Multiple Production of Particles and Hydrodynamical Aspect of Quantum Theory of Fields

In this lecture note, we present several topics on relativistic hydrodynamics and its application to relativistic heavy ion collisions. In the first part we give a brief introduction to relativistic hydrodynamics in the context of heavy ion collisions. In the second part we present the formalism and some fundamental aspects of relativistic ideal and viscous hydrodynamics. In the third part, we start with some basic checks of the fundamental observables followed by discussion of collective flow, in particular elliptic flow, which is one of the most exciting phenomenon in heavy ion collisions at relativistic energies. Next we discuss how to formulate the hydrodynamic model to describe dynamics of heavy ion collisions. Finally, we conclude the third part of the lecture note by showing some results from ideal hydrodynamic calculations and by comparing them with the experimental data.Comment: 40 pages, 35 figures; lecture given at the QGP Winter School, Jaipur, India, Feb.1-3, 2008; to appear in Springer Lecture Notes in Physic

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“…The following references might be very helpful to complement this section [8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24].…”

Section: Formalism Of the Relativistic Ideal/viscous Hydrodynamicsmentioning

confidence: 99%

Hydrodynamics and Flow

Hirano

Kolk

Bilandzic

2009

Lecture Notes in Physics

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“…local rest frame of the thermal medium. For the full-relativistic description of the space-time evolution of a hot and dense matter, we need to establish relativistic Navier-Stokes equation [12]. Taking correlation of appropriate currents, we can easily evaluate viscosities and heat conductivity in the same manner [13] .…”

Section: ============== Fig5mentioning

confidence: 99%

“…Taking correlation of appropriate currents, we can easily evaluate viscosities and heat conductivity in the same manner [13] . However, in relativistic transport theory, there exist several delicate points, e.g., relativistic property makes difference of mass and energy meaningless and, as a result, meaning of the "flow" of the fluid and "heat flow" become ambiguous [12] [14]. The choice of the current depends on the macroscopic phenomenological equations which contain transport coefficients.…”

Section: ============== Fig5mentioning

confidence: 99%

Calculation of the baryon diffusion constant in hot and dense hadronic matter based on an ultrarelativistic collision event generator

et al. 2000

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We evaluate thermodynamical quantities and transport coefficients of a dense and hot hadronic matter based on an event generator URASiMA (Ultra-Relativistic AA collision Simulator based on Multiple Scattering Algorithm). The statistical ensembles in equilibrium with fixed temperature and chemical potential are generated by imposing periodic boundary condition to the simulation of URASiMA, where energy density and baryon number density is conserved. Achievement of the thermal equilibrium and the chemical equilibrium are confirmed by the common value of slope parameter in the energy distributions and the saturation of the numbers of contained particles, respectively. By using the generated ensembles, we investigate the temperature dependence and the chemical potential dependence of the baryon diffusion constant of a dense and hot hadronic matter. : 13.75.-n, 25.75, 33.15.V, 28.20.G PACS

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“…I n the field of statistical mechanics, however, hydrodynamical description for a many particle system is not strange to us. NAMIKI and ISO [91] define the hydrodynamical quantities in terms of field theoretical operators with the help of an averaging procedure in quantum statistical mechanics. They show that the equation of state assumed by LANDAU holds when the interaction between meson and nucleon is of the first kind, while this is not the case for a second kind nucleon-meson interaction.…”

Section: Foundation Of H Ydrod Ynamical Descriptionmentioning

confidence: 99%

Theory of Multiple Particle Production at Extremely High Energy

Koba

Takagi

1959

Fortschr. Phys.

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PrefaceThe mechanism of multiple particle production a t ext.remely high energythis is undoubtedly one of the most challenging topics in contemporary nuclear physics. (By the word "extremely high" we mean here the energy region above lo3 Gev.) The problem remains still quite unsettled, though it has been intensively attacked both by experimental and theoretical workersl). Various theories and models have so far been proposed almost independently of each other and with little interrelation to each other; and we cannot tell for certain which of them, if any, reproduces the main aspects of the experiments. This situation is partly due to the incompetence of the current field theories a t this new domain of physics, and partly due to the lack of systematic knowledge on the characteristic features of the phenomena. l) Excellent review articles on this problem have been published by LEWIS [ I ] and by ROZENTAL' and CERNAVSKIJ [Z]. The latter, in particular, has given a systematic and detailed account of experimental and theoretical investigations, available at the time of its publication (1954). 1 Zeitschrift ,.Fortschritte der Physik"Z. KOBA and S. TAKAGI With the remarkable improvement of experimental techniques in recent years, available data have been and are being steadily accumulated, and rapid progress is expected also in the field of theoretical investigations. It would be sensible, therefore, for us to write a critical report on our present knowledge and understanding concerning this problem, in order to orientate ourselves for further development.I n Part I the empirical information on extremely high energy nuclear phenomena will be described, and in Part I1 a survey of some of the existing theories and models will be given. I n Part 111, more recent developments will be discussed, including the foundations and interrelations of various theories, models proposed recently, general reconsideration of theories and models, and the limit of applicability of the current field theories.A typical example at present would be something like the following: Giant stacks, containing 1 -10 1 emulsion (for instance, 200 plates of 30 cm x 40 cm X 0.6 mm) are flown up by a ballcon to an altitude of 20 -30 km and exposed during 6 -8 hours.Events of 5 lo5 Gev can be studied by such an experiment.The Texas project in 1958 is expected t o fly 200 1 emulsion (1,000 plates of 60 cmx 80 cm x 0.6 mm) and t o supply us with data of 5 lo6 Gev events. An ideal case, barely possible with the present technique, would be, according to~OCCON1, several days exposure of 1 m3 emulsion, which would catch lo7 Gev events [ 5 ] .There are also attempts to make the emulsion stack stilllarger at the sacrifice of altitude, by making use of airplanes or simply putting it on the top of a mountain. 1'1.3. Estimation of the primary energy 1.3.1. We make the assumption: The velocity of secondary relativistic particles, vi, (i = 1,2, . . ., n,) in the c. m. s.~), and the velocity of the c. m. s. to the 1. s .~) , vc, are very close t o each other, i. e., ...

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Multiple Production of Particles and Hydrodynamical Aspect of Quantum Theory of Fields

Cited by 22 publications

References 5 publications

Hydrodynamics and Flow

Hydrodynamics and Flow

Calculation of the baryon diffusion constant in hot and dense hadronic matter based on an ultrarelativistic collision event generator

Theory of Multiple Particle Production at Extremely High Energy

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