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

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Kraków 2006 Oleg Utyuzh 2 High-Energy collisions

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Kraków 2006 Oleg Utyuzh 3 Quantum Correlations (QS) x1x1 x2x2 p1p1 p2p2 BE enhancement

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Kraków 2006 Oleg Utyuzh 4 Correlation function (1D) – source size x1x1 x2x2 p1p1 p2p2 R source size R.Hunbury Brown and Twiss, Nature 178 (1956) 1046 G.Goldhaber, S.Goldhaber, W.Lee and A.Pais, Phys.Rev 120 (1960) 300

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Kraków 2006 Oleg Utyuzh 5 Correlation function (1D) - chaoticity x1x1 x2x2 p1p1 p2p2chaoticity resonances final state interactions final state interactions flows particles misindification particles misindification momentum resolution momentum resolution......

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Kraków 2006 Oleg Utyuzh 6 W. Zajc, Phys. Rev. D35 (1987) 3396 N π -particle state

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Kraków 2006 Oleg Utyuzh 7 W. Zajc, Phys. Rev. D35 (1987) 3396 Metropolis algorithm speckles speckles Numerical symmetrization – (A) TIME !!!

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Kraków 2006 Oleg Utyuzh 8 J. Cramer, Univ. of Washigton preprint (1996 unpublished) J. Cramer, Univ. of Washigton preprint (1996 unpublished) Numerical symmetrization – (B) Monte-Carlo rejection clusters TIME !!!

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Kraków 2006 Oleg Utyuzh 9 H. Merlitz, D. Pelte, Z. Phys. A357 (1997) 175 Numerical symmetrization – (C) TIME !!! FactorizationFactorization

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Kraków 2006 Oleg Utyuzh 10 H. Merlitz, D. Pelte, Z. Phys. A357 (1997) 175 clusters Numerical symmetrization – (C)

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Kraków 2006 Oleg Utyuzh 11 Problem with numerical symmetrization … TIME !!! Existing ways out: replace modeling by simulations … (afterburners) Examples: shifting of momenta shifting of momentashifting of momentashifting of momenta weighting procedures weighting proceduresweighting proceduresweighting procedures Problems: changing of initial distributions – changing of physics changing of initial distributions – changing of physics example exampleexample O.V.Utyuzh, G.Wilk and Z.Wlodarczyk; Phys. Lett. B522 (2001) 273 and Acta Phys. Polon. B33 (2002) 2681.

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Kraków 2006 Oleg Utyuzh 12 Numerical symmetrization CLUSTERS SPECKLES STATESSTATESSTATESSTATES BUNCHES CLANS CELLS

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Kraków 2006 Oleg Utyuzh 13 EECs – A.D M. Biyajima, N. Suzuki, G. Wilk, Z. Wlodarczyk, Phys. Lett. B386 (1996) 297 Elementary Emitting Cells (EEC)

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Kraków 2006 Oleg Utyuzh 14

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Kraków 2006 Oleg Utyuzh 15 Maximalization of Information Entropy (MIE) phase space (1D) MIEMIE T. Osada, M. Maruyama and F. Takagi, Phys. Rev. D59 (1999)

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Kraków 2006 Oleg Utyuzh 16 MIE - Results

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Kraków 2006 Oleg Utyuzh 17 symmetrization * non-identical VS identical Boltzmann VS Bose-Einstein QuantumstatisticsQuantumstatistics GEOMETRICAL K.ZalewskiK.Zalewski, Nucl. Phys. B (Proc. Suppl. ) 74 (1999) 65

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Kraków 2006 Oleg Utyuzh 18 phase space (1D) * O. Utyuzh, G. Wilk, Z. Włodarczyk, Acta Phys. Hung. (Heavy Ion Physics) A25 (2006) 83 cell formation until first failure Quantum Clan model (1d-QCM) smearing particle energy in the cells EEC

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Kraków 2006 Oleg Utyuzh 19 Algorithm... cell formation until first failure

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Kraków 2006 Oleg Utyuzh 20 Quantum Clan model Hadronic Source Independent production Bose-Einstein Bose-Einstein Bose-Einstein O. Utyuzh, G. Wilk and Z. Włodarczyk, Acta Phys. Hung. A25 (2006) 83

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Kraków 2006 Oleg Utyuzh 21 Some results …

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Kraków 2006 Oleg Utyuzh 22 Results … ( first application to Simple Cascade Model) Simple Cascade ModelSimple Cascade Model Results … ( first application to Simple Cascade Model) Simple Cascade ModelSimple Cascade Model

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Kraków 2006 Oleg Utyuzh 23 MIE vs 1d-QCM phase space (1D) y-space E-space

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Kraków 2006 Oleg Utyuzh 24 What we are proposing … symmetrization

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Kraków 2006 Oleg Utyuzh 25 model (3D) p-Spacex-Space x· p-correlations x· p-correlations symetrization plane waves

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Kraków 2006 Oleg Utyuzh 26 WT T P0P0 σnσn / / / / / /3.29 W - dependence

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Kraków 2006 Oleg Utyuzh 27 T T P0P0 σnσn / / / / / /2.42 T - dependence

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Kraków 2006 Oleg Utyuzh 28 T T P0P0 σnσn / / / / / /2.26 P 0 - dependence

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Kraków 2006 Oleg Utyuzh 29 - dependence T T P0P0 σnσn / / / / / /2.29

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Kraków 2006 Oleg Utyuzh 30 How to model numerically COS(…) ?

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Kraków 2006 Oleg Utyuzh 31 2-ways of modeling of COS(…) …

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Kraków 2006 Oleg Utyuzh Pairs counting … pairs misidentification effect ???

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Kraków 2006 Oleg Utyuzh N -particles via 2-particles

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Kraków 2006 Oleg Utyuzh 34 True N -particles

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Kraków 2006 Oleg Utyuzh 35

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Kraków 2006 Oleg Utyuzh 36 s s Fractal source

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Kraków 2006 Oleg Utyuzh 37 Fractal source

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Kraków 2006 Oleg Utyuzh 38 BE statistics => cells ?... A. Kisiel et al., A. Kisiel et al., Comput. Phys. Commun. 174 (2006) 669

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Kraków 2006 Oleg Utyuzh 39 qq qq qq qq qq qq Possible further applications …

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Kraków 2006 Oleg Utyuzh 40 Summary

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Kraków 2006 Oleg Utyuzh 41 Problem of λ interpretations Problem of λ interpretations Problem of normalization of C 2 (Q) Problem of normalization of C 2 (Q) Single-particle Single-particle spectra modifications Instead of summary …

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Kraków 2006 Oleg Utyuzh 42 Back-Up Slides

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Kraków 2006 Oleg Utyuzh 43 If one insists on representing photons by wave packets and demands an explanation in those terms of the extra fluctuation, such an explanation can be given. But I shall have to use language which ought, as a rule, to be used warily. Think, then, of a stream of wave packets, each about c/ long, in a random sequence. There is a certain probability that two such trains accidentally overlap. When this occurs they interfere and one may find (to speak rather loosely) four photons, or none, or something in between as a result. It is proper to speak of interference in this situation because the conditions of the experiment are just such as will ensure that these photons are in the same quantum state. To such interference one may ascribe the abnormal density fluctuations in any assemblage of bosons. E. M. Purcell, Nature 178 (1956) Quantum Optics - particles bunchings …

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Kraków 2006 Oleg Utyuzh 44 Quantum Optics - particles bunchings … Bosons Fermions M. Henny et. al., Science 284 (1999) 296

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Kraków 2006 Oleg Utyuzh 45 Roy J. GlauberRoy J. Glauber, nucl-th/ Quantum Optics and Heavy Ion Physics

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Kraków 2006 Oleg Utyuzh 47 B.B. Back, et al. (PHOBOS Coll.), Nucl.Phys. A774 (2006)

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Kraków 2006 Oleg Utyuzh 48 J.D. Bjorken, Phys. Rev. D 27 (1983) 140

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Kraków 2006 Oleg Utyuzh 49 From these comparisons one can conclude that both MC models reproduce the data well while neither of them is particularly preferred. The perturbative parton shower, on which both MC models are based, seems to play an important role in the origin of the dynamical fluctuations and correlations in e+e annihilation. The observed differences between the two MC descriptions indicate that the last steps of the hadronization process are not described correctly [2]. Contributions from additional mechanisms to the observed fluctuations and cor-relations are not excluded. G.Abbiendi et al., (OPAL Coll.) Eur.Phys.J. C11 (1999)

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Kraków 2006 Oleg Utyuzh 52 J.A.Casado and S.Daté, Phys. Lett. B344 (1995) 441

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Kraków 2006 Oleg Utyuzh 53 Numerical symmetrization – (C)

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Kraków 2006 Oleg Utyuzh 54

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