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Numerical modelling of BEC *

Numerical modelling of BEC *. Oleg Utyuzh. The Andrzej Sołtan Institute for Nuclear Studies (SINS) , Warsaw, Poland. * In collaboration with G.Wilk and Z.Wlodarczyk. High-Energy collisions. Quantum Correlations (QS). p 1. BE enhancement. x 1. x 2. p 2. p 2. x 2. R source size.

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Numerical modelling of BEC *

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  1. Numerical modelling of BEC* Oleg Utyuzh The Andrzej Sołtan Institute for Nuclear Studies (SINS), Warsaw, Poland * In collaboration with G.Wilk and Z.Wlodarczyk

  2. High-Energy collisions

  3. Quantum Correlations (QS) p1 BE enhancement x1 x2 p2

  4. p2 x2 R source size x1 p1 Correlationfunction (1D) – sourcesize R.Hunbury Brown and Twiss, Nature178 (1956) 1046 G.Goldhaber, S.Goldhaber, W.Lee and A.Pais, Phys.Rev120 (1960) 300

  5. resonances • finalstateinteractions • flows • particlesmisindification • momentum resolution • ... p2 x2 x1 p1 Correlationfunction (1D) - chaoticity chaoticity

  6. W. Zajc, Phys. Rev.D35 (1987) 3396 Nπ-particle state

  7. W. Zajc, Phys. Rev.D35 (1987) 3396 speckles speckles Metropolis algorithm TIME !!! Numerical symmetrization – (A)

  8. J. Cramer, Univ. of Washigton preprint (1996 unpublished) TIME !!! Monte-Carlo rejection clusters Numerical symmetrization – (B)

  9. TIME !!! Factorization H. Merlitz, D. Pelte, Z. Phys. A357 (1997) 175 Numerical symmetrization – (C)

  10. clusters H. Merlitz, D. Pelte, Z. Phys. A357 (1997) 175 Numerical symmetrization – (C)

  11. TIME !!! Problem with numerical symmetrization … replace modeling by simulations … (afterburners) Existing ways out: Examples: • shifting of momenta • weighting procedures Problems: • changing of initial distributions – changing of physics • example O.V.Utyuzh, G.Wilk and Z.Wlodarczyk; Phys. Lett. B522 (2001) 273 and Acta Phys. Polon. B33 (2002) 2681.

  12. STATES CELLS SPECKLES CLUSTERS BUNCHES CLANS Numerical symmetrization

  13. EEC’s – A.D. 1996 M. Biyajima, N. Suzuki, G. Wilk, Z. Wlodarczyk, Phys. Lett. B386 (1996) 297 Elementary Emitting Cells (EEC)

  14. T. Osada, M. Maruyama and F. Takagi, Phys. Rev.D59 (1999) 014024 phasespace (1D) Maximalization of Information Entropy (MIE) MIE

  15. MIE - Results

  16. K.Zalewski, Nucl. Phys. B(Proc. Suppl. ) 74 (1999) 65 non-identicalVSidenticalBoltzmannVSBose-Einstein Quantum statistics GEOMETRICAL symmetrization*

  17. cellformation untilfirst failure phasespace (1D) EEC smearing particleenergy inthecells Quantum Clan model (1d-QCM) *O. Utyuzh, G. Wilk, Z. Włodarczyk, Acta Phys. Hung. (Heavy Ion Physics) A25 (2006) 83

  18. Algorithm ... cellformation untilfirst failure

  19. O. Utyuzh, G.Wilk and Z. Włodarczyk, Acta Phys. Hung.A25 (2006) 83 Quantum Clan model Bose-Einstein Hadronic Source Independent production Bose-Einstein Bose-Einstein

  20. Some results …

  21. Results … (first application to Simple Cascade Model)

  22. phasespace (1D) y-space phasespace (1D) E-space MIE vs 1d-QCM

  23. What we are proposing … symmetrization 2 1 4 3 5

  24. model (3D) p-Space x-Space symetrization plane waves x·p-correlations

  25. W - dependence

  26. T - dependence

  27. P0 - dependence

  28.  - dependence

  29. How to model numerically COS(…) ?

  30. 2-ways of modeling of COS(…) …

  31. Pairs counting … 2 1 4 3 5 pairs misidentification effect ???

  32. N -particles via 2-particles 2 2 1 1 4 4 6 6 3 3 5 5

  33. True N -particles

  34. Fractal source s s

  35. Fractal source

  36. A. Kisiel et al., Comput. Phys. Commun.174 (2006) 669 BE statistics => cells ?...

  37. Possible further applications … q q q q q q q q q q q q

  38. Summary

  39. Instead of summary … • Problemofλinterpretations • Problem of normalization ofC2(Q) • Single-particle spectra modifications

  40. Back-Up Slides

  41. Quantum Optics - particles bunchings … ‘If one insists on representing photons by wave packets and demands an explanationin those terms of the extra fluctuation, such an explanation can begiven. But I shall have to use language which ought, as a rule, to be usedwarily. Think, then, of a stream of wave packets, each about c/ long, ina random sequence. There is a certain probability that two such trains accidentallyoverlap. When this occurs they interfere and one may find (to speakrather loosely) four photons, or none, or something in between as a result. Itis proper to speak of interference in this situation because the conditions ofthe experiment are just such as will ensure that these photons are in the samequantum state. To such interference one may ascribe the “abnormal” densityfluctuations in any assemblage of bosons’. E. M. Purcell, Nature178 (1956) 1449-1450

  42. Bosons Fermions M. Henny et. al. , Science 284 (1999) 296 Quantum Optics - particles bunchings …

  43. Roy J. Glauber, nucl-th/0604021 Quantum Optics and Heavy Ion Physics

  44. B.B. Back, et al.(PHOBOS Coll.), Nucl.Phys. A774 (2006) 631-634 B.B. Back, et al.(PHOBOS Coll.), Nucl.Phys. A774 (2006) 631-634

  45. J.D. Bjorken, Phys. Rev.D 27 (1983) 140

  46. G.Abbiendi et al., (OPAL Coll.) Eur.Phys.J.C11 (1999) 239-250 “ From these comparisons one can conclude that both MC models reproduce the data wellwhile neither of them is particularly preferred. The perturbative parton shower, on whichboth MC models are based, seems to play an important role in the origin of the dynamicalfluctuations and correlations in e+e− annihilation. The observed differences between the twoMC descriptions indicate that the last steps of the hadronization process are not describedcorrectly [2]. Contributions from additional mechanisms to the observed fluctuations and cor-relations are not excluded. “

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