arXiv subjects

Trambak Bhattacharyya

Publications and source records attributed to Trambak Bhattacharyya.

At least 19 recordsLinked to original sources

arXiv2025

A mathematical model of delay discounting with bi-faceted impulsivity

Existing mathematical models of delay discounting (e. g. exponential model, hyperbolic model, and those derived from nonextensive statistics) consider impulsivity as a single entity. However, the present article derives a novel mathematical model of delay discounting considering impulsivity as a multi-faceted quantity. It involves the bi-faceted characteristic of impulsivity, and considers impulsivity as a variable represented by two positive and fluctuating quantities (e.g. these facets may be trait and state impulsivity). To derive the model, the superstatistics method, which has been used to describe fluctuating physical systems like a thermal plasma, has been adapted. According to the standard practice in behavioural science, we first assume that the total impulsivity is a mere addition of the two facets. However, we also explore the possibility beyond an additive model and conclude that facets of impulsivity may also be combined in a non-additive way. We name this group of models the Extended Effective Exponential Model or $E^3M$. We find a good agreement between our model and experimental data.

physics.soc-ph↗

arXiv2025

Rapidity spectra in high-energy collisions and longitudinal nuclear suppression from nonadditive statistics

We investigate the longitudinal nuclear suppression factor defined by a scaled ratio of rapidity distributions. To study this experimental observable, we describe three approaches involving numerical and analytical calculations. We first approach this problem by conducting model studies using EPOS, FTFP$_{BERT}$, and HIJING, and notice that while EPOS shows a decreasing trend of this ratio at forward/backward rapidities, the latter two model calculations display an increment of the ratio. The analytical approaches involve, first, the quasi-exponential distribution obtained from the Tsallis statistics, and second, the nonadditive Boltzmann transport equation in the relaxation time approximation. We notice that our analytical results satisfactorily describe NA61 experimental data (for $\sqrt{s_{NN}}$=6.3, 7.6, 8.8, 12.3, and 17.3 GeV) for the negatively charged pions.

nucl-th↗

arXiv2025

A harmonic oscillator in nonadditive statistics and a novel transverse momentum spectrum in high-energy collisions

It is widely observed that particles produced in high-energy collisions follow a power-law distribution. One such power-law distribution used extensively in the phenomenological studies owes its origin to nonadditive statistics proposed by C. Tsallis. In this article, we derive a novel nonadditive generalization of the conventional Bose-Einstein distribution using a single-mode harmonic oscillator. The approach taken in this paper eliminates the need of a regularization procedure proposed in previous works. We observe that the spectra of the bosonic particles like the pions and kaons produced in high-energy collisions are well-described by the nonadditive bosonic distribution derived in this paper.

hep-ph↗

arXiv2024

Jet Quenching of the Heavy Quarks in the Quark-Gluon Plasma and the Nonadditive Statistics

Using the Plastino-Plastino (PP) equation, we calculate transport coefficients of the heavy-quarks traversing inside the quark-gluon plasma, and generalize their relationship with differential energy loss. The PP equation indicates anomalous diffusion of the probe particles and yields a quasi-exponential stationary distribution obtained also from the nonadditive statistics proposed by C. Tsallis. We estimate energy loss in a nonadditive quark-gluon medium, and calculate the jet-quenching parameter ($\hat{q}$) for the PP dynamics. With the help of the estimate of $\hat{q}$, we calculate the nuclear suppression factor ($R_{\text{AA}}$) of the heavy-quarks passing through a nonadditive quark-gluon plasma using the model proposed by Dokshitzer and Kharzeev. In many a case, the parameters in the analysis are fixed from the experimental results to minimize arbitrariness. There is a good agreement between the theoretical calculation and experimental $R_{\text{AA}}$ data, indicating that fast heavy-quarks may be subjected to anomalous diffusion inside the QGP.

hep-ph↗

arXiv2024

Nonlinear Pulse Dynamics in a Magnetized and Nonextensive Quark-Gluon Plasma

We investigate the propagation of nonlinear energy density waves in a nonextensive quark-gluon plasma under the influence of a magnetic field using the reductive perturbation technique. For a nonextensive MIT bag equation of state, we obtain the governing equation for the first order perturbation of the energy density. We observe that an increase in the strength of the magnetic field results in the localization of the waves.

hep-ph↗

arXiv2023

Non-extensive Boltzmann Transport Equation: the Relaxation Time Approximation and Beyond

We derive approximate iterative analytical solutions of the non-extensive Boltzmann transport equation in the relaxation time approximation. The approximate solutions almost overlap with the exact solution for a considerably wide range of the parameter values found in describing particle spectra originated in high-energy collisions. We also discuss the Landau kinetic approximation of the non-extensive Boltzmann transport equation and the emergence of the non-extensive Fokker-Planck equation, and use it to estimate the drag and diffusion coefficients of highly energetic light quarks passing through a gluonic plasma.

nucl-th↗

arXiv2023

A Tsallis-like effective exponential delay discounting model and its implications

We propose an effective exponential model of delay discounting considering fluctuation in impulsivity. This model is seen to be dual to the two-parameter Tsallis model of delay discounting proposed by Takahashi in 2007. We demonstrate that the parameters of the model can be related to the mean and the variance of impulsivity. Our findings provide an intuitive way to explore the origin of the Tsallis distribution in a social system.

physics.soc-ph↗

arXiv2022

Analytical calculations of the Quantum Tsallis thermodynamic variables

In this article, we provide an account of analytical results related to the Tsallis thermodynamics that have been the subject matter of a lot of studies in the field of high-energy collisions. After reviewing the results for the classical case in the massless limit and for arbitrarily massive classical particles, we compute the quantum thermodynamic variables. For the first time, the analytical formula for the pressure of a Tsallis-like gas of massive bosons has been obtained. Hence, this article serves both as a brief review of the knowledge gathered in this area, and as an original research that forwards the existing scholarship. The results of the present paper will be important in a plethora of studies in the field of high-energy collisions including the propagation of non-linear waves generated by the traversal of high-energy particles inside the quark-gluon plasma medium showing the features of non-extensivity.

cond-mat.stat-mech↗

arXiv2021

Nonlinear waves in a hot, viscous and nonextensive quark gluon plasma

The effects of the non-extensive statistics on the nonlinear propagation of perturbations have been studied within the scope of relativistic second order dissipative hydrodynamics with the non-extensive equation of state. We have shown that the equations, describing the propagation of nonlinear waves under such situation are KdV-type (Korteweg-De Vries). Apart from their preserved solitonic behaviour the dissipative nature of these waves are also observed. The waves with larger amplitude and width dissipate less and propagate faster and these waves deplete more for both smaller values of Tsallis parameter ($q$) and temperature ($T$) of the medium. For vanishingly small transport coefficients the nonlinear waves show breaking nature. These findings suggest that the nature of the propagation of the nonlinear waves may serve as a good probe to differentiate between the extensive and non-extensive thermodynamic nature of a fluid, such as the quark-gluon plasma, produced in relativistic nuclear collisions.

nucl-th↗

arXiv2021

Dynamics of QCD Matter -- current status

In this article, there are 18 sections discussing various current topics in the field of relativistic heavy-ion collisions and related phenomena, which will serve as a snapshot of the current state of the art. Section 1 reviews experimental results of some recent light-flavored particle production data from ALICE collaboration. Other sections are mostly theoretical in nature. Very strong but transient magnetic field created in relativistic heavy-ion collisions could have important observational consequences. This has generated a lot of theoretical activity in the last decade. Sections 2, 7, 9, 10 and 11 deal with the effects of the magnetic field on the properties of the QCD matter. There are several unanswered questions about the QCD phase diagram. Sections 3, 11 and 18 discuss various aspects of the QCD phase diagram and phase transitions. Recent years have witnessed interesting developments in foundational aspects of hydrodynamics and their application to heavy-ion collisions. Sections 12, 15, 16 and 17 of this article probe some aspects of this exciting field. Transport coefficients together with their temperature- and density-dependence, are essential inputs in hydrodynamical calculations. Sections 5, 8 and 14 deal with calculation/estimation of various transport coefficients (shear and bulk viscosity, thermal conductivity, relaxation times, etc.) of quark matter and hadronic matter. Sections 4, 6 and 13 deals with interesting new developments in the field. Section 4 discusses color dipole gluon distribution function at small transverse momentum in the form of a series of Bells polynomials. Section 6 discusses the properties of Higgs boson in the quark gluon plasma using Higgs-quark interaction. Section 13 discusses modification of coalescence model to incorporate viscous corrections and application of this model.

hep-ph↗

arXiv2020

Analytical Results for the Classical and Quantum Tsallis Hadron Transverse Momentum Spectra: the Zeroth Order Approximation and beyond

We derive the analytical expressions for the first and second order terms in the hadronic transverse momentum spectra obtained from the Tsallis normalized (Tsallis-1) statistics. We revisit the zeroth order quantum Tsallis distributions and obtain the corresponding analytical closed form expressions. It is observed that unlike the classical case, the analytical closed forms of the zeroth order quantum spectra do not resemble the phenomenological distributions used in the literature after $q \to q^{-1}$ substitution, where $q$ is the Tsallis entropic parameter. However, the factorization approximation increases the extent of similarity.

nucl-th↗

arXiv2020

Propagation of non-linear waves in hot, ideal, and non-extensive quark-gluon plasma

We study the propagation of energy density perturbation in a hot, ideal quark-gluon medium in which quarks and gluons follow the Tsallis-like momentum distributions. We have observed that a non-extensive MIT bag equation of state obtained with the help of the quantum Tsallis-like distributions gives rise to a breaking wave solution of the equation dictating the evolution of energy density perturbation. However, the breaking of waves is delayed when the value of the Tsallis q parameter and the Tsallis temperature T are higher.

nucl-th↗

arXiv2020

Thermal Field Theory of the Tsallis statistics

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 article we derive the expression for the thermal two-point functions for 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, thermal mass of the real scalar bosons subjected to phi^4 interaction has been calculated in the Tsallis statistics.

hep-ph↗

arXiv2018

Unintegrated dipole gluon distribution at small transverse momentum

We derive analytical results for unintegrated color dipole gluon distribution function at small transverse momentum. By Fourier transforming the $S$-matrix for large dipoles we derive the results in the form of a series of Bells polynomials. Interestingly, when resumming the series in leading log accuracy, the results showing up striking similarity with the Sudakov form factor with role play of coupling is being done by a constant that stems from the saddle point condition along the saturation line.

hep-ph↗

arXiv2017

Non-extensive Fokker-Planck transport coefficients of heavy quarks

In presence of the non-ideal plasma effects, Heavy Quarks (HQs) carry out non linear random walk inside Quark-Gluon Plasma (QGP) and in the small momentum transfer limit, the evolution of the HQ distribution is dictated by the Non Linear Fokker-Planck Equation (NLFPE). Using the NLFPE, we calculate the transport coefficients (drag and diffusion) of heavy quarks travelling through QGP. We observe substantial modification in the momentum and temperature variation of the transport coefficients; and this will modify the physical picture we are having about the transport of heavy quarks inside QGP, and hence, about the characterisation of the plasma.

hep-ph↗

arXiv2016

Soft Gluon Radiation off Heavy Quarks beyond Eikonal Approximation

We calculate the soft gluon radiation spectrum off heavy quarks (HQs) interacting with light quarks (LQs) beyond small angle scattering (eikon- ality) approximation and thus generalize the dead-cone formula of heavy quarks extensively used in the literatures of Quark-Gluon Plasma (QGP) phenomenology to the large scattering angle regime which may be im- portant in the energy loss of energetic heavy quarks in the deconfined Quark-Gluon Plasma medium. In the proper limits, we reproduce all the relevant existing formulae for the gluon radiation distribution off energetic quarks, heavy or light used in the QGP phenomenology.

hep-ph↗

arXiv2016

Nuclear Modification Factor Using Tsallis Non-extensive Statistics

The nuclear modification factor is derived using Tsallis non-extensive statistics in relaxation time approximation. The variation of nuclear modification factor with transverse momentum for different values of non-extensive parameter, $q$, is also observed. The experimental data from RHIC and LHC are analysed in the framework of Tsallis non-extensive statistics in a relaxation time approximation. It is shown that the proposed approach explains the $R_{AA}$ of all particles over a wide range of transverse momenta but doesn't seem to describe the rise in $R_{AA}$ at very high transverse momenta.

nucl-th↗

arXiv2016

Analytic results for the Tsallis thermodynamic variables

We analytically investigate the thermodynamic variables of a hot and dense system, in the framework of the Tsallis non-extensive classical statistics. After a brief review, we start by recalling the corresponding massless limits for all the thermodynamic variables. We then present the detail of calculation for the exact massive result regarding the pressure -- valid for all values of the $q$-parameter -- as well as the Tsallis $T$-, $μ$- and $m$- parameters, the former characterizing the non-extensivity of the system. The results for other thermodynamic variables, in the massive case, readily follow from appropriate differentiations of the pressure, for which we provide the necessary formulas. For the convenience of the reader, we tabulate all of our results. A special emphasis is put on the method used in order to perform these computations, which happens to reduce cumbersome momentum integrals into simpler ones. Numerical consistency between our analytic results and the corresponding usual numerical integrals are found to be perfectly consistent. Finally, it should be noted that our findings substantially simplify calculations within the Tsallis framework. The latter being extensively used in various different fields of science as for example, but not limited to, high-energy nucleus collisions, we hope to enlighten a number of possible applications.

cond-mat.stat-mech↗