arXiv subjects

T. Bhattacharyya

Publications and source records attributed to T. Bhattacharyya.

9 recordsLinked to original sources

arXiv2025

Nuclear modification factor within a dynamical approach to the complex entropic index

This work introduces a novel approach to the nuclear deformation factor $R_{\text{AA}}$, grounded in the dynamical effects of the Quark-Gluon Plasma on parton momentum. The approach uses the Blast-Wave method combined with Tsallis Statistics, within the Cooper-Frye freeze-out framework and, by profiting from appropriate simplifications, it gives analytical expressions that describe the observed $R_{\text{AA}}$ for two sets of independent measurements at $\sqrt{s}=2.76$ TeV and $\sqrt{s}=5.02$ TeV. A nonlinear dynamical equation describes the dynamics and leads to log-periodic oscillations. With the analytical solutions for that equation, it is possible to link the dynamical approach with the complex-$q$ formalism, which was proposed to describe the log-oscillations observed in experimental data.

hep-ph↗

arXiv2020

Hadron transverse momentum distributions of the Tsallis normalized and unnormalized statistics

The exact analytical formulas for the transverse momentum distributions of the Bose-Einstein, Fermi-Dirac and Maxwell-Boltzmann statistics of particles with nonzero mass in the framework of the Tsallis normalized and Tsallis unnormalized (also known as Tsallis-1 and Tsallis-2) statistics have been consistently derived. The final exact results were expressed in terms of the series expansions in the integral representation. The zeroth term approximation to both quantum and classical statistics of particles has been introduced. We have revealed that the phenomenological classical Tsallis distribution (widely used in high energy physics) is equal to the distribution of the Tsallis unnormalized statistics in the zeroth term approximation, but the phenomenological quantum Tsallis distributions (introduced by definition on the basis of the generalized entropy of the ideal gas) do not correspond to the distributions of the Tsallis statistics. We have found that in the ranges of the entropic parameter relevant to the processes of high-energy physics ($q<1$ for Tsallis-1 and $q>1$ for Tsallis-2) the Tsallis statistics is divergent. Therefore, to obtain physical results, we have regularized the Tsallis statistics by introducing an upper cut-off in the series expansion. The exact numerical results for the Bose-Einstein, Fermi-Dirac and Maxwell-Boltzmann statistics of particles in the Tsallis normalized and unnormalized statistics have been obtained. We observed that the exact results of the Tsallis statistics strongly enhanced the production of high-$p_{T}$ hadrons in comparison with the usual phenomenological Tsallis distribution function at the same values of $q$. The $q$-duality of the Tsallis normalized and unnormalized statistics for the massive particles was studied.

nucl-th↗

arXiv2020

Energy density at kinetic freeze-out in Pb-Pb collisions at the LHC using the Tsallis distribution

The thermodynamic parameters like energy density, pressure, entropy density, temperature and particle density are determined from the transverse momentum distributions of charged particles in Pb-Pb collisions at the LHC. The results show a clear increase with the centrality and the beam energy in all parameters. It is determined that in the final freeze-out stage the energy density reaches a value of about 0.039 GeV/fm$^3$ for the most central collisions at $\sqrt{s_{NN}}$ = 5.02 TeV. This is less than that at chemical freeze-out where the energy density is about 0.36 GeV/fm$^3$. This decrease approximately follows a $T^4$ law. The results for the pressure and entropy density are also presented for each centrality class at $\sqrt{s_{NN}}$ = 2.76 and 5.02 TeV.

hep-ph↗

arXiv2019

Remarks on the phenomenological Tsallis distributions and their link with the Tsallis statistics

From the Tsallis unnormalized (or Tsallis-2) statistical mechanical formulation, Büyükkiliç {\it et al.} [Phys. Lett. A 197, 209 (1995)] derived the expressions for the single-particle distribution functions (known as the phenomenological Tsallis distributions) for particles obeying the Maxwell-Boltzmann, Bose-Einstein and the Fermi-Dirac statistics using the factorization approximation. In spite of the fact that this paper was published long time ago, its results are still extensively used in many fields of physics, and it is considered that it was this paper that established the connection between the phenomenological Tsallis distributions and the Tsallis statistics. Here we show that this result is incorrect: the mistake lies in the fact that the probability distribution function was derived using the definition of the generalized expectation values (of the Tsallis-2 statistics), but the single-particle distribution function was calculated from this probability distribution using the standard definition of the expectation values of the Tsallis normalized (or Tsallis-1) statistics. Considering the definition of the expectation values which is consistent with the Tsallis-2 formulation, we have proved that the single-particle (classical and quantum) distribution functions in the factorization approximation differ from the phenomenological Tsallis distributions.

cond-mat.stat-mech↗

arXiv2018

Non-extensivity of the QCD pT spectra

We try to establish a connection between the hadronic distributions, in proton-proton collisions at very high transverse momentum $p_{\mathrm{T}}$, obtained via perturbative QCD and the Tsallis non extensive statistics. Our motivation is that while the former is expected to be valid at extremely high momentum, due to asymptotic freedom, the latter has been very successful in describing experimental spectra over a wide range of momentum. Matching the non extensive statistics with the asymptotic $p_{\mathrm{T}}$ behaviour expected from QCD leads to the value of $q=1.25$.

hep-ph↗

arXiv2018

On the precise determination of the Tsallis parameters in proton - proton collisions at LHC energies

A detailed analysis is presented of the precise values of the Tsallis parameters obtained in $p-p$ collisions for identified particles, pions, kaons and protons at the LHC at three beam energies $\sqrt{s} = 0.9, 2.76$ and $7$ TeV. Interpolated data at $\sqrt{s} = $ 5.02 TeV have also been included. It is shown that the Tsallis formula provides reasonably good fits to the $p_T$ distributions in $p-p$ collisions at the LHC using three parameters $dN/dy$, $T$ and $q$. However, the parameters $T$ and $q$ depend on the particle species and are different for pions, kaons and protons. As a consequence there is no $m_T$ scaling and also no universality of the parameters for different particle species.

hep-ph↗

arXiv2016

Analytic Model of Doubly Commuting Contractions

An n-tuple (n \geq 2), T = (T_1, \ldots, T_n), of commuting bounded linear operators on a Hilbert space \mathcal{H} is doubly commuting if T_i T_j^* = T_j^* T_i for all $1 \leq i < j \leq n$. If in addition, each T_i \in C_{\cdot 0}, then we say that T is a doubly commuting pure tuple. In this paper we prove that a doubly commuting pure tuple $T$ can be dilated to a tuple of shift operators on some suitable vector-valued Hardy space H^2_{\mathcal{D}_{T^*}}(\mathbb{D}^n). As a consequence of the dilation theorem, we prove that there exists a closed subspace \mathcal{S}_T of the form \[\mathcal{H}_{T} := \sum_{i=1}^n Φ_{T_i} H^2_{\mathcal{E}_{T_i}}(\mathbb{D}^n),\] where \{\mathcal{E}_{T_i}\}_{i=1}^n are Hilbert spaces, Φ_{T_i} \in H^\infty_{\mathcal{B}(\mathcal{E}_{T_i}, \mathcal{D}_{T^*})}(\mathbb{D}^n) such that each Φ_{T_i} (1 \leq i \leq n) is either a one variable inner function in z_i, or the zero function. Moreover, \mathcal{H} \cong \mathcal{S}_T^\perp and \[(T_1, \ldots, T_n) \cong P_{\mathcal{S}_T^\perp} (M_{z_1}, \ldots, M_{z_n})|_{\mathcal{S}_T^\perp}.\]

math.FA↗

arXiv2010

Coherent States on Hilbert Modules

We generalize the concept of coherent states, traditionally defined as special families of vectors on Hilbert spaces, to Hilbert modules. We show that Hilbert modules over $C^*$-algebras are the natural settings for a generalization of coherent states defined on Hilbert spaces. We consider those Hilbert $C^*$-modules which have a natural left action from another $C^*$-algebra say, $\mathcal A$. The coherent states are well defined in this case and they behave well with respect to the left action by $\mathcal A$. Certain classical objects like the Cuntz algebra are related to specific examples of coherent states. Finally we show that coherent states on modules give rise to a completely positive kernel between two $C^*$-algebras, in complete analogy to the Hilbert space situation. Related to this there is a dilation result for positive operator valued measures, in the sense of Naimark. A number of examples are worked out to illustrate the theory.

math-ph↗

arXiv2006

On c.n.c. commuting contractive tuples

The characteristic function has been an important tool for studying completely non unitary contractions on Hilbert spaces. In this note, we consider completely non-coisometric contractive tuples of commuting operators on a Hilbert space $\clh$. We show that the characteristic function, which is now an operator valued analytic function on the open Euclidean unit ball in $\mathbb{C}^n$, is a complete unitary invariant for such a tuple. We prove that the characteristic function satisfies a natural transformation law under biholomorphic mappings of the unit ball. We also characterize all operator-valued analytic functions which arise as characteristic functions of pure commuting contractive tuples.

math.OA↗