Maps of zeros of the grand canonical partition function in a statistical model of high energy collisions

Brambilla, Michele; Giovannini, Alberto; Ugoccioni, R.

doi:10.1088/0954-3899/32/6/009

Cited by 4 publications

(6 citation statements)

References 9 publications

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“…At this point, we would also like to bring into attention the difference between our result and an earlier study conducted by Brooks et al [13] and Giovannini et al [14], namely that GMD's Lee-Yang zeros exhibit both left-right symmetry as well as top-bottom symmetry. This feature distinguishes the zeros from GMD and those from NBD, as NBD's Lee-yang circle exhibits only top-bottom symmetry, i.e.…”

Section: Resultscontrasting

confidence: 61%

“…In particular, by truncating (4) and set it to zero, one can always find a set of complex solutions which, upon plotting, will form a circle in the complex plane as studied by Lee and Yang [11,12]. This has further been studied by Brooks et al [13] and Brambilla et al [14] for the case of Poisson distribution and NBD. Next we consider…”

Section: Formalism and Derivation Of Generalized Multiplicity Distribmentioning

confidence: 95%

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Lee-Yang circle analysis of e + e − and $p\overline{p}$ generalized multiplicity distribution

Dewanto¹,

Chan²,

Oh³

et al. 2008

Eur. Phys. J. C

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We study the evolution of Lee-Yang zeros structure of generalized multiplicity distribution (GMD) in high energy collision. Starting our study with electron-positron e + e − scattering data, we extend the study by Chan and Chew (Z. Phys. C 55:503, 1992) on TASSO and AMY multiplicity data for √ s = 14, 22, 34.8, 43.6 and 57 GeV to the ones from DELPHI and OPAL Collaboration for √ s = 91, 133, 161, 172, 183 and 189 GeV. We compare the results with the Lee-Yang structure for proton-antiproton pp at √ s = 200, 546 and 900 GeV from UA5 Collaboration. Our preliminary result shows that there is indeed a change in the shape and size of the Lee-Yang zeros with increasing energy, accompanied by the development of the so-called "ear"-like structure in the Lee-Yang plot. We expect that the development of this "ear"-like structure is related to the "shoulder" structure in the multiplicity data, which further indicates an ongoing phase transition from soft to semihard scattering. We also extend our prediction to LHC's √ s = 14 TeV. Insert your abstract here.

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Section: Resultscontrasting

confidence: 61%

Section: Formalism and Derivation Of Generalized Multiplicity Distribmentioning

confidence: 95%

Lee-Yang circle analysis of e + e − and $p\overline{p}$ generalized multiplicity distribution

Dewanto¹,

Chan²,

Oh³

et al. 2008

Eur. Phys. J. C

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“…This search is interesting also in view of the fact discussed in Ref. [7] that NB parameter k controls the geometry of the zeroes distribution in the complex z-fugacity plane of the M-order algebraic equation of the M-truncated grand canonical partition function…”

Section: A Summary Of Previous Results On Clan Thermodynamicsmentioning

confidence: 96%

“…[8] that P [N B] n vs. n plot for the semihard class of events from concave k semihard > 1 is becoming convex with k hard < 1); II. that in the maps of zeroes of the truncated NB (Pascal) MD grand canonical partition function in the rescaled complex u-plane u = 1 is an accumulation point of zeroes (from inside for k semihard > 1 and from outside for k hard < 1 [7]). Assume then that the partonic clan gas of the semihard component in pp collisions has below the critical c.m.…”

Section: A Summary Of Previous Results On Clan Thermodynamicsmentioning

confidence: 99%

On statistical mechanics developments of clan concept in multiparticle production

Brambilla¹,

Giovannini²,

Ugoccioni³

2008

Physica A: Statistical Mechanics and its Applications

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Clan concept has been introduced in multiparticle dynamics in order to interpret the wide occurrence of negative binomial (NB) regularity in n-charged particle multiplicity distributions (MDs) in various high energy collisions. The centrality of clan concept led to the attempt to justify its occurrence within a statistical model of clan formation and evolution. In this framework all thermodynamical potentials have been explicitely calculated in terms of NB parameters. Interestingly it was found that NB parameter k corresponds to the one particle canonical partition function. The goal of this paper is to explore a possible temperature T and volume V dependence of parameter k in various classes of events in high energy hadron-hadron collisions. It is shown that the existence of a phase transition at parton level from the ideal clan gas associated to the semihard component with k > 1 to the ideal clan gas of the hard component with k < 1 implies a discontinuity in the average number of particles at hadron level.

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“…The theorem has numerous applications, which range from asymptotics of partial sums of power series [11] or a local-global stability principle for discrete-time systems [28], to coding theory [13], the economic theory of 10 depreciation and reinvestment [41], stability analysis of delay filters [36] and to models of high energy collisions [10] in physics. In this paper we are concerned with an extension of the Eneström-Kakeya theorem to operators in Hilbert space, which is different from the ones given by Furuta and Nakamura [21] and by Fuji and Kubo [18].…”

Section: 2)mentioning

confidence: 99%

Spectraloid operator polynomials, the approximate numerical range and an Eneström–Kakeya theorem in Hilbert space

Swoboda

Wimmer

2010

Studia Math.

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Mathematical Subject Classifications (2000): 47A10, 47A56, 47A12Keywords: Operator polynomials, Eneström-Kakeya theorem, normal approximate eigenvalues, semisimple eigenvalues, Jordan chains, approximate point spectrum, residual spectrum, spectral radius, numerical range, numerical radius, spectraloid operator. Running title: Operator polynomialsAbstract: In this paper we study a class of operator polynomials in Hilbert space, which are spectraloid in the sense that spectral radius and numerical radius coincide. The focus is on the spectrum in the boundary of the numerical range. As an application the Eneström-Kakeya-Hurwitz theorem on zeros of real polynomials is generalized to Hilbert space.

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Maps of zeros of the grand canonical partition function in a statistical model of high energy collisions

Cited by 4 publications

References 9 publications

Lee-Yang circle analysis of e + e − and $p\overline{p}$ generalized multiplicity distribution

Lee-Yang circle analysis of e + e − and $p\overline{p}$ generalized multiplicity distribution

On statistical mechanics developments of clan concept in multiparticle production

Spectraloid operator polynomials, the approximate numerical range and an Eneström–Kakeya theorem in Hilbert space

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