Measuring the temperature

3. Measuringthetemperature • Thermometer (directcontact) • dilatation • air pressure • mechanicalorelectricstress • Chemistry (mixture) • color • massratios • hadroniccomposition • Spectra (telemetrics) • astronomy (photons) • pTspectra of light and heavyparticles • multiplicityfluctuations

4. Measuringthetemperature • Thermometer (directcontact) • dilatation • air pressure • mechanicalorelectricstress • Chemistry (mixture) • color • massratios • hadroniccomposition • Spectra (telemetrics) • astronomy (photons) • pTspectra of light and heavyparticles • multiplicityfluctuations

5. Interpretingthetemperature • Thermodynamics (universality of equilibrium) • zeroththeorem (Biro+Van PRE 2011) • derivative of entropy • Boyle-Mariottetypeequation of state • Kinetictheory (equipartition) • energy / degree of freedom • fluctuation - dissipation • otheraveragevalues • Spectralstatistics (abstract) • logarithmicslopeparameter • observedenergyscale • dispersion / power-laweffects

6. arXiV: 1111.4817 Unruh gamma radiationat RHIC ? Constant acceleration = temperature ? Soft bremsstrahlung interpolates between high k_T exponential and low k_T 1 / square Why do thermal models work? Aretherealternatives? T.S.Biró¹, M.Gyulassy², Z. Schram³ ¹ MTA KFKI RMKI ² Columbia University ³University of Debrecen Zimányi School 2011, Dec. 1. 2011, KFKI RMKI Budapest, HU.EU

7. Tsallis quark matter + transverse flow + quark coalescence fits to hadron spectra with Károly Ürmössy RHIC data SQM 2008, Beijing

8. Tsallis quark matter + transverse flow + quark coalescence fits to hadron spectra with Károly Ürmössy RHIC data SQM 2008, Beijing

9. Blast wave fits and quark coalescence with Károly Ürmössy arXiV: 1011.3442 SQM 2008, Beijing

10. All particle types follow power-law with Károly Ürmössy B E T T E R ! E G O O D L(E)

11. Power-law tailed spectra • particles and heavyions: (SPS) RHIC, LHC • fluctuationsinfinancialreturns • naturalcatastrophes (earthquakes, etc.) • fractalphasespacefilling • preferentialconnectioninnetworks • turbulence, criticalbehavior • nearBosecondensates • citation of scientificpapers….

12. Whydostatisticswork ? • Independentobservation over 100M events • Universallawsforlargenumbers • Steadynoiseinenvironment: ‚reservoir’ • Phasespacedominance • Bychancethedynamicsmimicsthermalbehavior

13. Experimentalmotivation RHIC: PHENIX

14. Theoreticalmotivation • Decelerationduetostopping • Schwingerformula + Newton + Unruh = Boltzmann Satz, Kharzeev, …

15. Arxiv: 1111.4817

16. WhyPhotons (gammas) ? • Zeromass: flow – Doppler, easykinematics • Colorneutral: escapesstronginteraction • Couplestocharge: Z / A sensitive • Classicalfieldtheoryalsopredictsspectra

17. Soft bremsstrahlung • Jackson formula for the amplitude: With , and the retarded phase

18. Soft bremsstrahlung • Covariant notation: IR div, coherenteffects Feynmangraphs The Unruheffectcannot be calculatedbyanyfinitenumber of Feynmangraphs!

19. Kinematics, source trajectory • Rapidity: Trajectory: Let us denote by in the followings!

20. Kinematics, photon rapidity • Angle and rapidity:

21. Kinematics, photon rapidity • Doppler factor: Phase: Magnitude of projected velocity:

22. Intensity, photon number Amplitude as an integral over rapidities on the trajectory: Here is a characteristic length.

23. Intensity, photon number Amplitude as an integral over infinite rapidities on the trajectory (velocity goes from –c to +c): With K1 Bessel function! Flatinrapidity !

24. Photon spectrum, limits Amplitude as an integral over infinite rapidities on the trajectory (velocity goes from –c to +c): for for

25. Photonspectrumfrom pp backgroound, PHENIX experiment

26. Apparent temperature • High - infinite proper time acceleration: Connection to Unruh: proper time Fourier analysis of a monochromatic wave

27. Unruh temperature • Entirely classical effect • Special Relativity suffices Unruh Constant ‚g’ acceleration in a comoving system: dv/d = -g(1-v²) Max Planck

28. Unruh temperature Planck-interpretation: The temperature in Planck units: The temperature more commonly:

29. Unruh temperature On Earth’ surface ist is 10^(-19) eV, while at room temperature about 10^(-3) eV.

30. Unruh temperature Braking from +c to-cin a Compton wavelength: kT ~ 150 MeV if mc² ~ 940 MeV (proton)

31. Bekenstein-Hawking entropy • Unruh temperature at the event horizon • Clausius: 1 / T is an integrating factor Hawking Bekenstein

32. Connection to Unruh Fourier component for the retarded phase:

33. Connection to Unruh Fourier component for the projected acceleration: Photon spectrum in the incoherent approximation:

34. Connection to Unruh Fourier component for the retarded phase at constant acceleration: KMS relation and Planck distribution:

35. Connection to Unruh KMS relation and Planck distribution:

36. Connection to Unruh Note: It is peaked around k = 0, but relatively wide! (an unparticle…)

37. Bessel-K compendium 1. 2. 3. 3  1 : expand Dirac delta as Fourier integral, 3  2 : rewrite integral over difference and the sum bx = x1 + x2

38. Transverse flow interpretation Mathematica knows: ( I derived it using Feynman variables) Alike Jüttner distributions integrated over the flow rapidity…

39. Finite time (rapidity) effects = with Short-timedeceleration Non-uniform rapiditydistribution;  Landauhydrodynamics Long-timedeceleration uniform rapiditydistribution;  Bjorkenhydrodynamics

40. Short time constant acceleration Non-uniform rapidity distribution;  Landau hydrodynamics

41. The reverse problem • Photon spectrum  amplitude • Amplitude  Fourier component • Phase  velocity • Velocity  rapidity • Rapidity  acceleration • Acceleration  Path in t -- x

42. Analytic results x(t), v(t), g(t), τ(t), 𝒜, dN/kdkd limit

49. LargepT: NLO QCD SmallerpT: plus directgammas

50. Glauber model