Narrow Results

We present the systematic analysis of transverse momentum (p_T) spectra of identified hadrons in p+p collisions at Relativistic Heavy Ion Collider ( and 200 GeV) and at Large Hadron Collider (LHC) energies (, 2.76 and 7.0 TeV) using phenomenological fit functions. We review various forms of Hagedorn and Tsallis distributions and show their equivalence. We use Tsallis distribution which successfully describes the spectra in p+p collisions using two parameters, Tsallis temperature T which governs the soft bulk spectra and power n which determines the initial production in partonic collisions. We obtain these parameters for pions, kaons and protons as a function of center-of-mass energy . It is found that the parameter T has a weak but decreasing trend with increasing . The parameter n decreases with increasing which shows that production of hadrons at higher energies are increasingly dominated by point like qq scatterings. Another important observation is with increasing , the separation between the powers for protons and pions narrows down hinting that the baryons and mesons are governed by same production process as one moves to the highest LHC energy.

We present a systematic study of transverse momentum $(p_T)$ spectra of charged particles in $p+p$ and Xe$+$Xe collisions at $\sqrt{s_{NN}}=5.44$ TeV. The published data of invariant yields of charged particles as a function of $p_T$ is taken from ALICE at LHC in the mid-pseudorapidity region $\left|\eta \right|<0.8$. The modified form of Tsallis distribution is used here to analyze the $p_T$ spectra of charged particles. The power law of Tsallis/Hagedorn form gives very good description of the charged particle spectra in $p+p$ collisions within a $p_T$ range of 0.15 GeV/$c$ to 50 GeV/$c$. When we go from $p+p$ collisions to heavy-ion (Xe$+$Xe) collisions, the original form of Tsallis/Hagedorn distribution is not able to describe the $p_T$ spectra of charged particles properly. This may be occurred due to the medium effects or the final state effects. Here we discuss two types of medium effects of charged particles in Xe$+$Xe collisions, one is the transverse flow in the low to intermediate $p_T$ region ($p_T\le 7$ GeV/$c$) and the other is the energy loss in the high $p_T$ region ($p_T>7$ GeV/$c$), using the modified Tsallis distribution.

Classical and quantum Tsallis distributions have been widely used in many branches of natural and social sciences. But, the quantum field theory of the Tsallis distributions is relatively a less explored arena. In this paper, we derive the expression for the thermal two-point functions in the Tsallis statistics with the help of the corresponding statistical mechanical formulations. We show that the quantum Tsallis distributions used in the literature appear in the thermal part of the propagator much in the same way the Boltzmann–Gibbs distributions appear in the conventional thermal field theory. As an application of our findings, we calculate the thermal mass in the ${\varphi }^4$ scalar field theory within the realm of the Tsallis statistics.

We present the published data of ALICE at mid-rapidity region ($\left|y\right|<0.5$) to study the $p_T$ spectra of light-flavor hadrons in different charged-particle multiplicities ($\frac{d{N}_{\mathrm{\text{ch}}}}{d\eta }$) for $p+p$ collisions at $\sqrt{s}=7$ TeV. We parametrize the $p_T$ spectra of different hadrons such as pion (${\pi }^{+}+{\pi }^{-}$), kaon ($K^{+}+K^{-}$), $K_S^0$, $K^{\ast 0}$ ($K^{\ast 0}+\overline{K^{\ast 0}}$), $\varphi$, proton ($p+\bar{p}$), lambda ($\mathrm{\Lambda }+\bar{\mathrm{\Lambda }}$), cascade (${\mathrm{\Xi }}^{-}+{\bar{\mathrm{\Xi }}}^{+}$) and omega (${\mathrm{\Omega }}^{-}+{\bar{\mathrm{\Omega }}}^{+}$) using Tsallis distribution. We perform this analysis by considering both differential and single freeze-out scenarios. In the differential freeze-out scenario, both the Tsallis parameters $n$ and $T$ increase with charged multiplicities for most of the particles. This implies that the multipartonic interactions increase the multiplicities in $p+p$ collisions and it brings the system towards thermal equilibrium. Here we observe that both $n$ and $T$ have different trends with different masses of particles. The parameters $n$ and $T$ are higher for massive particles (except for multistrange baryons) in comparison to lighter ones, which supports the differential freeze-out scenario and suggests that massive particles freeze-out earlier from the system. In the case of single freeze-out scenario, the value of parameter $n$ has a little variation with multiplicity and the parameter $T$ increases with multiplicity. This implies that the degree of thermalization remains similar for the events of different multiplicity classes.

Based on the experimental measurement results of fluid particle transverse accelerations in fully developed pipe turbulence published in Nature (2001) by La Porta et al, the present authors recently develop a multiscale statistical model which considers both normal diffusion in molecular scale and anomalous diffusion in vortex scale. This model gives rise to a new probability density function, called Power-Stretched Gaussian Distribution model (PSGD). In this study, we make a further comparison of this statistical distribution model with the well-known Lévy distribution, Tsallis distribution and stretched-exponential distribution. Our model is found to have the following merits: 1) fewer parameters, 2) better fitting with experimental data, 3) more explicit physical interpretation.

In this paper, we investigate the effects of convexity and concavity of states on entanglement of the system under thermal non-equilibrium condition. In this regard, we consider a system consisting of two spin 1/2 particles with Dzyaloshinskii–Moriya (DM) interaction that follows the Tsallis statistics.Also, according to the desired statistics, the effect of environment parameters and the convexity or concavity of the input states on the output behavior of the SWAP gate is obtained.

The effects of the Tsallis distribution which has two parameters, $q$ and $T$, on physical quantities are studied using the linear sigma model in chiral phase transitions. The Tsallis distribution approaches the Boltzmann–Gibbs distribution as $q$ approaches one. The parameter $T$ dependences of the condensate and mass for various $q$ are shown, where $T$ is called temperature. The critical temperature and energy density are described with digamma function, and the $q$ dependences of these quantities and the extension of Stefan–Boltzmann limit of the energy density are shown. The following facts are clarified. The chiral symmetry restoration at $q>1$ occurs at low temperature, compared with the restoration at $q=1$. The sigma mass and pion mass reflect the restoration. The critical temperature decreases monotonically as $q$ increases. The small deviation from the Boltzmann–Gibbs distribution results in the large deviations of physical quantities, especially the energy density. It is displayed from the energetic point of view that the small deviation from the Boltzmann–Gibbs distribution is realized for $q>1$. The physical quantities are affected by the Tsallis distribution even when $|q-1|$ is small.

The parametric resonance was studied in chiral phase transitions when the momentum distribution is described by a Tsallis distribution. A Tsallis distribution has two parameters, the temperature $T$ and the entropic index $q$. The amplification was estimated in two cases: (1) expansionless case and (2) one-dimensional (1D) expansion case. In an expansionless case, the temperature $T$ is constant, and the amplified modes as a function of $T$ were calculated for various $q$. In 1D expansion case, the temperature $T$ decreases as a function of the proper time, and the amplification as a function of the transverse momentum was calculated for various $q$. In the expansionless case, the following facts were found: (1) the larger the value $q$ is, the softer the amplified modes are for the first and second resonance bands, (2) the amplified mode of the first resonance band decreases and vanishes, as the temperature $T$ increases and (3) the amplified mode of the second resonance band decreases and approaches to zero, as the temperature $T$ increases. In 1D expansion case, the following facts were found: (1) the soft mode is amplified, (2) the amplification is extremely strong around the amplified mode of the first resonance band at $T=0$ and (3) the magnitude of the amplification as a function of transverse momentum oscillates around the amplified mode of the first resonance band at $T=0$.

We studied the effects of the Tsallis distribution on the transverse momentum fluctuation in high energy collisions. The parton–hadron duality and the Bose–Einstein type correlation between partons were assumed. The fluctuation was calculated in the boost-invariant picture for the expectation value used in the Boltzmann–Gibbs (BG) statistics and for the expectation value used in the Tsallis nonextensive statistics. It was shown that the fluctuation is a function of $\eta$ which is the ratio of the inverse temperature to the correlation length. We found the following points: (1) the fluctuation depends on the form of the distribution and depends weakly on the definition of the expectation value used in the statistics, (2) the fluctuation increases as the entropic parameter value of the Tsallis distribution increases, and (3) the variation of the fluctuation as a function of the entropic parameter for the expectation value used in the BG statistics is larger than that for the expectation value used in the Tsallis nonextensive statistics in the wide range of $\eta$.

We implement a non-conventional statistical distribution, the canonical Tsallis distribution for lattice field theoretical calculations. We use a so called super-statistical approach: here the application of the Tsallis distribution is realized via introducing a fluctuating temperature. The fluctuations of the inverse temperature follow a Gamma distribution. We study the possibilities to evaluate expectation values in the superstatistical system and generalize the usual direct numerical method using a Metropolis algorithm. Our method is suitable for performing numerical calculations in order to investigate the thermodynamical properties of the strongly interacting superstatistical matter, or to derive the equation of state in this non-extensive approach.