42,679 research outputs found
Classical Strongly Coupled QGP: VII. Energy Loss
We use linear response analysis and the fluctuation-dissipation theorem to
derive the energy loss of a heavy quark in the SU(2) classical Coulomb plasma
in terms of the monopole and non-static structure factor. The result is
valid for all Coulomb couplings , the ratio of the mean potential
to kinetic energy. We use the Liouville equation in the collisionless limit to
assess the SU(2) non-static structure factor. We find the energy loss to be
strongly dependent on . In the liquid phase with , the
energy loss is mostly metallic and soundless with neither a Cerenkov nor a Mach
cone. Our analytical results compare favorably with the SU(2) molecular
dynamics simulations at large momentum and for heavy quark masses.Comment: 18 pages, 15 figures. v2: added references, changed title, replaced
figures for Fig. 7, corrected typo
Genuine Non-Self-Averaging and Ultra-Slow Convergence in Gelation
In irreversible aggregation processes droplets or polymers of microscopic
size successively coalesce until a large cluster of macroscopic scale forms.
This gelation transition is widely believed to be self-averaging, meaning that
the order parameter (the relative size of the largest connected cluster)
attains well-defined values upon ensemble averaging with no sample-to-sample
fluctuations in the thermodynamic limit. Here, we report on anomalous gelation
transition types. Depending on the growth rate of the largest clusters, the
gelation transition can show very diverse patterns as a function of the control
parameter, which includes multiple stochastic discontinuous transitions,
genuine non-self-averaging and ultra-slow convergence of the transition point.
Our framework may be helpful in understanding and controlling gelation.Comment: 8 pages, 10 figure
Warped brane-world compactification with Gauss-Bonnet term
In the Randall-Sundrum (RS) brane-world model a singular delta-function
source is matched by the second derivative of the warp factor. So one should
take possible curvature corrections in the effective action of the RS models in
a Gauss-Bonnet (GB) form. We present a linearized treatment of gravity in the
RS brane-world with the Gauss-Bonnet modification to Einstein gravity. We give
explicit expressions for the Neumann propagator in arbitrary D dimensions and
show that a bulk GB term gives, along with a tower of Kaluza-Klein modes in the
bulk, a massless graviton on the brane, as in the standard RS model. Moreover,
a non-trivial GB coupling can allow a new branch of solutions with finite
Planck scale and no naked bulk singularity, which might be useful to avoid some
of the previously known ``no--go theorems'' for RS brane-world
compactifications.Comment: 23 pages, typos in Secs. 5 & 6 corrected, expanded/published version
(IJMPA
Percolation Transitions in Scale-Free Networks under Achlioptas Process
It has been recently shown that the percolation transition is discontinuous
in Erd\H{o}s-R\'enyi networks and square lattices in two dimensions under the
Achlioptas Process (AP). Here, we show that when the structure is highly
heterogeneous as in scale-free networks, a discontinuous transition does not
always occur: a continuous transition is also possible depending on the degree
distribution of the scale-free network. This originates from the competition
between the AP that discourages the formation of a giant component and the
existence of hubs that encourages it. We also estimate the value of the
characteristic degree exponent that separates the two transition types.Comment: 4 pages, 6 figure
Finite-size scaling theory for explosive percolation transitions
The finite-size scaling (FSS) theory for continuous phase transitions has
been useful in determining the critical behavior from the size dependent
behaviors of thermodynamic quantities. When the phase transition is
discontinuous, however, FSS approach has not been well established yet. Here,
we develop a FSS theory for the explosive percolation transition arising in the
Erd\H{o}s and R\'enyi model under the Achlioptas process. A scaling function is
derived based on the observed fact that the derivative of the curve of the
order parameter at the critical point diverges with system size in a
power-law manner, which is different from the conventional one based on the
divergence of the correlation length at . We show that the susceptibility
is also described in the same scaling form. Numerical simulation data for
different system sizes are well collapsed on the respective scaling functions.Comment: 5 pages, 5 figure
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