Search results for "Initial value problem"
showing 10 items of 96 documents
Superfield commutators for D = 4 chiral multiplets and their apppications
1987
The superfield commutators and their corresponding equal-time limits are derived in a covariant way for the D=4 free massive chiral multiplet. For interesting chiral multiplets, the general KAllen-Lehmann representation is also introduced. As applications of the free superfield commutators, the general solution of the Cauchy problem for chiral superfields is given, and an analysis of the closure of the bilinear products of superfields which desrcibe the extension of the internal currents for free supersymmetric chiral matter is performed.
Numerical study of a multiscale expansion of the Korteweg de Vries equation and Painlev\'e-II equation
2007
The Cauchy problem for the Korteweg de Vries (KdV) equation with small dispersion of order $\e^2$, $\e\ll 1$, is characterized by the appearance of a zone of rapid modulated oscillations. These oscillations are approximately described by the elliptic solution of KdV where the amplitude, wave-number and frequency are not constant but evolve according to the Whitham equations. Whereas the difference between the KdV and the asymptotic solution decreases as $\epsilon$ in the interior of the Whitham oscillatory zone, it is known to be only of order $\epsilon^{1/3}$ near the leading edge of this zone. To obtain a more accurate description near the leading edge of the oscillatory zone we present a…
On the gluon spectrum in the glasma
2010
We study the gluon distribution in nucleus-nucleus collisions in the framework of the Color-Glass-Condensate. Approximate analytical solutions are compared to numerical solutions of the non-linear Yang-Mills equations. We find that the full numerical solution can be well approximated by taking the full initial condition of the fields in Coulomb gauge and using a linearized solution for the time evolution. We also compare kt-factorized approximations to the full solution.
Energy and system size dependence of subnucleonic fluctuations
2018
The energy evolution of the fluctuating proton structure is studied by solving the JIMWLK renormalization group equation. The initial condition at moderate $x$ is obtained by fitting the charm reduced cross section data from HERA, requiring that the proton size remains compatible with the diffractive vector meson production measurements. Additionally, we show that the nucleon shape fluctuations are visible in exclusive vector meson production off nuclei.
The 3rd Flow Component as a QGP Signal
2004
Earlier fluid dynamical calculations with QGP show a softening of the directed flow while with hadronic matter this effect is absent. On the other hand, we indicated that a third flow component shows up in the reaction plane as an enhanced emission, which is orthogonal to the directed flow. This is not shadowed by the deflected projectile and target, and shows up at measurable rapidities, $y_cm = 1-2$. To study the formation of this effect initial stages of relativistic heavy ion collisions are studied. An effective string rope model is presented for heavy ion collisions at RHIC energies. Our model takes into account baryon recoil for both target and projectile, arising from the acceleratio…
Particle production from the Color Glass Condensate: proton-nucleus collisions in light of the HERA data
2014
We compute single inclusive hadron production in proton-proton and proton-nucleus collisions consistently within the CGC framework. The parameters in the calculations are obtained from electron-proton DIS and standard nuclear geometry. We obtain a good description of the DIS data without an anomalous dimension in the initial condition of the BK evolution and get a good agreement with the available single inclusive proton-proton and proton-nucleus data.
Gluon spectrum in the glasma from JIMWLK evolution
2011
The JIMWLK equation with a "daughter dipole" running coupling is solved numerically starting from an initial condition given by the McLerran-Venugopalan model. The resulting Wilson line configurations are then used to compute the spectrum of gluons comprising the glasma inital state of a high energy heavy ion collision. The development of a geometrical scaling region makes the spectrum of produced gluons harder. Thus the ratio of the mean gluon transverse momentum to the saturation scale grows with energy. Also the total gluon multiplicity increases with energy slightly faster than the saturation scale squared.
Impact parameter dependent JIMWLK evolution meets HERA data
2019
We calculate the small-$x$ evolution of protons with finite size by solving numerically the JIMWLK evolution equation. The initial condition is constrained by the HERA measurements of charm reduced cross section and of exclusive vector meson production. We compute the energy dependence of diffractive cross sections in order to access the energy evolution of the event-by-event fluctuating proton density profile. The fundamental problems arising from the regime sensitive to non-perturbatively large dipoles are also discussed.
Monte Carlo model for nuclear collisions from SPS to LHC energies
2001
A Monte Carlo model to simulate nuclear collisions in the energy range going from SPS to LHC, is presented. The model includes in its initial stage both soft and semihard components, which lead to the formation of color strings. Collectivity is taken into account considering the possibility of strings in color representations higher than triplet or antitriplet, by means of string fusion. String breaking leads to the production of secondaries. At this point, the model can be used as initial condition for further evolution by a transport model. In order to tune the parameters and see the results in nucleus-nucleus collisions, a naif model for rescattering of secondaries is introduced. Results…
Oscillations of the purity in the repeated-measurement-based generation of quantum states
2008
Repeated observations of a quantum system interacting with another one can drive the latter toward a particular quantum state, irrespectively of its initial condition, because of an {\em effective non-unitary evolution}. If the target state is a pure one, the degree of purity of the system approaches unity, even when the initial condition of the system is a mixed state. In this paper we study the behavior of the purity from the initial value to the final one, that is unity. Depending on the parameters, after a finite number of measurements, the purity exhibits oscillations, that brings about a lower purity than that of the initial state, which is a point to be taken care of in concrete appl…