Bleicher at 08:03, 10 May 2021

2021-05-10T08:03:51Z

Tomasik: Created page with "Statistical model is very successful in describing the production of particles."

2018-10-29T21:44:34Z

Created page with "Statistical model is very successful in describing the production of particles."

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Statistical model is very successful in describing the production of particles.

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−	~~Statistical~~ model is very ~~successful~~ in ~~describing~~ the ~~production~~ of ~~particles~~.	+	{{short description\|Temperature at which the partition function of a statistical-mechanical system diverges}}
		+	The '''Hagedorn temperature,''' ''T''<sub>H</sub>, is the temperature in [[theoretical physics]] where [[hadron]]ic matter (i.e. ordinary matter) is no longer stable, and must either "evaporate" or convert into [[quark matter]]; as such, it can be thought of as the "boiling point" of hadronic matter. The Hagedorn temperature exists because the amount of energy available is high enough that matter particle ([[quark]]–[[antiquark]]) pairs can be spontaneously pulled from vacuum. Thus, naively considered, a system at Hagedorn temperature can accommodate as much energy as one can put in, because the formed quarks provide new degrees of freedom, and thus the Hagedorn temperature would be an impassable [[absolute hot]]. However, if this phase is viewed as quarks instead, it becomes apparent that the matter has transformed into [[quark matter]], which can be further heated.
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		+	The Hagedorn temperature, ''T''<sub>H,</sub> is about {{val\|150\|u=MeV}} or about {{val\|1.7\|e=12\|u=K}},<ref>{{Citation\|last=Gaździcki\|first=Marek\|title=Hagedorn's Hadron Mass Spectrum and the Onset of Deconfinement\|date=2016\|work=Melting Hadrons, Boiling Quarks – From Hagedorn Temperature to Ultra-Relativistic Heavy-Ion Collisions at CERN\|pages=87–92\|editor-last=Rafelski\|editor-first=Johann\|publisher=Springer International Publishing\|language=en\|doi=10.1007/978-3-319-17545-4_11\|isbn=978-3-319-17544-7\|last2=Gorenstein\|first2=Mark I.\|editor-link=Johann Rafelski\|doi-access=free}}</ref> the same as the mass–energy of the lightest hadrons, the [[pion]].<ref name="iop">{{cite web \|last=Cartlidge \|first=Edwin \|title=Quarks break free at two trillion degrees \|url=http://physicsworld.com/cws/article/news/2011/jun/23/quarks-break-free-at-two-trillion-degrees \|work=[[Physics World]] \|access-date=27 January 2014 \|date=23 June 2011 }}</ref> Matter at Hagedorn temperature or above will spew out fireballs of new particles, which can again produce new fireballs, and the ejected particles can then be detected by particle detectors. This [[QCD matter\|quark matter]] has been detected in heavy-ion collisions at [[Super Proton Synchrotron\|SPS]] and [[Large Hadron Collider\|LHC]] in [[CERN]] (France and Switzerland) and at [[Relativistic Heavy Ion Collider\|RHIC]] in [[Brookhaven National Laboratory]] (USA).
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		+	In string theory, a separate Hagedorn temperature can be defined for strings rather than hadrons. This temperature is extremely high (10<sup>30</sup> K) and thus of mainly theoretical interest.<ref name="NPB">{{cite journal \|last=Atick \|first=Joseph J. \|last2=Witten \|first2=Edward \|year=1988 \|title=The Hagedorn transition and the number of degrees of freedom of string theory \|journal=[[Nuclear Physics B]] \|volume=310 \|issue=2 \|pages=291 \|bibcode=1988NuPhB.310..291A \|doi=10.1016/0550-3213(88)90151-4 }}</ref>
		+
		+	== History ==
		+	The Hagedorn temperature was discovered by German physicist [[Rolf Hagedorn]] in the 1960s while working at CERN. His work on the [[statistical bootstrap model]] of hadron production showed that because increases in energy in a system will cause new particles to be produced, an increase of collision energy will increase the entropy of the system rather than the temperature, and "the temperature becomes stuck at a limiting value".<ref name="tale" /><ref>{{Cite book\|title=Melting Hadrons, Boiling Quarks – From Hagedorn Temperature to Ultra-Relativistic Heavy-Ion Collisions at CERN\|date=2016\|publisher=Springer International Publishing\|isbn=978-3-319-17544-7\|editor-last=Rafelski\|editor-first=Johann\|location=Cham\|language=en\|doi=10.1007/978-3-319-17545-4}}</ref>
		+
		+	== Technical explanation ==
		+	Hagedorn temperature is the temperature above which the [[partition sum]] diverges in a system with exponential growth in the density of states.<ref name="tale">{{cite web \|last=Ericson \|first=Torleif \|last2=Rafelski \|first2=Johann \|date=4 September 2003 \|title=The tale of the Hagedorn temperature \|url=http://cerncourier.com/cws/article/cern/28919 \|work=[[CERN Courier]] \|access-date=2016-12-09 }}</ref><ref>{{cite web \|last=Tyson \|first=Peter \|date=December 2007 \|title=Absolute Hot: Is There an Opposite to Absolute Zero? \|url=https://www.pbs.org/wgbh/nova/zero/hot.html \|work=[[Nova (American TV program)\|NOVA]] \|access-date=2008-12-21 }}</ref>
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		+	:<math>\lim_{T\rightarrow T_H^-} \operatorname{Tr}\left[e^{-\beta H}\right] = \infty</math>
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		+	Because of the divergence, people may come to the incorrect conclusion that it is impossible to have temperatures above the Hagedorn temperature, which would make it the [[absolute hot]] temperature, because it would require an infinite amount of [[energy]]. In equations:
		+
		+	:<math>\lim_{T\rightarrow T_H^-}E = \lim_{T\rightarrow T_H^-}\frac{\operatorname{Tr}\left[H e^{-\beta H}\right]}{\operatorname{Tr}\left[e^{-\beta H}\right]} = \infty</math>
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		+	This line of reasoning was well known to be false even to Hagedorn. The partition function for creation of hydrogen–antihydrogen pairs diverges even more rapidly, because it gets a finite contribution from energy levels that accumulate at the ionization energy. The states that cause the divergence are spatially big, since the electrons are very far from the protons. The divergence indicates that at a low temperature hydrogen–antihydrogen will not be produced, rather proton/antiproton and electron/antielectron. The Hagedorn temperature is only a maximum temperature in the physically unrealistic case of exponentially many species with energy E and finite size.
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		+	The concept of exponential growth in the number of states was originally proposed in the context of [[condensed matter physics]]. It was incorporated into high-energy physics in the early 1970s by [[Steven Frautschi]] and Hagedorn. In hadronic physics, the Hagedorn temperature is the deconfinement temperature.
		+
		+	== In string theory ==
		+	In [[string theory]], it indicates a phase transition: the transition at which very long strings are copiously produced. It is controlled by the size of the string tension, which is smaller than the [[Planck energy\|Planck scale]] by the some power of the coupling constant. By adjusting the tension to be small compared to the Planck scale, the Hagedorn transition can be much less than the [[Planck temperature]]. Traditional [[Grand Unified Theory\|grand unified]] string models place this in the magnitude of {{val\|e=30\|u=[[kelvin]]}}, two orders of magnitude smaller than the Planck temperature. Such temperatures have not been reached in any experiment and are far beyond the reach of current, or even foreseeable technology.
		+
		+	==See also==
		+	* [[Heat]]
		+	* [[Absolute hot]]
		+	* [[Thermodynamic temperature]]
		+	* [[Non-extensive self-consistent thermodynamical theory]]
		+
		+	==References==
		+	{{reflist}}
		+
		+	[[Category:Particle physics]]
		+	[[Category:Nuclear physics]]
		+	[[Category:Statistical mechanics]]
		+	[[Category:String theory]]
		+	[[Category:Quantum chromodynamics]]
		+	[[Category:Quark matter]]

Statistical model - Revision history

Bleicher at 08:03, 10 May 2021

Tomasik: Created page with "Statistical model is very successful in describing the production of particles."