Energy and transverse momentum fluctuations in the equilibrium quantum systems

Abstract

The fluctuations in the ideal quantum gases are studied using the strongly intensive measures ∆[A, B] and Σ[A, B] defined in terms of two extensive quantities A and B. In the present paper, these extensive quantities are taken as the motional variable, A = X, the system energy E or transverse momentum P T , and number of particles, B = N . This choice is most often considered in studying the event-by-event fluctuations and correlations in high energy nucleus-nucleus collisions. The recently proposed special normalization ensures that ∆ and Σ are dimensionless and equal to unity for fluctuations given by the independent particle model. In statistical mechanics, the grand canonical ensemble formulation within the Boltzmann approximation gives an example of independent particle model.Our results demonstrate the effects due to the Bose and Fermi statistics. Estimates of the effects of quantum statistics in the hadron gas at temperatures and chemical potentials typical for thermal models of hadron production in high energy collisions are presented. In the case of massless particles and zero chemical potential the ∆ and Σ measures are calculated analytically.

Measurement of event-by-event transverse momentum and multiplicity fluctuations using strongly intensive measuresΔ[PT,N]andΣ[Antičić1, Grebieszkow2, Słodkowski3 et al. 2015Phys. Rev. CSelf Cite172170View full textAdd to dashboardCite

“…The parametrization of P T /N versus N was taken from the NA49 p + p data [12] (in the current paper the same p + p data are used), resulting in ∆[P T , N ] = 0.816(0.005) and Σ[P T , N ] = 1.008(0.002). This shows that Bose-Einstein correlations are not the only candidate for the explanation of ∆[P T , N ] < 1 and Σ[P T , N ] > 1 [15,19], but this observation, especially for smaller systems, may also be explained as due to the known P T /N versus N anti-correlation [18].…”

“…It was suggested in Refs. [15,19] that values of ∆[P T , N ] < 1 and Σ[P T , N ] > 1 can be explained as due to effects of Bose-Einstein statistics. Similarly, Φ p T > 0 was predicted in Refs.…”

“…Finally, the effects of quantum statistics were discussed in Ref. [19]. The general conclusion is that ∆[P T , N ] and Σ[P T , N ] measure deviations from the superposition model in different ways.…”

New theoretical results on event-by-event fluctuations

“…These measures were also studied in Ref. [50] for the ideal Bose and Fermi gases within the GCE. The GCE for the Boltzmann approximation satisfies the conditions of the IPM, i.e., Eq.…”

Multiplicity and transverse momentum fluctuations in inelastic proton–proton interactions at the CERN Super Proton Synchrotron

“…The effects of acceptance losses, efficiency losses, quantum (Bose-Einstein and Fermi-Dirac) statistics and centrality dependence (UrQMD) were investigated in Ref. [18]. Finally, the system size and energy dependence in the UrQMD model was studied in Ref.…”