Effects In Small Systems Research Articles

Measurement of R 2(Δη, Δφ) and P 2(Δη, Δφ) correlation functions in pp collisions at TeV with ALICE

In high-energy collisions, the mechanism of particle production, diffusivity, and conservation of charge and momentum are all revealed by the two-particle normalised cumulants of particle number correlations (R 2) and transverse momentum, p T, correlations (P 2), which are measured as a function of relative pseudorapidity and relative azimuthal angle difference (Δη, Δφ). We measure these observables in pp collisions at TeV with transverse momentum (p T) range of 0.2 - 2.0 GeV/c, to complement the recent ALICE measurements in Pb–Pb collisions and for a better understanding of the jet contribution and nature of collectivity in small systems. The observed correlations on the near- and away-side are qualitatively similar, but differ quantitatively. Additionally, it is shown that the near-side peak of P 2 is much narrower than the near-side peak of R 2 for both charge-independent (CI) and charge-dependent (CD) combinations, similar to the recently published ALICE results in p—Pb and Pb—Pb collisions. These results not only establish a baseline for heavy-ion collisions but also help one to better understand signals that are compatible with the existence of collective effects in small systems because they are sensitive to the interplay between the underlying event and mini-jets in pp collisions.

Highlights from the PHENIX Collaboration

PHENIX presented several new results at Quark Matter 2019 in 7 parallel talks and 7 posters. These proceedings highlight a sampling of the measurements presented during the conference. PHENIX results on flow in small systems, published in Nature Physics, indicate that the flow in small systems is driven by the initial state geometry. Additional measurements exploring QGP effects in small systems have also been explored. Two-particle correlations in d+Au and 3He+Au suggest potential modification compared to those in p+p collisions. PHENIX has also measured J/Ψ in the forward and backward rapidity regions in d+Au and 3He+Au collisions. Thermal photon measurements are also consistent with QGP formation in small systems. A new measurement of thermal photons using the Au+Au data set collected by PHENIX in 2014 verifies the scaling relationship previously observed for thermal photons. New results for a variety of hadron species with increasing precsion are now available and provide both insight into hadronization as well as crucial information for energy loss models that use RAA to tune their parameters. Jet modification is also studied via a new observable extracted from π0-hadron correlations in Au+Au collisions.

A microcanonical entropy correcting finite-size effects in small systems

In a recent paper (Franzosi (2018 Physica A 494 302)), we have suggested to use the surface entropy, namely the logarithm of the area of a hypersurface of constant energy in the phase space, as an expression for the thermodynamic microcanonical entropy, in place of the standard definition usually known as Boltzmann entropy. In the present manuscript, we have tested the surface entropy on the Fermi–Pasta–Ulam model for which we have computed the caloric equations that derive from both the Boltzmann entropy and the surface entropy. The results achieved clearly show that in the case of the Boltzmann entropy there is a strong dependence of the caloric equation from the system size, whereas in the case of the surface entropy there is no such dependence. We infer that the issues that one encounters when the Boltzmann entropy is used in the statistical description of small systems could be a clue to a deeper defect of this entropy that derives from its basic definition. Furthermore, we show that the surface entropy is well founded from a mathematical point of view, and we show that it is the only admissible entropy definition, for an isolated and finite system with a given energy, which is consistent with the postulate of equal a priori probability.

Electromagnetic fields in small systems from a multiphase transport model

We calculate the electromagnetic fields generated in small systems by using a multiphase transport (AMPT) model. Compared to $A+A$ collisions, we find that the absolute electric and magnetic fields are not small in $p$+Au and $d$+Au collisions at energies available at the BNL Relativistic Heavy Ion Collider and in $p$+Pb collisions at energies available at the CERN Large Hadron Collider. We study the centrality dependencies and the spatial distributions of electromagnetic fields. We further investigate the azimuthal fluctuations of the magnetic field and its correlation with the fluctuating geometry using event-by-event simulations. We find that the azimuthal correlation $\left\langle \cos2(\Psi_B - \Psi_{2}) \right\rangle$ between the magnetic field direction and the second harmonic participant plane is almost zero in small systems with high multiplicities, but not in those with low multiplicities. This indicates that the charge azimuthal correlation, $\left\langle \cos(\phi_{\alpha}+\phi_{\beta} - 2\Psi_{RP}) \right\rangle$, is not a valid probe to study the chiral magnetic effect (CME) in small systems with high multiplicities. However, we suggest searching for possible CME effects in small systems with low multiplicities.

Effect of the fluctuating proton size on the study of the chiral magnetic effect in proton-nucleus collisions

High energy proton-nucleus (pA) collisions provide an important constraint on the study of the chiral magnetic effect in QCD matter. Naively, in pA collisions one expects no correlation between the orientation of event plane as reconstructed from the azimuthal distribution of produced hadrons and the orientation of magnetic field. If this is the case, any charge-dependent hadron correlations can only result from the background. Nevertheless, in this paper we point out that in high multiplicity pA collisions a correlation between the magnetic field and the event plane can appear. This is because triggering on the high hadron multiplicity amounts to selecting Fock components of the incident proton with a large number of partons that are expected to have a transverse size much larger than the average proton size. We introduce the effect of the fluctuating proton size in the Monte Carlo Glauber model and evaluate the resulting correlation between the magnetic field and the second-order event plane in both pA and nucleus-nucleus (AA) collisions. The fluctuating proton size is found to result in a significant correlation between magnetic field and the event plane in pA collisions, even though the magnitude of the correlation is still much smaller than in AA collisions. This result opens a possibility of studying the chiral magnetic effect in small systems.

Mass hierarchy and energy scaling of the Tsallis – Pareto parameters in hadron productions at RHIC and LHC energies

The latest, high-accuracy identified hadron spectra measurements in highenergy nuclear collisions led us to the investigation of the strongly interacting particles and collective effects in small systems. Since microscopical processes result in a statistical Tsallis – Pareto distribution, the fit parameters q and T are well suited for identifying system size scalings and initial conditions. Moreover, parameter values provide information on the deviation from the extensive, Boltzmann – Gibbs statistics in finite-volumes. We apply here the fit procedure developed in our earlier study for proton-proton collisions [1, 2]. The observed mass and center-of-mass energy trends in the hadron production are compared to RHIC dAu and LHC pPb data in different centrality/multiplicity classes. Here we present new results on mass hierarchy in pp and pA from light to heavy hadrons.

Initial state and pre-equilibrium effects in small systems

We discuss the importance of initial state and early time effects with regard to the theoretical understanding of long range azimuthal correlations observed in high-multiplicity p+p and p+A collisions.

Effects produced by multi-parton interactions and color reconnection in small systems

Multi-parton interactions and color reconnection can produce QGP-like effects in small systems, specifically, radial flow-like patterns. For pp collisions simulated with Pythia 8.212, in this work we investigate their effects on different observables like event multiplicity, event shapes and transverse momentum distributions.

Erratum: “Ground-State Phase Diagram of Frustrated Antiferromagnetic S = 1 Chain with Uniaxial Single-Ion-Type Anisotropy” [J. Phys. Soc. Jpn. 71, 319 (2002)

In the paper, it was incorrectly mentioned that by the exactdiagonalization calculation for small systems, the ground state of the model (1.4) was found to belong to the subspace of Stotal 1⁄4 0 with even parity.1) Although it is the case for the periodic chains and for a wide parameter region of the open chains, we have noticed that the ground state with odd parity appears in some parameter points of the open chains, as shown in Fig. 1 of this erratum. We note that this is a boundary effect in small systems with frustration, and the infinite-system density-matrix renormalization-group (DMRG) calculation in the original paper, which was performed for the subspace of Stotal 1⁄4 0 with even parity, should capture the ground-state properties in the thermodynamic limit correctly. Indeed, we have newly performed the infinite-system DMRG for the whole subspace of Stotal 1⁄4 0 including both even and odd parity states, and obtained the same results as the previous ones within a numerical accuracy. Therefore, our conclusions remain the same. We also correct misprints, which do not affect our conclusions. (i) In Figs. 2(a), 4(a), and 6(a), the distance r of the chiral correlation C ðrÞ was shifted by one due to a simple error in the data processing. The label for the x-axis should read r þ 1 instead of r. (ii) In Figs. 2(b), 3, 4(b), and 5(a), the sign of the string correlation was reversed erroneously: The minus sign should be removed. (iii) In Fig. 4, the number of kept states m for d 1⁄4 1:10 was not 350 but 300. We have checked that the results with these m’s are almost identical. In Fig. 6(a), in addition to j 1⁄4 0:800, the data for j 1⁄4 0:810 were obtained with m 1⁄4 500. Accordingly, in Fig. 1, a cross, which indicates the point of high-precision calculation, should be added at ðj; dÞ 1⁄4 ð0:810; 0:30Þ.

Erratum: “Ground State Phase Diagram of Frustrated S = 1 XXZ Chains: Chiral Ordered Phases” [J. Phys. Soc. Jpn. 69, 259 (2000)

In the paper, it was incorrectly mentioned that the exactdiagonalization calculation for small systems found that the ground state of the model (1.1) belonged to the subspace of S total 1⁄4 0 with even parity.1) (We call this subspace PE below.) While it is the case for the periodic chains2) and for a wide parameter region of the open chains, we have noticed that the ground state with odd parity appears in some narrow parameter regions of the open chains, as shown in Fig. 1 of this erratum. We note that this is a boundary effect in small systems with frustration, and the infinite-system density-matrix renormalization-group (DMRG) calculation for the subspace PE performed in the original paper should capture the groundstate properties in the thermodynamic limit correctly. Indeed, we have newly performed the infinite-system DMRG for the whole subspace of S total 1⁄4 0 including both even and odd parity states (we call this subspace PEO), and obtained essentially the same results as the previous ones for the subspace PE. For example, as for the estimates of jc1 and jc2 shown in Table II, those for 1⁄4 0, 0.2, and 0.4 remain the same, while comparing the results for PE and PEO, we modify the errors of the estimates for 1⁄4 0:6 (0.8) from ðjc1; jc2Þ 1⁄4 ð0:642 0:002; 0:660 0:003Þ [ð0:715 0:003; 0:720 0:002Þ] to ð0:642þ0:004 0:002; 0:660þ0:009 0:003Þ [ð0:715þ0:005 0:003; 0:720þ0:009 0:002Þ]. The other results in the paper, including the phase diagram and the estimates of critical exponents, remain the same within a numerical accuracy. Therefore, our conclusions remain valid. We also correct misprints and typographical errors, which do not affect our conclusions. (i) In Figs. 2(b) and 5, the distance r of the chiral correlation C ðrÞ was shifted by one due to a simple error in the data processing. The label for the x-axis should read r + 1 instead of r. (ii) Equation (3.2) should read

Erratum: “Spin and Chiral Orderings of Frustrated Quantum Spin Chains” [J. Phys. Soc. Jpn. 68, 3185 (1999)

In p. 3186, below Eq. (3), it was incorrectly stated that by the exact-diagonalization (ED) calculation for the open chains with even N [8 N 20 (S = 1/2) and 8 N 16 (S = 1)], the ground state was found to belong to the subspace of S total 1⁄4 0 with even parity.1) In fact, for the S = 1/2 XY and Heisenberg open chains, the ground state belongs to the subspace of S total 1⁄4 0 with even (odd) parity when N = 4n (4n + 2), where n is an integer. For the S = 1 case, the ground state for a wide parameter region belongs to the subspace of S total 1⁄4 0 with even parity, while the ground state with odd parity appears in some parameter regions, whose position is confined within a range 0:3 . j . 0:6 and changes depending on the system size N and on whether XY or Heisenberg. This correction has no effect on the other parts of the paper. The data of the Binder parameter shown in Fig. 1 were obtained by the ED calculation for the whole subspace of S total 1⁄4 0 including both the even and odd parity states, and therefore, they are not affected by the correction. As for the density-matrix renormalization-group (DMRG) calculation for the S = 1 XY chains, we note that the appearance of the odd-parity ground state found by the ED is a boundary effect in small systems with frustration, and the infinite-system DMRG for the subspace of S total 1⁄4 0 with even parity should capture the ground-state properties in thermodynamic limit correctly. Indeed, we have newly performed the DMRG calculation for the whole subspace of S total 1⁄4 0 and obtained the same results as the previous ones within a numerical accuracy. As to the data shown in Fig. 2, for example, the differences between the previous and newly-obtained results averaged on the distance r are at most 1:2 10 3 (chiral correlation), 1:5 10 4 (string correlation), and 4:8 10 4 (spin correlation), except for the chiral and string correlations at the transition point j 1⁄4 jc1 1⁄4 0:473 for which the averaged differences are 1:2 10 2 or less (chiral) and 1:1 10 3 (string). These differences have no effect on our argument on the behaviors of the correlation functions, and therefore, our conclusions in the paper remain the same. We also correct a misprint in Fig. 2(a): The distance r of the chiral correlation C ðrÞ was shifted by one due to a simple error in the data processing. Therefore, the label for the x-axis should read r + 1 instead of r. Finally, we note that, although the ED data of the Binder parameter in Fig. 1 suggested the absence of the chiral order in the S = 1/2 XY chains, it has been revealed by the DMRG that the chiral order indeed appears in the S = 1/2 chains with easy-plane anisotropy. The DMRG results and the reason why the ED analysis missed the chiral order in the S = 1/2 chains have already been reported in Ref. 2.

The Effects of Small System on the Type I Antifreeze Protein ‘HPLC-6’

According to Hill’s thermodynamics theory for small system, the effect of small system on the type I antifreeze protein ‘HPLC-6’ is discussed in this article. We conclude that when the solution is very dilute, the effect is not visible, and as the concentration increases, the effect becomes more visible than before, and the result also shows that the number of molecules on the ice surface becomes larger when the effect of small system is considered.

The Thermal Hysteresis of the Type I Antifreeze Protein ‘HPLC-6’: The Effect of Small System

According to Hill’s thermodynamics theory for small system, the effect of small system on the thermal hysteresis activity of type I antifreeze protein ‘HPLC-6’ is discussed in this article. We conclude that when the solution is very dilute, the effect is not visible, and as the concentration increases, the effect becomes more visible than before, and the result also shows that the thermal hysteresis temperature becomes larger when the effect of small system is considered.

Hidden scaling in the quantum Hall metal-insulator transition

Scaling properties of the quantum Hall metal-insulator transition are severely affected by finite-size effects in small systems. Surprisingly, despite the narrow spatial range where probability structure functions exhibit multifractal scaling, we clearly verify the existence of extended self-similarity---a hidden infrared scaling phenomenon related to the peculiar form of the crossover at the onset of nonmultifractal behavior. As finite-size effects get stronger for structure functions with negative orders, the parabolic approximation for the multifractal spectrum loses accuracy. However, by means of an extended self-similarity analysis, an improved evaluation of the multifractal exponents is attained for negative orders too, rendering them consistent with previous results, which rely on computations performed for considerably larger systems.

Magnetoresistance of small Kondo systems.

Results for the low-temperature magnetoresistance of thin Au films containing \ensuremath{\sim}30 ppm Fe are reported. As expected, we observe contributions from both the classical magnetoresistance and the local magnetic moments (i.e., the Fe). The local-moment magnetoresistance is a strong function of film thickness, and is suppressed as the thickness is reduced. This finding is compared with previous results for the Kondo effect in small systems, and with recent theoretical predictions. \textcopyright{} 1996 The American Physical Society.

Thermal kinetics in small systems. III. Isotopic effects

We consider here kinetic isotope effects in small systems excited to some common energy as measured from their respective zero points. A transparent and model-free expression is derived relating these effects to their counterparts in a heat bath. The expression affords an immediate understanding of the origin of these effects. Its use is illustrated by application to the dissociation of benzene and substituted-benzene cations.

On application of statistical virial theorems

view Abstract Citations (9) References (17) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS On application of statistical virial theorems. Geller, M. J. ; Davis, M. Abstract Two effects which could bias statistical virial-theorem determinations of the mean mass density of the universe (Omega) are examined. In order to check for effects due to mass segregation, luminosity-weighted statistics for the galaxy distribution are developed. Systematic error in the determination of the characteristic peculiar velocity dispersion for galaxies is also investigated. Such bias can result from (1) correlation between the peculiar velocities of galaxies and their masses or (2) determining the mean peculiar velocity by averaging over the number of pairs of galaxies rather than the number of individual galaxies in the sample. These effects bias the estimates of Omega toward higher values, but it is found that, taken together, they have at most a 20%-30% effect on estimates of Omega. It is concluded that the value of Omega is in the range from roughly 0.2 to 0.3. The luminosity-weighted statistics offer a basis for a statistical test for relaxation effects in small systems of galaxies. With a sample deeper than those currently available, these tests could be applied effectively to a 'distance-limited' galaxy catalog. Publication: The Astrophysical Journal Pub Date: October 1978 DOI: 10.1086/156463 Bibcode: 1978ApJ...225....1G Keywords: Cosmology; Galaxies; Mass Distribution; Statistical Analysis; Virial Theorem; Hubble Diagram; Kinetic Energy; Luminous Intensity; Velocity Distribution; Weighting Functions; Astrophysics; Galaxies:Space Distribution; Galaxies:Virial Theorem; Mass Density:Universe full text sources ADS |