468 research outputs found
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
Regularized Renormalization Group Reduction of Symplectic Map
By means of the perturbative renormalization group method, we study a
long-time behaviour of some symplectic discrete maps near elliptic and
hyperbolic fixed points. It is shown that a naive renormalization group (RG)
map breaks the symplectic symmetry and fails to describe a long-time behaviour.
In order to preserve the symplectic symmetry, we present a regularization
procedure, which gives a regularized symplectic RG map describing an
approximate long-time behaviour succesfully
Precursor of Color Superconductivity in Hot Quark Matter
We investigate possible precursory phenomena of color superconductivity in
quark matter at finite temperature T with use of a simple Nambu-Jona-Lasinio
model. It is found that the fluctuating pair field exists with a prominent
strength even well above the critical temperature T_c. We show that the
collective pair field has a complex energy located in the second Riemann sheet,
which approaches the origin as T is lowered to T_c. We discuss the possible
relevance of the precursor to the observables to be detected in heavy ion
collisions.Comment: 5 pages, 3 figures, version to appear in Phys. Rev. D. Discussions
are enlarged on the physical origin of the large fluctuation of the pair
field and its phenomenological consequences. References are adde
Chiral and Color-superconducting Phase Transitions with Vector Interaction in a Simple Model (Addenda)
In the preceding paper(Prog.Theor.Phys.108(2002)929 or hep-ph/0207255), we
have shown that the critical line of the first order chiral transition of QCD
can have two endpoints. In this addendum, we elucidate the mechanism to realize
the two-endpoint structure in the QCD phase diagram and argue the robustness
for the appearance of such an interesting phase structure
Dynamical Reduction of Discrete Systems Based on the Renormalization Group Method
The renormalization group (RG) method is extended for global asymptotic
analysis of discrete systems. We show that the RG equation in the discretized
form leads to difference equations corresponding to the Stuart-Landau or
Ginzburg-Landau equations. We propose a discretization scheme which leads to a
faithful discretization of the reduced dynamics of the original differential
equations.Comment: LaTEX. 12pages. 1 figure include
Pseudogap of Color Superconductivity in Heated Quark Matter
We show that the pseudogap of the quark density of states is formed in hot
quark matter as a precursory phenomenon of the color superconductivity on the
basis of a low-energy effective theory. We clarify that the decaying process of
quarks near Fermi surface to a hole and the diquark soft mode (qq)_{soft} is
responsible for the formation of the pseudogap. Our result suggests that the
pseudogap is a universal phenomenon in strong coupling superconductors.Comment: Introduction is largely rewritten and minor changes are made in other
parts of the text. Some referenes with comments are added. Numerical errors
in the figures are corrected. To appear in Phys. Rev.
Renormalization Group Method Applied to Kinetic Equations: roles of initial values and time
The so-called renormalization group (RG) method is applied to derive kinetic
and transport equations from the respective microscopic equations. The derived
equations include Boltzmann equation in classical mechanics, Fokker-Planck
equation, a rate equation in a quantum field theoretical model. Utilizing the
formulation of the RG method which elucidates the important role played by the
choice of the initial conditions, the general structure and the underlying
assumptions in the derivation of kinetic equations in the RG method is
clarified. It is shown that the present formulation naturally leads to the
choice for the initial value of the microscopic distribution function at
arbitrary time to be on the averaged distribution function to be
determined. The averaged distribution function may be thought as an integral
constant of the solution of microscopic evolution equation; the RG equation
gives the slow dynamics of the would-be initial constant, which is actually the
kinetic equation governing the averaged distribution function. It is further
shown that the averaging as given above gives rise to a coarse-graining of the
time-derivative which is expressed with the initial time , thereby leads
to time-irreversible equations even from a time-reversible equation. It is
shown that a further reduction of Boltzmann equation to fluid dynamical
equations and the adiabatic elimination of fast variables in Fokker-Planck
equation are also performed in a unified way in the present method.Comment: The detailed derivations are added to section 5 (fluiddynamical limit
of Boltzmann equation) and to Appendix B (Adiabatic elimination of fast
variables in Fokker-Planck equation) which is moved to the text as a section.
Other minor corrections are made all over the text including typo
Precursor of Color Superconductivity
We investigate possible precursory phenomena of color superconductivity at
finite temperature with an effective theory of QCD. It is found that the
fluctuation of the diquark pair field exists with a prominent strength even
well above the critical temperature . We show that such a fluctuaiton
forms a collective mode, the corresponding pole of which approaches the origin
as is lowered to in the complex energy plane. We discuss the possible
relevance of the precursor to the observables to be detected in heavy-ion
collisions.Comment: 4 pages, 5 figures, Talk presented at the XVIth International
Conference on Particles and Nuclei (PANIC02), Osaka, Japan, Sep.30 - Oct.4,
2002, Uses espcrc1.st
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