13,109 research outputs found
Extreme value distributions of noncolliding diffusion processes
Noncolliding diffusion processes reported in the present paper are
-particle systems of diffusion processes in one-dimension, which are
conditioned so that all particles start from the origin and never collide with
each other in a finite time interval , . We consider
four temporally inhomogeneous processes with duration , the noncolliding
Brownian bridge, the noncolliding Brownian motion, the noncolliding
three-dimensional Bessel bridge, and the noncolliding Brownian meander. Their
particle distributions at each time are related to the
eigenvalue distributions of random matrices in Gaussian ensembles and in some
two-matrix models. Extreme values of paths in are studied for these
noncolliding diffusion processes and determinantal and pfaffian representations
are given for the distribution functions. The entries of the determinants and
pfaffians are expressed using special functions.Comment: v2: LaTeX2e, 21 pages, 2 figures, correction mad
Dynamical Density Fluctuations around QCD Critical Point Based on Dissipative Relativistic Fluid Dynamics-possible fate of Mach cone at the critical point-
The purpose of this paper is twofold. Firstly, we study the dynamical density
fluctuations around the critical point(CP) of Quantum Chromodynamics(QCD) using
dissipative relativistic fluid dynamics in which the coupling of the density
fluctuations to those of other conserved quantities is taken into account. We
show that the sound mode which is directly coupled to the mechanical density
fluctuation is attenuated and in turn the thermal mode becomes the genuine soft
mode at the QCD CP. We give a speculation on the possible fate of a Mach cone
in the vicinity of the QCD CP as a signal of the existence of the CP on the
basis of the above findings. Secondly, we clarify that the so called
first-order relativistic fluid dynamic equations have generically no problem to
describe fluid dynamic phenomena with long wave lengths contrary to a naive
suspect whereas even Israel-Stewart equation, a popular second-order equation,
may not describe the hydrodynamic mode in general depending on the value of the
relaxation time.Comment: 29pages, 4figures; accepted version for publication in Prog. Theor.
Phys. Introduction and Sec.3 are somewhat modified to make clearer the
purpose of this paper and the discussions on the critical behaviors,
respectively. A few references are added. The conclusions are not changed at
al
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