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Papers by Mahfuzur Rahaman

Research paper thumbnail of Dispersion and suppression of sound near QCD critical point

We have used Israel-Stewart relativistic hydrodynamics equipped with equation of state that inclu... more We have used Israel-Stewart relativistic hydrodynamics equipped with equation of state that includes critical point to study the propagation of perturbation in a relativistic QCD fluid. Dispersion relation for the sound wave has been derived to ascertain the fate of the perturbation in the fluid near the QCD critical end point. We observe that the threshold value of the wavelength of the sound that can propagate in the fluid diverges at the critical point. This indicates that all the modes of the perturbations will be dissipated at the critical point. Some consequences of the suppression of sound near the critical point have been discussed.

Research paper thumbnail of Dynamical spectral structure of density fluctuation near the QCD critical point

The European Physical Journal A

The expression for the dynamical spectral structure of the density fluctuation near the QCD criti... more The expression for the dynamical spectral structure of the density fluctuation near the QCD critical point has been derived using linear response theory within the purview of Israel-Stewart relativistic viscous hydrodynamics. The change in spectral structure of the system as it moves toward critical end point has been studied. The effects of the critical point have been introduced in the system through a realistic equation of state and the scaling behaviour of various transport coefficients and thermodynamic response functions. We have found that the Brillouin and the Rayleigh peaks are distinctly visible when the system is away from critical point but the peaks tend to merge near the critical point. The sensitivity of structure of the spectral function on wave vector (k) of the sound wave has been demonstrated. It has been shown that the Brillouin peaks get merged with the Rayleigh peak because of the absorption of sound waves in the vicinity of the critical point.

Research paper thumbnail of Recent progresses in the "Dynamics of QCD Matter

arXiv: High Energy Physics - Phenomenology, 2020

This writeup is a compilation of the contributions as presented in the `Workshop on Dynamics of Q... more This writeup is a compilation of the contributions as presented in the `Workshop on Dynamics of QCD Matter' held from 15th to 17th August 2019 in NISER Bhubaneswar, India. The aim of this workshop was to enhance the direct exchange of scientific information among the younger members of the Relativistic Heavy Ion community in India, both from the experiments and theory. The focus of the discussions was on the fundamental understanding of strongly-interacting matter at extreme conditions, as formed in ultra-relativistic nucleus-nucleus collisions, as well as on emergent QCD phenomena in high-multiplicity proton-proton and proton-nucleus collisions.

Research paper thumbnail of 2 2 M ay 2 01 8 Effects of causality on the fluidity and viscous horizon of quark-gluon plasma

The second order Israel-Stewart-Müller relativistic hydrodynamics has been applied to study the e... more The second order Israel-Stewart-Müller relativistic hydrodynamics has been applied to study the effects of causality on the acoustic oscillation in relativistic fluid. Causal dispersion relations have been derived with non-vanishing shear viscosity, bulk viscosity and thermal conductivity at nonzero temperature and baryonic chemical potential. These relations have been used to investigate the fluidity of Quark Gluon Plasma (QGP) at finite temperature (T ). Results of the first order dissipative hydrodynamics have been obtained as limiting case of the second order theory. The effects of the causality on the fluidity near the transition point and on viscous horizon are found to be significant. We observe that the inclusion of causality increases the value of fluidity measure of QGP near Tc and hence makes the flow strenuous. It has also been shown that the inclusion of large magnetic field in the causal hydrodynamics alters the fluidity of QGP.

Research paper thumbnail of Thermal Field Theory of the Tsallis statistics

arXiv: High Energy Physics - Phenomenology, 2019

Classical and quantum Tsallis distributions have been widely used in many branches of natural and... more 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.

Research paper thumbnail of Nonlinear waves in a hot, viscous and nonextensive quark gluon plasma

The effects of the nonextensive statistics on the nonlinear propagation of perturbations have bee... more The effects of the nonextensive statistics on the nonlinear propagation of perturbations have been studied within the scope of relativistic second order dissipative hydrodynamics and the nonextensive equation of state. We have shown that the equations which describe the propagation of nonlinear waves under such situation are KdV-like (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 and propagate faster. The waves deplete more with smaller values of Tsallis parameter, q and lower temperature 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 discern the extensive and non-extensive thermodynamic nature of a fluid such as the quark gluon plasma produced in relativistic nuclear collisions. ∗ go...

Research paper thumbnail of Effect of magnetic screening mass on the diffusion of heavy quarks

International Journal of Modern Physics E

The drag and diffusion coefficients of heavy quarks propagating through quark–gluon plasma (QGP) ... more The drag and diffusion coefficients of heavy quarks propagating through quark–gluon plasma (QGP) have been estimated by shielding the infra-red divergences using electric and magnetic screening masses. The electric-type screening in perturbative quantum chromodynamics (pQCD) has been widely studied and used in evaluating the diffusion coefficient of heavy quarks (HQs). The impact of magnetic screening on diffusion coefficients of HQs is not studied before to the best of our knowledge. We explore the effect of magnetic screening mass on the drag and diffusion coefficients of HQs and found it to be non-negligible. Therefore, the effect of magnetic screening should be taken into consideration to characterize hot and dense matter formed in the collisions of nuclei at ultra-relativistic energies. We estimate the suppression of heavy flavored mesons in heavy ion collisions compared to proton+proton collisions at high transverse momenta and found that the suppression is less with the inclu...

Research paper thumbnail of The fate of nonlinear perturbations near the QCD critical point

Golam Sarwar, ∗ Md Hasanujjaman, † Mahfuzur Rahaman, 4, ‡ Abhijit Bhattacharyya, § and Jan-e Alam... more Golam Sarwar, ∗ Md Hasanujjaman, † Mahfuzur Rahaman, 4, ‡ Abhijit Bhattacharyya, § and Jan-e Alam 4, ¶ Department of Physics,University of Calcutta, 92, A.P.C. Road, Kolkata-700009, India Department of Physics, Darjeeling Government College, Darjeeling734101, India Variable Energy Cyclotron Centre, 1/AF Bidhan Nagar, Kolkata700064, India Homi Bhabha National Institute, Training School Complex, Mumbai 400085, India

Research paper thumbnail of Phenomenological Tsallis distribution from thermal field theory

International Journal of Modern Physics A

Classical and quantum Tsallis distributions have been widely used in many branches of natural and... more 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 [Formula: see text] scalar field theory within the realm of the Tsallis statistics.

Research paper thumbnail of Effects of causality on the fluidity and viscous horizon of quark-gluon plasma

Physical Review C, May 14, 2018

Research paper thumbnail of Dynamics of QCD matter — current status

International Journal of Modern Physics E

In this article, there are 18 sections discussing various current topics in the field of relativi... more 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. More specifically, Sec. 2 discusses mass of [Formula: see text] in the linear sigma model coupled to quarks at zero temperature. In Sec. 7, one-loop calculation of the anisotropic pressure are discussed in the presence of strong magnetic field. In Sec. 9, chiral transition and chiral susceptibility in th...

Research paper thumbnail of Contribution of a kaon component in the viscosity and conductivity of a hadronic medium

With the help of effective Lagrangian densities of strange hadrons, we have calculated kaon relax... more With the help of effective Lagrangian densities of strange hadrons, we have calculated kaon relaxation time from several loop and scattering diagrams at tree-level, which basically represent contributions from 1 ↔ 2 and 2 ↔ 2 type of collisions. Using the total relaxation time of kaon, shear viscosity and electrical conductivity of this kaon component have been estimated. The high temperature, close to transition temperature, where kaon relaxation time is lower than life time of RHIC or LHC matter, may be the only relevant domain for this component to contribute in hadronic dissipation. Our results suggest that kaon can play an important role in the enhancement of shear viscosity and electrical conductivity of hadronic matter near the transition temperature.

Research paper thumbnail of Dispersion and suppression of sound near the QCD critical point

Physical Review C

We have used second-order relativistic hydrodynamics equipped with an equation of state which inc... more We have used second-order relativistic hydrodynamics equipped with an equation of state which includes the critical point to study the propagation of a perturbation in a relativistic QCD fluid. The dispersion relation for the sound wave has been derived to ascertain the fate of the perturbation in the fluid near the QCD critical end point (CEP). We observe that the threshold value of the wavelength of the sound in the fluid diverges at the CEP, implying that all the modes of the perturbation are dissipated at this point. Some consequences of the suppression of sound near the critical point have been discussed.

Research paper thumbnail of Dispersion and suppression of sound near QCD critical point

We have used Israel-Stewart relativistic hydrodynamics equipped with equation of state that inclu... more We have used Israel-Stewart relativistic hydrodynamics equipped with equation of state that includes critical point to study the propagation of perturbation in a relativistic QCD fluid. Dispersion relation for the sound wave has been derived to ascertain the fate of the perturbation in the fluid near the QCD critical end point. We observe that the threshold value of the wavelength of the sound that can propagate in the fluid diverges at the critical point. This indicates that all the modes of the perturbations will be dissipated at the critical point. Some consequences of the suppression of sound near the critical point have been discussed.

Research paper thumbnail of Dynamical spectral structure of density fluctuation near the QCD critical point

The European Physical Journal A

The expression for the dynamical spectral structure of the density fluctuation near the QCD criti... more The expression for the dynamical spectral structure of the density fluctuation near the QCD critical point has been derived using linear response theory within the purview of Israel-Stewart relativistic viscous hydrodynamics. The change in spectral structure of the system as it moves toward critical end point has been studied. The effects of the critical point have been introduced in the system through a realistic equation of state and the scaling behaviour of various transport coefficients and thermodynamic response functions. We have found that the Brillouin and the Rayleigh peaks are distinctly visible when the system is away from critical point but the peaks tend to merge near the critical point. The sensitivity of structure of the spectral function on wave vector (k) of the sound wave has been demonstrated. It has been shown that the Brillouin peaks get merged with the Rayleigh peak because of the absorption of sound waves in the vicinity of the critical point.

Research paper thumbnail of Recent progresses in the "Dynamics of QCD Matter

arXiv: High Energy Physics - Phenomenology, 2020

This writeup is a compilation of the contributions as presented in the `Workshop on Dynamics of Q... more This writeup is a compilation of the contributions as presented in the `Workshop on Dynamics of QCD Matter' held from 15th to 17th August 2019 in NISER Bhubaneswar, India. The aim of this workshop was to enhance the direct exchange of scientific information among the younger members of the Relativistic Heavy Ion community in India, both from the experiments and theory. The focus of the discussions was on the fundamental understanding of strongly-interacting matter at extreme conditions, as formed in ultra-relativistic nucleus-nucleus collisions, as well as on emergent QCD phenomena in high-multiplicity proton-proton and proton-nucleus collisions.

Research paper thumbnail of 2 2 M ay 2 01 8 Effects of causality on the fluidity and viscous horizon of quark-gluon plasma

The second order Israel-Stewart-Müller relativistic hydrodynamics has been applied to study the e... more The second order Israel-Stewart-Müller relativistic hydrodynamics has been applied to study the effects of causality on the acoustic oscillation in relativistic fluid. Causal dispersion relations have been derived with non-vanishing shear viscosity, bulk viscosity and thermal conductivity at nonzero temperature and baryonic chemical potential. These relations have been used to investigate the fluidity of Quark Gluon Plasma (QGP) at finite temperature (T ). Results of the first order dissipative hydrodynamics have been obtained as limiting case of the second order theory. The effects of the causality on the fluidity near the transition point and on viscous horizon are found to be significant. We observe that the inclusion of causality increases the value of fluidity measure of QGP near Tc and hence makes the flow strenuous. It has also been shown that the inclusion of large magnetic field in the causal hydrodynamics alters the fluidity of QGP.

Research paper thumbnail of Thermal Field Theory of the Tsallis statistics

arXiv: High Energy Physics - Phenomenology, 2019

Classical and quantum Tsallis distributions have been widely used in many branches of natural and... more 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.

Research paper thumbnail of Nonlinear waves in a hot, viscous and nonextensive quark gluon plasma

The effects of the nonextensive statistics on the nonlinear propagation of perturbations have bee... more The effects of the nonextensive statistics on the nonlinear propagation of perturbations have been studied within the scope of relativistic second order dissipative hydrodynamics and the nonextensive equation of state. We have shown that the equations which describe the propagation of nonlinear waves under such situation are KdV-like (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 and propagate faster. The waves deplete more with smaller values of Tsallis parameter, q and lower temperature 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 discern the extensive and non-extensive thermodynamic nature of a fluid such as the quark gluon plasma produced in relativistic nuclear collisions. ∗ go...

Research paper thumbnail of Effect of magnetic screening mass on the diffusion of heavy quarks

International Journal of Modern Physics E

The drag and diffusion coefficients of heavy quarks propagating through quark–gluon plasma (QGP) ... more The drag and diffusion coefficients of heavy quarks propagating through quark–gluon plasma (QGP) have been estimated by shielding the infra-red divergences using electric and magnetic screening masses. The electric-type screening in perturbative quantum chromodynamics (pQCD) has been widely studied and used in evaluating the diffusion coefficient of heavy quarks (HQs). The impact of magnetic screening on diffusion coefficients of HQs is not studied before to the best of our knowledge. We explore the effect of magnetic screening mass on the drag and diffusion coefficients of HQs and found it to be non-negligible. Therefore, the effect of magnetic screening should be taken into consideration to characterize hot and dense matter formed in the collisions of nuclei at ultra-relativistic energies. We estimate the suppression of heavy flavored mesons in heavy ion collisions compared to proton+proton collisions at high transverse momenta and found that the suppression is less with the inclu...

Research paper thumbnail of The fate of nonlinear perturbations near the QCD critical point

Golam Sarwar, ∗ Md Hasanujjaman, † Mahfuzur Rahaman, 4, ‡ Abhijit Bhattacharyya, § and Jan-e Alam... more Golam Sarwar, ∗ Md Hasanujjaman, † Mahfuzur Rahaman, 4, ‡ Abhijit Bhattacharyya, § and Jan-e Alam 4, ¶ Department of Physics,University of Calcutta, 92, A.P.C. Road, Kolkata-700009, India Department of Physics, Darjeeling Government College, Darjeeling734101, India Variable Energy Cyclotron Centre, 1/AF Bidhan Nagar, Kolkata700064, India Homi Bhabha National Institute, Training School Complex, Mumbai 400085, India

Research paper thumbnail of Phenomenological Tsallis distribution from thermal field theory

International Journal of Modern Physics A

Classical and quantum Tsallis distributions have been widely used in many branches of natural and... more 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 [Formula: see text] scalar field theory within the realm of the Tsallis statistics.

Research paper thumbnail of Effects of causality on the fluidity and viscous horizon of quark-gluon plasma

Physical Review C, May 14, 2018

Research paper thumbnail of Dynamics of QCD matter — current status

International Journal of Modern Physics E

In this article, there are 18 sections discussing various current topics in the field of relativi... more 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. More specifically, Sec. 2 discusses mass of [Formula: see text] in the linear sigma model coupled to quarks at zero temperature. In Sec. 7, one-loop calculation of the anisotropic pressure are discussed in the presence of strong magnetic field. In Sec. 9, chiral transition and chiral susceptibility in th...

Research paper thumbnail of Contribution of a kaon component in the viscosity and conductivity of a hadronic medium

With the help of effective Lagrangian densities of strange hadrons, we have calculated kaon relax... more With the help of effective Lagrangian densities of strange hadrons, we have calculated kaon relaxation time from several loop and scattering diagrams at tree-level, which basically represent contributions from 1 ↔ 2 and 2 ↔ 2 type of collisions. Using the total relaxation time of kaon, shear viscosity and electrical conductivity of this kaon component have been estimated. The high temperature, close to transition temperature, where kaon relaxation time is lower than life time of RHIC or LHC matter, may be the only relevant domain for this component to contribute in hadronic dissipation. Our results suggest that kaon can play an important role in the enhancement of shear viscosity and electrical conductivity of hadronic matter near the transition temperature.

Research paper thumbnail of Dispersion and suppression of sound near the QCD critical point

Physical Review C

We have used second-order relativistic hydrodynamics equipped with an equation of state which inc... more We have used second-order relativistic hydrodynamics equipped with an equation of state which includes the critical point to study the propagation of a perturbation in a relativistic QCD fluid. The dispersion relation for the sound wave has been derived to ascertain the fate of the perturbation in the fluid near the QCD critical end point (CEP). We observe that the threshold value of the wavelength of the sound in the fluid diverges at the CEP, implying that all the modes of the perturbation are dissipated at this point. Some consequences of the suppression of sound near the critical point have been discussed.