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A new approach of chaos and complex network method to study fluctuation and phase transition in nuclear collision at high energy

  • Regular Article - Experimental Physics
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Abstract.

In the endeavour to study fluctuation and a signature of phase transition in ultrarelativistic nuclear collision during the process of particle production, an approach based on chaos and complex network is proposed. In this work we have attempted an exhaustive study of pion fluctuation in \(\eta\) space, \(\phi\) space, their cross-correlation and finally two-dimensional fluctuation in terms of scaling of void probability distribution. The analysis is done on the \(\eta\) values and their corresponding \( \phi\) values extracted from the 32S-Ag/Br interaction at an incident energy of 200GeV per nucleon. The methods used are Multifractal Detrended Cross-Correlation Analysis (MF-DXA) and a chaos-based rigorous complex network method --Visibility Graph. The analysis reveals that the highest degree of cross-correlation between pseudorapidity and azimuthal angles exists in the most central region of the interaction. The analysis further shows that two-dimensional void distribution corresponding to the \(\eta\) - \(\phi\) space reveals a strong scaling behaviour. Both cross-correlation coefficients of MF-DXA and PSVG (Power of the Scale-freeness in Visibility Graph, which is implicitly connected with the Hurst exponent) can be effectively used for the quantitative assessment of pion fluctuation in a very precise manner and have the capability to assess the tendency of approaching criticality for phase transitions.

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References

  1. A. Bialas, B. Ziaja, Phys. Lett. B 378, 319 (1996)

    Article  ADS  Google Scholar 

  2. W. Kittel, E.A. De Wolf, Soft Multihadron Dynamics (World Scientific, 2005)

  3. E. De Wolf, I. Dremin, W. Kittel, Phys. Rep. 270, 1 (1996)

    Article  ADS  Google Scholar 

  4. D. Ghosh, A. Deb, S. Bhattacharyya, J.G.R. Das, S. Mukherjee, Int. J. Mod. Phys. E 12, 407 (2003)

    Article  ADS  Google Scholar 

  5. S. Sarkar, T. Goswami, D. Ghosh, A. Deb, Czechoslov. J. Phys. 53, 133 (2003)

    Article  ADS  Google Scholar 

  6. D. Ghosh, P. Ghosh, A. Ghosh, J. Roy, Phys. Rev. C 49, R1747 (1994)

    Article  ADS  Google Scholar 

  7. A.D. Dipak Ghosh, M.L.A. Dey, S.A. Hossain, S. Das, S. Sen, S. Halder, J. Roy, Phys. Rev. D 49, 3113 (1994)

    Article  ADS  Google Scholar 

  8. D. Ghosh, P. Ghosh, A. Ghosh, J. Roy, J. Phys. G: Nucl. Part. Phys. 20, 1077 (1994)

    Article  ADS  Google Scholar 

  9. A.K.J. Dipak Ghosh, A. Deb, S. Sarkar, R. Chattopadhyay, S. Das, Phys. Rev. C 59, 2286 (1999)

    Article  ADS  Google Scholar 

  10. P.L. Jain, G. Singh, Nucl. Phys. A 596, 700 (1996)

    Article  ADS  Google Scholar 

  11. R.P.A. Bialas, Nucl. Phys. B 273, 703 (1986)

    Article  ADS  Google Scholar 

  12. R. Hwa, Q.h. Zhang, Phys. Rev. C 62, 054902 (2000)

    Article  ADS  Google Scholar 

  13. R. Hwa, Phys. Rev. D 41, 1456 (1990)

    Article  ADS  Google Scholar 

  14. G. Paladin, A. Vulpiani, Phys. Rep. 156, 147 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  15. I.P.P. Grassberger, Physica D 13, 34 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  16. M.J.T.C. Halsey, L. Kadanoff, I. Procaccia, B. Shriman, Phys. Rev. A 33, 1141 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  17. F. Takagi, Phys. Rev. Lett. 72, 32 (1994)

    Article  ADS  Google Scholar 

  18. D. Ghosh, A. Mukhopadhyay, A. Ghosh, J. Roy, Mod. Phys. Lett. A 04, 1197 (1989)

    Article  ADS  Google Scholar 

  19. D. Ghosh, M. Lahiri, A. Deb, S. Das, K. Purkait, B. Biswas, J. Roychoudhury, R. Chatterjee, A.K. Zafri, Phys. Rev. C 52, 2092 (1995)

    Article  ADS  Google Scholar 

  20. A.D. Dipak Ghosh, M. Mondal, J. Ghosh, Phys. Rev. 68, 024908 (2003)

    Google Scholar 

  21. P.G. Dipak Ghosh, A. Deb, D. Halder, S. Das, A. Hossain, A. Dey, J. Roy, Phys. Rev. 46, 3712 (1992)

    Google Scholar 

  22. S.S. Dipak Ghosh, J. Roy, Phys. Rev. D 47, 1235 (1993)

    Article  ADS  Google Scholar 

  23. D. Ghosh, A. Deb, S.R. Sahoo, P.K. Haldar, Europhys. Lett. 56, 639 (2001)

    Article  ADS  Google Scholar 

  24. D. Ghosh, A. Deb, M. Mondal, J. Ghosh, Phys. Lett. B 540, 52 (2002)

    Article  ADS  Google Scholar 

  25. D. Ghosh, A. Deb, M. Mondal, J. Ghosh, J. Phys. G: Nucl. Part. Phys. 29, 2087 (2003)

    Article  ADS  Google Scholar 

  26. A.D. Dipak Ghosh, P. Bandyopadhyay, M. Mondal, S. Bhattacharyya, J. Ghosh, K.K. Patra, Phys. Rev. C 65, 067902 (2002)

    Article  ADS  Google Scholar 

  27. D. Ghosh, A. Deb, M. Mondal, J. Ghosh, J. Phys. G: Nucl. Part. Phys. 29, 2087 (2003)

    Article  ADS  Google Scholar 

  28. A.D. Dipak Ghosh, S. Bhattacharyya, U. Datta, J. Phys. G: Nucl. Part. Phys. 39, 035101 (2012)

    Article  ADS  Google Scholar 

  29. S.B.C.K. Peng, S. Havlin, M. Simons, H. Stanley, A. Goldberger, Phys. Rev. E 49, 1685 (1994)

    Article  ADS  Google Scholar 

  30. W.W.M.S. Taqqu, V. Teverovsky, Fractals 3, 785 (1995)

    Article  Google Scholar 

  31. P.I.Z. Chen, K. Hu, H. Stanley, Phys. Rev. E 65, 041107 (2002)

    Article  ADS  Google Scholar 

  32. J.W. Kantelhardt, S.A. Zschiegner, E. Koscielny-Bunde, A. Bunde, S. Havlin, H.E. Stanley, Physica A 02, 01383 (2002)

    Google Scholar 

  33. B. Podobnik, H.E. Stanley, Phys. Rev. Lett. 100, 084102 (2008)

    Article  ADS  Google Scholar 

  34. J.W. Kantelhardta, E. Koscielny-Bundea, H.H.A. Rego, S. Havlinb, A. Bundea, Physica A 295, 441 (2001)

    Article  ADS  Google Scholar 

  35. F. Wang, G.p. Liao, X.y. Zhou, W. Shi, Nonlinear Dyn. 72, 353 (2013)

    Article  Google Scholar 

  36. S. Dutta, D. Ghosh, S. Samanta, Physica A: Stat. Mech. Appl. 413, 195 (2014)

    Article  ADS  Google Scholar 

  37. S. Bhaduri, D. Ghosh, Curr. Sci. 110, 1817 (2016)

    Article  Google Scholar 

  38. S. Bhaduri, R. Das, D. Ghosh, J. Neurol. Neurosci. 7, 1 (2016)

    Google Scholar 

  39. S. Dutta, J. Stat. Mech. Theory Exp. 2010, P12021 (2010)

    Article  Google Scholar 

  40. S.C.S. Dutta, D. Ghosh, Front. Physiol. 4, 274 (2013)

    Article  Google Scholar 

  41. D. Ghosh, S. Dutta, S. Chakraborty, Chaos Solit. Fractals 67, 1 (2014)

    Article  ADS  Google Scholar 

  42. Y. Zhang, W. Qian, C. Yang, Int. J. Mod. Phys. A 23, 2809 (2008)

    Article  ADS  Google Scholar 

  43. C. Albajar, O.C. Allkofer, R.J. Apsimon, R. Apsimon, S. Bartha, A. Bezaguet, A. Boehrer, B. Buschbeck, P. Cennini, S. Cittolin et al., Z. Phys. C 56, 37 (1992)

    Article  ADS  Google Scholar 

  44. M.K. Suleymanov, M. Sumbera, I. Zborovsky, arXiv:hep-ph/0304206v1 (2003)

  45. E.G. Ferreiro, C. Pajares, Phys. Rev. C 86, 034903 (2012)

    Article  ADS  Google Scholar 

  46. A.D. Dipak Ghosh, M. Lahiri, Phys. Rev. D 51, 3298 (1995)

    Article  ADS  Google Scholar 

  47. D. Ghosh, A. Deb, S. Pal, P.K. Haldar, S. Bhattacharyya, P. Mandal, S. Biswas, M. Mondal, Fractals 13, 04 (2005)

    Article  Google Scholar 

  48. S. Dutta, D. Ghosh, S. Chatterjee, Int. J. Mod. Phys. A 29, 1450084 (2014)

    Article  ADS  Google Scholar 

  49. S.S.P. Mali, S. Ghosh, A. Mukhopadhyay, G. Singh, Phys. A 424, 25 (2015)

    Article  Google Scholar 

  50. L. Lacasa, B. Luque, F. Ballesteros, J. Luque, J.C. Nuno, Proc. Natl. Acad. Sci. USA 105, 4972 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  51. L. Lacasa, B. Luque, J. Luque, J.C. Nuno, EPL 86, 30001 (2009)

    Article  ADS  Google Scholar 

  52. S. Jiang, C. Bian, X. Ning, Q.D.Y. Ma, Appl. Phys. Lett. 102, 253 (2013)

    Google Scholar 

  53. S. Bhaduri, D. Ghosh, Clin. EEG Neurosci. 46, 218 (2015)

    Article  Google Scholar 

  54. A. Bhaduri, D. Ghosh, Front. Physiol. 7, 44 (2016)

    Article  Google Scholar 

  55. P. Nilanjana, B. Anirban, B. Susmita, G. Dipak, Transl. Biomed. 7, 79 (2016)

    Google Scholar 

  56. S. Bhaduri, A. Chakraborty, D. Ghosh, J. Neurol. Neurosci. 7, 100 (2016)

    Google Scholar 

  57. G.F. Zebende, M.V.S. Da Silva, A.C.P. Rosa, A.S. Alves, J.C.O. De Jesus, M.A. Moret, Physica A: Stat. Mech. Appl. 342, 322 (2004)

    Article  ADS  Google Scholar 

  58. L. Zhao, W. Li, C. Yang, J. Han, Z. Su, Y. Zou, X. Cai, arXiv:1601.07715 (2016)

  59. S. Bhaduri, D. Ghosh, Int. J. Mod. Phys. A 31, 1650185 (2016)

    Article  ADS  Google Scholar 

  60. S. Bhaduri, D. Ghosh, Acta Phys. Pol. B 48, 741 (2017)

    Article  ADS  Google Scholar 

  61. N.S. Amelin, E.F. Staubo, L.P. Csernai, V.D. Toneev, K.K. Gudima, D. Strottman, Phys. Rev. Lett. 67, 1523 (1991)

    Article  ADS  Google Scholar 

  62. J.Y. Ollitrault, Phys. Rev. D 46, 229 (1992)

    Article  ADS  Google Scholar 

  63. S. Mrówczyński, Phys. Lett. B 314, 118 (1993)

    Article  ADS  Google Scholar 

  64. S. Bhaduri, D. Ghosh, Adv. High Energy Phys. 2016, 1 (2016)

    Article  Google Scholar 

  65. S. Bhaduri, D. Ghosh, Mod. Phys. Lett. A 31, 1650158 (2016)

    Article  ADS  Google Scholar 

  66. A. Bhaduri, S. Bhaduri, D. Ghosh, in preparation

  67. D. Hofstadter, New Soc. 54, 431 (1980)

    Google Scholar 

  68. M.A. Stern, J. Reine Angew. Math. 55, 193 (1858)

    Article  MathSciNet  Google Scholar 

  69. M. Schroeder, K. Wiesenfeld, Phys. Today 44, 91 (1991)

    Article  Google Scholar 

  70. J.M. Hausdorff, P.L. Purdon, C.K. Peng, Z. Ladin, J.Y. Wei, A.L. Goldberger, J. Appl. Physiol. 80, 1448 (1996)

    Google Scholar 

  71. A.L. Goldberger, L.A.N. Amaral, J.M. Hausdorff, P.C. Ivanov, C.K. Peng, H.E. Stanley, Proc. Natl. Acad. Sci. USA 99, 2466 (2002)

    Article  ADS  Google Scholar 

  72. M. Ahmadlou, H. Adeli, A. Adeli, J. Neural Transm. 117, 1099 (2010)

    Article  Google Scholar 

  73. A. Clauset, C.R. Shalizi, M.E.J. Newman, SIAM Rev. 51, 661 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  74. D. Ghosh, A. Deb, S. Bhattacharyya, U. Datta, Pramana J. Phys. 77, 297 (2011)

    Article  ADS  Google Scholar 

  75. Carroll F. Powell, Peter H. Fowler, Donald Hill Perkins, The Study of Elementary Particles by the Photographic Method: An Account of the Principal Techniques and Discoveries, Illustrated by an Atlas of Photomicrographs, (Pergamon Press, Oxford, 1959)

  76. D. Ghosh, A. Deb, J. Ghosh, R. Chattopadhyay, A. Kayum Jafri, M. Azizar Rahman, Sharmila Roy (Sarkar), Astroparticle Physics 15, 329 (2001)

    Article  ADS  Google Scholar 

  77. D. Ghosh, A. Deb, S. Bhattacharyya, U. Datta, Phys. Scripta 85, 065205 (2012)

    Article  ADS  Google Scholar 

  78. K. Pearson, Philos. Mag. Ser. 50, 157 (1900)

    Article  Google Scholar 

  79. R.L. Plackett, Int. Stat. Rev. 51, 59 (1983)

    Article  Google Scholar 

  80. N. Agababyan, M. Atayan, M. Charlet, J. Czyewski, E. De Wolf, K. Dziunikowska, A. Endler, Z. Garutchava, H. Gulkanyan, R. Hakobyan et al., Phys. Lett. B 382, 305 (1996)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Deepa Ghosh Research Foundation, 60/7/1 Maharaja Tagore Road, Kolkata, India

    Susmita Bhaduri, Anirban Bhaduri & Dipak Ghosh

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  1. Susmita Bhaduri
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  2. Anirban Bhaduri
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Correspondence to Susmita Bhaduri.

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Communicated by P. Salabura

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Bhaduri, S., Bhaduri, A. & Ghosh, D. A new approach of chaos and complex network method to study fluctuation and phase transition in nuclear collision at high energy. Eur. Phys. J. A 53, 135 (2017). https://doi.org/10.1140/epja/i2017-12332-4

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