50 research outputs found
Traveling waves in high energy QCD
Saturation is expected to occur when a high density of partons (mainly
gluons)- or equivalently strong fields in Quantum Chromodynamics (QCD) - is
realized in the weak coupling regime. A way to reach saturation is through the
high-energy evolution of an extended target probed at a fixed hard scale. In
this case, the transition to saturation is expected to occur from nonlinear
perturbative QCD dynamics. We discuss this approach to saturation, which is
mathematically characterized by the appearance of traveling wave patterns in a
suitable kinematical representation. A short review on traveling waves in high
energy QCD and a first evidence of this phenomenon in deep-inelastic proton
scattering are presented.Comment: 10 pages, 5 figures, talk given at the XXXVth International Symposium
on Multiparticle Dynamics (ISMD05), Kromeriz, Czech Republic, August 9-15
200
Dynamical entropy of dense QCD states
We discuss dense states of QCD matter formed in high-energy hadronic and
heavy-ion collisions from the point of view of statistical physics of
non-equilibrium processes. For this sake, we first propose a formulation of the
dynamical entropy of dense QCD states in the "saturation regime" leading to a
color glass condensate (CGC). The statistical physics description amounts to
describe the modification of the color correlation length with energy as a
compression process for which non equilibrium thermodynamic properties are
applicable. We derive an expression of the dynamical entropy in terms of the
rapidity evolution of the unintegrated gluon distributions in the colliding
nuclei, verifying suitable positivity and irreversibility properties. We extend
this approach to the initial pre-equilibrium (glasma) state of an heavy-ion
collision. It allows for a definition of the initial entropy before the
evolution towards the hydrodynamic regime as a function of the glasma
correlation length and an overlap parameter characterizing the low-momentum
spectrum of the glasma state. This initial entropy, by extension to the N=4 SYM
theory, is then matched as the key input parameter to the strong coupling
evaluation of thermalization towards the hydrodynamic regime based on the
AdS/CFT correspondence. It thus allows to cast a bridge between the weak and
strong coupling phases of an heavy-ion reaction.Comment: Version mildly updated to match publication. Adding a discussion of
the k_T factorization formula. Results and conclusions unchange
Gauge/Cosmology Brane-to-Brane Duality
We introduce a duality relation between two distinct branes, a cosmological
brane with macroscopic matter and a holographic brane with microscopic gauge
fields. Using brane-world cosmology with a single brane in a 5-dimensional AdS5
background, we find an explicit time-dependent holographic correspondence
between the bulk metric surrounding the cosmological brane and the N=4 gauge
field theory living on the boundary of the Z2-symmetric mirror bulk, identified
with the holographic brane. We then relate the cosmic acceleration on the
cosmological brane to the conformal anomaly of the gauge theory on the
holographic brane. This leads to a dual microscopic interpretation of the
number of e-foldings of the cosmological eras on the cosmological brane.Comment: 21 pages, 1 figur
On the positivity of Fourier transforms
Characterizing in a constructive way the set of real functions whose Fourier
transforms are positive appears to be yet an open problem. Some sufficient
conditions are known but they are far from being exhaustive. We propose two
constructive sets of necessary conditions for positivity of the Fourier
transforms and test their ability of constraining the positivity domain. One
uses analytic continuation and Jensen inequalities and the other deals with
Toeplitz determinants and the Bochner theorem. Applications are discussed,
including the extension to the two-dimensional Fourier-Bessel transform and the
problem of positive reciprocity, i.e. positive functions with positive
transforms.Comment: 12 pages, 9 figures (in 4 groups
From "Dirac combs" to Fourier-positivity
Motivated by various problems in physics and applied mathematics, we look for
constraints and properties of real Fourier-positive functions, i.e. with
positive Fourier transforms. Properties of the "Dirac comb" distribution and of
its tensor products in higher dimensions lead to Poisson resummation, allowing
for a useful approximation formula of a Fourier transform in terms of a limited
number of terms. A connection with the Bochner theorem on positive definiteness
of Fourier-positive functions is discussed. As a practical application, we find
simple and rapid analytic algorithms for checking Fourier-positivity in 1- and
(radial) 2-dimensions among a large variety of real positive functions. This
may provide a step towards a classification of positive positive-definite
functions.Comment: 17 pages, 14 eps figures (overall 8 figures in the text