Sensitivity of Pion versus Parton-Jet Nuclear Modification Factors to the Path-Length Dependence of Jet-Energy Loss at RHIC and LHC

We compare the jet-path length and beam-energy dependence of the pion nuclear modification factor and a patton-jet nuclear modification factor at RHIC and LHC, and contrast the predictions based on a linear pQCD and a highly non-linear hybrid AdS holographic model of jet-energy loss. It is found that both models require a reduction of the jet-medium coupling from RHIC to LHC to account for the measured pion nuclear modification factor. In the case of the parton-jet nuclear modification factor, however, which serves as a lower bound for the LO jet nuclear modification factor of reconstructed jets, the extracted data can be characterized without a reduced jet-medium coupling at LHC energies. It is concluded that when the reconstructed jets are sensitive to both quarks and gluons and thus provide more information than the pion nuclear modification factor, their information regarding the jet-medium coupling is limited due to the superposition with NLO and medium effects. Hence, a detailed description of the underlying physics requires both the leading hadron and the reconstructed jet nuclear modification factor. Unfortunately, the results for both the pion and the parton-jet nuclear modification factor are insensitive to the jet-path dependence of the models considered.

The central limit theorem and chaos

Let X be a compact metric space studies some relationships between stochastic and f ： X→ X be a continuous map. This paper and topological properties of dynamical systems. It is shown that if f satisfies the central limit theorem, then f is topologically ergodic and / is sensitively dependent on initial conditions if and only if / is neither minimal nor equicontinuous.

An Equivalent Condition of Weak Mixing

Let X be a compact metric space containing at least two points and let f ： X → X be continuous. In this paper, we introduce the notion of totally maximum sensitive （TMS, for short） and prove that f is weakly mixing if and only if it is TMS, and if X = [0, 1], then f is weakly mixing if and only if it is 2-maximum sensitive.

Pointwise Pseudo-Orbit Tracing Property and Its Application

In this paper, the pointwise pseudo-orbit tracing property is defined on a compact metric space, and it is a generalization of pseudo-orbit tracing property. As applications, we prove the following results: (i) If / has pointwise pseudo-orbit tracing property, for any k ∈ Z+, and fk is chain transitive, then for any k ∈ Z+, fk has open set transitive ; (ii) If f has pointwise pseudo-orbit tracing property, and for any n ∈ Z+,fn is chain transitive, then f has sensitive dependence on initial conditions; (iii) If f is open set mixing and has pointwise pseudo-orbit tracing property, then f has property P; (iv) Let f : (X, d) →(X, d) be a homeomophism, then f is pointwise pseudo-orbit tracing property if and only if the shift map σf is pointwise pseudo-orbit tracing property.

Recent Development of Chaos Theory in Topological Dynamics

We give a summary on the recent development of chaos theory in topological dynamics, focusing on Li-Yorke chaos, Devaney chaos, distributional chaos, positive topological entropy, weakly mixing sets and so on, and their relationships.