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La température de Hagedorn, TH est, en physique théorique, la température à laquelle la matière hadronique (c'est-à-dire la matière ordinaire) n'est plus stable et doit soit « s'évaporer », soit se transformer matière à quarks (en). En tant que tel, elle peut être considérée comme le "point d'ébullition" de la matière hadronique. Elle a été découverte par Rolf Hagedorn (en).
La température de Hagedorn existe parce que la quantité d'énergie disponible est suffisamment élevée pour que les paires de particules de matière (quark–antiquark) puissent être spontanément extraites du vide. Ainsi, considéré naïvement, un système à la température du Hagedorn peut accueillir autant d'énergie qu'il peut y mettre, car les quarks formés offrent de nouveaux degrés de liberté, et la température du Hagedorn serait donc une chaleur absolue infranchissable. Cependant, si cette phase est plutôt considérée comme celle des quarks, il devient évident que la matière s'est transformée en matière à quarks (en), qui peut être chauffée davantage.
The Hagedorn temperature, TH, is about 150 MeV/kB or about 1,7 × 1012 K,[1] little above the mass–energy of the lightest hadrons, the pion.[2] 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 quark matter has been detected in heavy-ion collisions at SPS and LHC in CERN (France and Switzerland)[citation nécessaire] and at RHIC in Brookhaven National Laboratory (USA)[citation nécessaire].
In string theory, a separate Hagedorn temperature can be defined for strings rather than hadrons. This temperature is extremely high (1030 K) and thus of mainly theoretical interest.[3]
History[modifier | modifier le code]
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".[4][5]
Technical explanation[modifier | modifier le code]
Hagedorn temperature is the temperature TH above which the partition sum diverges in a system with exponential growth in the density of states.[4][6]
![{\displaystyle \lim _{T\rightarrow T_{\rm {H}}^{-}}\operatorname {Tr} \left[e^{-\beta H}\right]=\infty }](https://wikimedia.org/api/rest_v1/media/math/render/svg/a723e00b121aa8d98c5e7bb98f0f21043ad0e137)
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:
![{\displaystyle \lim _{T\rightarrow T_{\rm {H}}^{-}}E=\lim _{T\rightarrow T_{\rm {H}}^{-}}{\frac {\operatorname {Tr} \left[He^{-\beta H}\right]}{\operatorname {Tr} \left[e^{-\beta H}\right]}}=\infty }](https://wikimedia.org/api/rest_v1/media/math/render/svg/f584d8b8795a020031dbebaefd51892290705441)
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.
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[modifier | modifier le code]
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 scale by 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 string models place this in the magnitude of 1030 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[modifier | modifier le code]
References[modifier | modifier le code]
- « {{{1}}} »
- Edwin Cartlidge, « Quarks break free at two trillion degrees », Physics World, (consulté le )
- Joseph J. Atick et Edward Witten, « The Hagedorn transition and the number of degrees of freedom of string theory », Nuclear Physics B, vol. 310, no 2, , p. 291 (DOI 10.1016/0550-3213(88)90151-4, Bibcode 1988NuPhB.310..291A)
- Torleif Ericson et Johann Rafelski, « The tale of the Hagedorn temperature », CERN Courier, (consulté le )
- (en) Melting Hadrons, Boiling Quarks – From Hagedorn Temperature to Ultra-Relativistic Heavy-Ion Collisions at CERN, Cham, Springer International Publishing, (ISBN 978-3-319-17544-7, DOI 10.1007/978-3-319-17545-4, Bibcode 2016mhbq.book.....R)
- Peter Tyson, « Absolute Hot: Is There an Opposite to Absolute Zero? », NOVA, (consulté le )
Category:Nuclear physics Category:Statistical mechanics Category:String theory Category:Quantum chromodynamics Category:Quark matter Category:Threshold temperatures