of its integral, then it is a sum of a strongly measurable selection and of a variationally Henstock integrable multifunction that is also Birkhoff integrable.
An isoperimetric type problem for primitive Pythagorean hodograph curves
2012
An isoperimetric type problem for primitive Pythagorean hodograph curves is studied. We show how to compute, for each possible degree, the Pythagorean hodograph curve of a given perimeter enclosing the greatest area. We also discuss the existence and construction of smooth solutions, obtaining a relationship with an interesting sequence of Appell polynomials.
Riemann-Hilbert approach to the time-dependent generalized sine kernel
2011
We derive the leading asymptotic behavior and build a new series representation for the Fredholm determinant of integrable integral operators appearing in the representation of the time and distance dependent correlation functions of integrable models described by a six-vertex R-matrix. This series representation opens a systematic way for the computation of the long-time, long-distance asymptotic expansion for the correlation functions of the aforementioned integrable models away from their free fermion point. Our method builds on a Riemann–Hilbert based analysis.
Derivatives not first return integrable on a fractal set
2018
We extend to s-dimensional fractal sets the notion of first return integral (Definition 5) and we prove that there are s-derivatives not s-first return integrable.
Comments on `A new efficient method for calculating perturbation energies using functions which are not quadratically integrable'
1996
The recently proposed method of calculating perturbation energies using a non-normalizable wavefunction by Skala and Cizek is analysed and rigorously proved.
Asymptotic analysis of the form-factors of the quantum spin chains
2020
Since a long-time, the quantum integrable systems have remained an area where modern mathematical methods have given an access to interesting results in the study of physical systems. The exact computations, both numerical and asymptotic, of the correlation function is one of the most important subject of the theory of the quantum integrable models. In this context an approach based on the calculation of form factors has been proved to be a more effective one. In this thesis, we develop a new method based on the algebraic Bethe ansatz is proposed for the computation of the form-factors in thermodynamic limit. It is applied to and described in the context of isotropic XXX Heisenberg chain, w…
Rains of solitons in a figure-of-eight passively mode-locked fiber laser
2014
International audience; We report experimental observation of rains of solitons in figure-of-eight fiber laser passively mode-locked through nonlinear optical loop mirror. Soliton pulses are created from an extended noisy background and drift until they reach a condensed phase comprising several tens of aggregated solitons. The observation of this dynamics tends to strengthen the idea of the universality of the collective behavior of solitons.
Top physics studies at the LHC in the standard model and beyond with the ATLAS detector
2009
The LHC will be a Top quark factory, producing large numbers of Top quarks even at the initial low luminosities. This will enable a rich program of Top quark Physics to be explored, both within the Standard Model and using Top quarks as probes of Physics Beyond the Standard Model. Recent studies from ATLAS will be presented, including prospects for the measurements of the production of Top pairs and single Top production, angular correlations in the Top decay, and the precision measurement of the Top quark mass. The search for Physics beyond the Standard Model will be illustrated with searches for rare Top decays involving Flavour Changing Neutral Currents, and the reconstruction of tt-bar …
The soliton-soliton interaction in the Chiral Dilaton Model
2012
We study the interaction between two B = 1 states in the Chiral Dilaton Model where baryons are described as nontopological solitons arising from the interaction of chiral mesons and quarks. By using the hedgehog solution for B = 1 states we construct, via a product ansatz, three possible B = 2 configurations to analyse the role of the relative orientation of the hedgehog quills in the dynamics of the soliton-soliton interaction and investigate the behavior of these solutions in the range of long/intermediate distance. One of the solutions is quite binding due to the dynamics of the pi and sigma fields at intermediate distance and should be used for nuclear matter studies. Since the product…
Search for scalar top quark pair production in natural gauge mediated supersymmetry models with the ATLAS detector in pp collisions at s=7 TeV
2012
The results of a search for pair production of the lighter scalar partners of top quarks () in 2.05 fb−1 of pp collisions at TeV using the ATLAS experiment at the LHC are reported. Scalar top quar ...