arXiv subjects

N. Sadooghi

Publications and source records attributed to N. Sadooghi.

At least 19 recordsLinked to original sources

arXiv2026

Weak Bose-Einstein condensation in a rigidly rotating magnetized charged Bose gas

We investigate the weak Bose-Einstein condensation (BEC) scenario of a noninteracting charged Bose gas simultaneously subjected to a strong magnetic field and rigid rotation. Using standard methods of finite-temperature quantum field theory and the generalized Fock-Schwinger formalism, we derive the corresponding thermodynamic potential in the nonrelativistic and lowest Landau level approximations. An appropriate modification of the effective chemical potential yields a consistent thermodynamic description and naturally introduces a magnetorotational fugacity. Within the high-temperature approximation, rigid rotation enters the thermodynamics solely through the Tolman-Ehrenfest local temperature. We demonstrate that rigid rotation does not qualitatively modify the weak BEC scenario induced by Landau quantization. The magnetorotational fugacity remains below unity throughout the phenomenologically relevant temperature range, while the continuous evolution of the ground state population and the absence of a singularity in the specific heat provide complementary signatures of the persistence of weak BEC. We further study the thermodynamic properties of the system under conditions relevant to quark-gluon plasma and neutron-star matter. We show that rotational effects are much more pronounced in the former. Our analysis reveals a new magnetic response to rigid rotation: while magnetic fields enhance diamagnetism, rotation drives it toward paramagnetism. This behavior reflects a competition between magnetic quantization and rotational orbital motion, emphasizing the role of rotation in shaping the magnetic response of bosonic matter.

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arXiv2026

Relativistic Barnett effect and Curie law in a rigidly rotating free Fermi gas

By combining methods from thermal field theory and statistical mechanics, we reexamine the spin polarization caused by the relativistic Barnett effect in a rigidly rotating Fermi gas. We determine the pressure of this medium and show that it depends on an effective chemical potential, which includes contributions from orbital angular momentum-rotation and spin-rotation coupling. We introduce a specific regularization scheme to sum over the angular momentum quantum numbers. As a result, the thermal pressure and all thermodynamic quantities are separated into two parts that differ only in the spin fugacities of spin-up and spin-down fermions. We calculate the Fermi energy for both components and show that the Fermi energy of the spin-down fermions is lower than that of the spin-up ones. This difference arises from the spin-rotation coupling and leads to a spin polarization consistent with the Barnett effect. In particular, we introduce the spin-chemicorotational ratio $\eta\equiv \Omega^{(0)}/2\mu^{(0)}$, which adjusts the spin polarization of the Fermi gas. Here, $\Omega^{(0)}$ and $\mu^{(0)}$ represent the angular velocity and chemical potential at zero temperature, respectively. The factor $1/2$ accounts for the fermion's spin. We explore the temperature dependence of $\mu$ and $\Omega$, while assuming that the number of spin-up and spin-down fermions remains temperature independent. Our findings indicate that the spin-down component of the rotating Fermi gas dilutes at lower temperatures compared to the spin-up component. Additionally, we calculate the magnetic susceptibility arising from the Barnett magnetization and demonstrate that it is proportional to the moment of inertia $I$ of the rotating Fermi gas. Finally, we prove that $I$ exhibits a $1/T$ behavior in the high-temperature limit, similar to the Curie law of paramagnetism.

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arXiv2025

Wigner function of a rigidly rotating and magnetized QED plasma

We determine the Wigner function of a rigidly rotating quantum electrodynamics (QED) plasma in the presence of a constant magnetic field by utilizing the Riemannian normal coordinate approximation, which has been previously proposed in the literature. In this approach, the angular velocity appears only in a specific phase factor, allowing us to compute the point-split fermion two-point correlation function in flat spacetime. To ensure that the fermion correlation function is gauge invariant, we introduce a background gauge field that is fixed to produce a constant magnetic field. Using this Wigner function, we derive the energy-momentum tensor for this medium, which consists of both diagonal and off-diagonal components. By comparing our results with the energy-momentum tensor of an ideal spinful and vortical magnetized fluid, we establish a connection between these components and thermodynamic quantities, such as energy density and different types of pressure. We demonstrate that rigid rotation leads to pressure anisotropy in plasma. Additionally, we compute the associated vector and axial vector currents for this medium, utilizing the previously presented Wigner function. Our results are consistent with existing literature on the subject.

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arXiv2025

Chiral vortical conductivities and the moment of inertia of a rigidly rotating Fermi gas

We determine the chiral vortical conductivities, as well as the orbital and spin moment of inertia of a charged, chiral, and rigidly rotating free Fermi gas. To this purpose, we begin by calculating the vacuum expectation values of a vector and axial vector current using the free fermion propagator in this medium. This propagator is derived by employing the Fock-Schwinger method based on the solutions of the Dirac equation in the presence of rotation and finite axial chemical potential. We present a complete derivation of these solutions. We demonstrate that in the first approximation, the chiral vortical conductivity associated with the vector current is proportional to the product of the vector and axial chemical potentials. In contrast, the chiral vortical conductivity related to the axial vector current depends on the temperature, the vector, and the axial vector chemical potential squares. We use the relation between the axial vector current and the angular momentum density associated with spin to determine the spin and the orbital moment of inertia of a rigidly rotating Fermi gas in a charged and chirally imbalanced medium separately. In addition, we compute the total moment of inertia by utilizing the methods presented in the first part of the paper and show that the orbital moment of inertia of a free fermion gas vanishes.

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arXiv2025

Spontaneous breaking of global U(1) symmetry in an interacting Bose gas under rigid rotation

We investigate the impact of rigid rotation on the spontaneous breaking of U(1) symmetry in a Bose gas, which is described by a self-interacting complex scalar field Lagrangian. Rigid rotation is introduced through a specific metric that explicitly depends on the angular velocity $Ω$. We begin by determining the free propagator for this model at finite temperature $T$ and chemical potential $μ$. Using this propagator, we calculate the thermodynamic potential in terms of an energy dispersion relation $ε_{k}$. It is found that in both the U(1) symmetric phase and the symmetry-broken phase, two energy branches emerge. In the symmetry-broken phase, they are identified with a massive phonon and a massless roton mode. Notably, rotation does not alter $ε_{k}$ at low momentum. Setting $μ=0$, we use the total thermodynamic potential, which includes classical, thermal, vacuum, and nonperturbative ring contributions, to explore how the condensate depends on $T$ and $Ω$. We first focus on the classical and thermal parts of the thermodynamic potential and find that the critical temperature of the U(1) phase transition scales as $Ω^{1/3}$. By identifying the (pseudo-)Goldstone and non-Goldstone modes of this model with $π$ and $σ$ mesons, we calculate the $T$ and $Ω$ dependence of masses $m_π$ and $m_σ$. We demonstrate that the Goldstone theorem holds only when the one-loop (thermal) corrections to $m_σ$ and $m_π$ are taken into account. We further explore the $T$ and $Ω$ dependence of the condensate, determine the $σ$ dissociation temperatures for fixed $Ω$, and compare them with the critical temperature of the phase transition. Additionally, we emphasize the role played by the nonperturbative ring potential, especially in altering the order of the phase transition with and without rotation.

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arXiv2025

Bose-Einstein condensation in a rigidly rotating relativistic boson gas

We study the Bose-Einstein condensation (BEC) of a free Bose gas under rigid rotation. The aim is to explore the impact of rotation on the thermodynamic quantities associated with BEC, including the Bose-Einstein (BE) transition temperature and condensate fraction. We begin by introducing the rotation in the Lagrangian density of free charged Klein-Gordon fields and determine the corresponding grand canonical partition function at finite temperature, chemical potential, and finite angular velocity. Assuming slow rotation, we derive analytical expressions for the pressure, energy, number, and angular momentum densities of a free Bose gas in nonrelativistic and ultrarelativistic limits in terms of the corresponding fugacities. We then focus on the phenomenon of BEC. We calculate the critical temperature of BEC transition and the condensate fraction in a slowly rotating Bose gas including only particles. Our findings indicate that the critical exponent associated with the BE transition in a rotating gas is lower compared to that in a nonrotating Bose gas. We also determine the fugacity in a rotating Bose gas in the aforementioned limits and examine how rotation affects its temperature dependence, both below and above the critical temperature. By analyzing the behavior of heat capacity at these temperatures, we demonstrate that in a nonrelativistic Bose gas, the rotation transforms the nature of the BE phase transition from a continuous to a discontinuous transition. In general, we find that a nonrelativistic Bose gas under rotation behaves similarly to a nonrotating Bose gas in ultrarelativistic limit.

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arXiv2024

Boson propagator under rigid rotation; Mode expansion approach

To explore how rigid rotation affects the thermodynamic properties of free relativistic bosons, we employ the standard imaginary time formalism of thermal field theory to calculate the free propagator of complex scalar fields under rotation. We introduce the corresponding partition function and explicitly compute it by expanding the modes in cylindrical coordinates. The resulting propagator is in full agreement with similar findings in the existing literature.

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arXiv2024

Thermodynamic properties of a relativistic Bose gas under rigid rotation

We study the thermodynamic properties of a rigidly rotating relativistic Bose gas. First, we derive the solution of the equation of motion corresponding to a rotating complex Klein-Gordon field and determine the free propagator of this model utilizing the Fock-Schwinger proper-time method. Using this propagator, we then obtain the thermodynamic potential of this model in the zeroth and first perturbative level. In addition, we compute the nonperturbative ring contribution to this potential. Our focus is on the dependence of these expressions on the angular velocity, which effectively acts as a chemical potential. Using this thermodynamic potential, we calculate several quantities, including the pressure, angular momentum and entropy densities, heat capacity, speed of sound, and moment of inertia of this rigidly rotating Bose gas as functions of temperature ($T$), angular velocity ($Ω$), and the coupling constant ($α$). We show that certain thermodynamic instabilities appear at high temperatures and large couplings. They are manifested as zero and negative values of the above quantities, particularly the moment of inertia and heat capacity. Zero moment of inertia leads to the phenomenon of supervorticity at certain $T$ or $α$. Supervortical temperatures (couplings) decrease with increasing coupling (temperature). We also observe superluminal sound velocities at high $T$ and for large $α$.

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arXiv2023

Relativistic magnetohydrodynamics of a spinful and vortical fluid: Entropy current analysis

We generalize a recently introduced formulation of relativistic spinful and vortical fluid to relativistic magnetohydrodynamics (MHD). We refer to it as the "Spinful-Vortical MHD" (SVMHD). The aim is to scrutinize the interplay between the vorticity, magnetic field, and spin, which is treated as a quantum object, in contrast to other formulations of spin hydrodynamics. To this purpose, we first perform a standard entropy current analysis up to first-order gradient expansion, $\mathcal{O}\left(\partial\right)$ as well as $\mathcal{O}\left(\hbar\partial\right)$, where $\hbar$ is the Planck constant. In contrast to alternative formulations of spin MHD, in the absence of vorticity, the zeroth-order energy-momentum tensor includes an additional magneto-vorticity mixed term and reduces, as expected, to the energy-momentum tensor of MHD. We show that in the first-order of gradient expansion, $36$ dissipative transport coefficients appear. They satisfy certain constraints that guarantee the positive definiteness of the entropy production rate. We then modify the formulation of SVMHD by replacing the magnetic part of the thermal vorticity tensor with its electric part. Carrying out the same analysis as in the standard formulation, we show that in this case, the first-order constitutive relations consist of $11$ nondissipative Hall-like coefficients, apart from $25$ dissipative coefficients. This difference arises from different behavior of the electric and magnetic part of the thermal vorticity under time-reversal transformation.

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arXiv2023

The magnetic dual chiral density wave phase in a rotating cold quark matter

The effect of rotation on the formation of the magnetic dual chiral density wave (\MD) in a dense and magnetized cold quark matter is studied. This phase is supposed to exist in the extreme conditions prevailing, e.g., in a neutron star. These conditions are, apart from high densities and strong magnetic fields, a relatively large angular velocity. To answer the question of whether the rotation enhances or suppresses the formation of this phase, we first determine the effect of rotation on the energy dispersion relation of a fermionic system in the presence of a constant magnetic field and then focus on the thermodynamic potential of the model at low temperature $T$ and finite chemical potential $μ$. The thermodynamic potential consists, in particular, of an anomalous part leading to certain topological effects. We show that in comparison with the nonrotating case, a term proportional to the angular velocity appears in this anomalous potential. We then solve the corresponding gap equations to the chiral and spatial modulation condensates, and study the dependence of these dynamical variables on the chemical potential ($μ$), magnetic field ($eB$), and angular velocity ($Ω$). It turns out that the interplay between these parameters suppresses the formation of the \MD~phase in relevant regimes for cold neutron stars. This is interpreted as the manifestation of the inverse magnetorotational catalysis, which is also reflected in the phase portraits $eB$-$μ$, $eB$-$ΩR$, and $μ$-$ΩR$, explored in this work.

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arXiv2021

Inverse magneto-rotational catalysis and the phase diagram of a rotating hot and magnetized quark matter

We study the properties of a hot and magnetized quark matter in a rotating cylinder in the presence of a constant magnetic field. To do this, we solve the corresponding Dirac equation using the Ritus eigenfunction method. This leads to the energy dispersion relation, Ritus eigenfunctions, and the quantization relation for magnetized fermions. To avoid causality-violating effects, we impose a certain global boundary condition, and study its effect, in particular, on the energy eigenmodes and the quantization relations of fermions. Using the fermion propagator arising from this method, we then solve the gap equation at zero and nonzero temperatures. At zero temperature, the dynamical mass $\bar{m}$ does not depend on the angular frequency, as expected. We thus study its dependence on the distance $r$ relative to the axis of rotation and the magnetic field $B$, and explore the corresponding finite size effect for various couplings $G$. We then consider the finite temperature case. The dependence of $\bar{m}$ on the temperature $T$, magnetic field $B$, angular frequency $Ω$, and distance $r$ for various $G$ is studied. We show that $\bar{m}$ decreases, in general, with $B$ and $Ω$. This is the ''inverse magneto-rotational catalysis (IMRC)'' or the ''rotational magnetic inhibition'', previously discussed in the literature. To explore the evidence of this effect in the phase diagrams of our model, we examine the phase portraits of the critical temperature $T_c$ as well as the critical angular frequency $Ω_c$ with respect to $G, B,Ω$, and $r$ as well as $G, B, T$, and $r$, respectively. We show that $T_{c}$ and $Ω_c$ decrease, in particular, with $B$. This is interpreted as clear evidence for IMRC.

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arXiv2021

Anomalous Hall instability in the Chern-Simons magnetohydrodynamics

The Chern-Simons magnetohydrodynamics (CSMHD) is introduced using a Maxwell-Chern-Simons (MCS) Lagrangian including an axion-like field $Θ$. The MCS equation of motion derived from this Lagrangian consists of a modified current, including a chiral magnetic (CM) and an anomalous Hall (AH) current, in addition to the ordinary Ohm current of resistive magnetohydrodynamics (MHD). The former consists of an axial chemical potential, which is given in terms of the temporal comoving derivative of $Θ$, and the latter arises from the spatial gradient of $Θ$. As it turns out, the existence of the axial chemical potential is a nonequilibrium effect that plays no role in the linear stability analysis, whereas the AH current arises as in the first-order linear perturbation of the thermal equilibrium. We analyze the linear stability and causality of the CSMHD in a resistive and chiral medium. We show that the Alfven modes propagating sufficiently close to the direction of the magnetic field are unstable but causal. They are also accompanied by a genuine nonhydro mode. A stable mode in a particular direction can correspond to an unstable mode propagating in the exact opposite direction. The AH instability is a manifestation of a breakdown of the parity. A numerical analysis of the phase velocity confirms these results.

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arXiv2020

Wigner function formalism and the evolution of thermodynamic quantities in an expanding magnetized plasma

By combining the Wigner function formalism of relativistic quantum kinetic theory with fundamental equations of relativistic magnetohydrodynamics (MHD), we present a novel approach to determine the proper time evolution of the temperature and other thermodynamic quantities in a uniformly expanding hot, magnetized, and weakly interacting plasma. The aim is to study the contribution of quantum corrections to this evolution. We first determine the corresponding Wigner function in terms of the solution of the Dirac equation in the presence of a constant magnetic field. Using this function, we then compute the energy-momentum tensor of the above-mentioned plasma, which eventually yields its energy density and pressure. Plugging these quantities in the energy equation of relativistic MHD, we arrive, after choosing an appropriate coordinate system, at a differential equation for the temperature as a function of the proper time. The numerical solution of this equation leads finally to the proper time evolution of the temperature. The latter is then used to determine the evolution of a large number of thermodynamic quantities in this expanding and magnetized plasma. We compare our results with other existing results from relativistic MHD. We also comment on the effect of point to point decaying magnetic fields on the thermodynamic properties of this plasma.

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arXiv2019

Paramagnetic squeezing of a uniformly expanding quark-gluon plasma in and out of equilibrium

The plasma of quarks and gluons created in ultrarelativistic heavy-ion collisions turns out to be paramagnetic. In the presence of a background magnetic field, this paramagnetism thus leads to a pressure anisotropy, similar to anisotropies appearing in a viscous fluid. In the present paper, we use this analogy, and develop a framework similar to anisotropic hydrodynamics, to take the pressure anisotropy caused, in particular, by the nonvanishing magnetization of a plasma of quarks and gluons into account. We consider the first two moments of the classical Boltzmann equation in the presence of an electromagnetic source in the relaxation-time approximation, and derive a set of coupled differential equations for the anisotropy parameter $ξ_0$ and the effective temperature $λ_0$ of an ideal fluid with nonvanishing magnetization. We also extend this method to a dissipative fluid with finite magnetization in the presence of a strong and dynamical magnetic field. We present a systematic method leading to the one-particle distribution function of this magnetized dissipative medium in a first-order derivative expansion, and arrive at analytical expressions for the shear and bulk viscosities in terms of the anisotropy parameter $ξ$ and effective temperature $λ$. We then solve the corresponding differential equations for $(ξ_0,λ_0)$ and $(ξ,λ)$ numerically, and determine, in this way, the proper time and temperature dependence of the energy density, directional pressures, speed of sound, and the magnetic susceptibility of a longitudinally expanding magnetized quark-gluon plasma in and out of equilibrium.

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arXiv2019

Proper time evolution of magnetic susceptibility in a magnetized quark-gluon plasma

In ultrarelativistic heavy-ion collisions, enormous magnetic fields are generated because of fast-moving charged particles. In the presence of these magnetic fields, the spin of particles is aligned either in the parallel or in the antiparallel direction with respect to the direction of the magnetic field. A finite magnetization is thus produced. It is known that a finite magnetic susceptibility, $χ_{m}$, changes the evolution of the energy density of the quark-gluon plasma (QGP), which is believed to be created in these collisions. Depending on whether the system under consideration is a paramagnetic ($χ_{m}>0$) or diamagnetic ($χ_{m}<0$) fluid, it slows down or speeds up the decay of the energy density, and affects other thermodynamic quantities. In general, one expects that the magnetic susceptibility depends on the magnetic field and temperature. Bearing in mind that these parameters evolve with the evolution of the fluid, a nonuniform magnetic susceptibility in this system is thus expected. In this work, we first determine $χ_{m}$ by using a certain analogy to the standard anisotropic kinetic theory, where the one-particle distribution function is replaced by the corresponding anisotropic distribution function. We then determine the proper time dependence of the magnetic susceptibility in the framework of the ideal transverse magnetohydrodynamics. We also study the effect of dissipation on the evolution of $χ_{m}$.

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arXiv2019

Evolution of magnetic fields in a transversely expanding highly conductive fluid

Due to the absence of a transverse expansion with respect to the beam direction, the Bjorken flow is unable to describe certain observables in heavy ion collisions. This caveat has motivated the introduction of analytical relativistic hydrodynamics (RH) solutions with transverse expansion, in particular, the 3+1 self-similar (SSF) and Gubser flows. Inspired by recent generalizations of the Bjorken flow to the relativistic magnetohydrodynamics (RMHD), we present a procedure for a generalization of RH solutions to RMHD. Our method is mainly based on symmetry arguments. Using this method, we find the relation between RH degrees of freedom and the magnetic field evolution in the ideal limit for an infinitely conductive fluid, and determine the proper time dependence of the magnetic field in aforementioned flows. In the case of SSF, a family of solutions are found that are related through a certain differential equation. To find the magnetic field evolution in the Gubser flow, we solve RMHD equations for a stationary fluid in a conformally flat $dS^3\times E^1$ spacetime. The result is then Weyl transformed back into the Minkowski spacetime. In this case, the temporal evolution of the magnetic field exhibits a transmission between $1/t$ to $1/t^3$ near the center of the collision. The longitudinal component of the magnetic field is found to be sensitive to the transverse size of the fluid. We also find the radial evolution of the magnetic field for both flows. The radial domain of validity in the case of SSF is highly restricted, in contrast to the Gubser flow. A comparison of the results suggests that the Gubser RMHD may give a more appropriate qualitative picture of the magnetic field decay in the quark-gluon plasma (QGP).

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arXiv2019

Rotating solutions of nonideal transverse Chern-Simons magnetohydrodynamics and the anomalous Hall current

In order to gain deeper insight into the physics of the novel rotating solution of nonideal transverse magnetohydrodynamics (MHD), presented in one of our recent works, we replace the previously considered Maxwell theory with the ${\cal{CP}}$ violating Maxwell-Chern-Simons (MCS) theory. In this way, dissipationless chiral magnetic (CM) and anomalous Hall (AH) currents appear in the MCS equation of motion, that, together with equations of relativistic hydrodynamics, builds the set of constitutive equations of the nonideal transverse Chern-Simons magnetohydrodynamics (CSMHD). We are, in particular, interested in the effect of these currents on the evolution of electromagnetic fields in a uniformly and longitudinally expanding quark-gluon plasma with chirality imbalance. Combining the constitutive equations of CSMHD under these assumptions, we arrive, as expected, at two distinct rotating and nonrotating solutions for electromagnetic fields. The rotation occurs with increasing rapidity and a constant angular velocity $ω_{0}$. Remarkably, the relative angle between the electric and magnetic fields, $δ$, turns out to be given by the coefficient of AH current $κ_{E}$ and the electric conductivity of the medium $σ$, as $δ=\tan^{-1}(κ_{E}/σ)$. Whereas the nonrotating solution implies the AH coefficient to be vanishing, and thus nonrotating electric and magnetic fields to be either parallel or antiparallel, the relative orientation of rotating electric and magnetic fields and the evolution of the CM conductivity $κ_{B}$ are strongly affected by nonvanishing $κ_{E}$. We explore the effect of positive and negative $ω_{0}$ on the evolution of the CM current, and show, in particular, that a rotation of electromagnetic fields with negative $ω_{0}$ implies a sign flip of the CM current in a chiral fluid with nonvanishing AH current.

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arXiv2018

Evolution of magnetic fields from the 3+1 dimensional self-similar and Gubser flows in ideal relativistic magnetohydrodynamics

Motivated by the recently found realization of the $1+1$ dimensional Bjorken flow in ideal and nonideal relativistic magnetohydrodynamics (MHD), we use appropriate symmetry arguments, and determine the evolution of magnetic fields arising from the $3+1$ dimensional self-similar and Gubser flows in an infinitely conductive relativistic fluid (ideal MHD). In the case of the $3+1$ dimensional self-similar flow, we arrive at a family of solutions, that are related through a differential equation arising from the corresponding Euler equation. To find the magnetic field evolution from the Gubser flow, we solve the MHD equations of a stationary fluid in a conformally flat $dS^{3}\times E^{1}$ spacetime. The results are then Weyl transformed back into the Minkowski spacetime. In this case, the temporal evolution of the resulting magnetic field is shown to exhibit a transition between an early time $1/t$ decay to a $1/t^{3}$ decay at a late time. Here, $t$ is the time coordinate. Transverse and longitudinal components of the magnetic fields arising from these flows are also found. The latter turns out to be sensitive to the transverse size of the fluid. In contrast to the result arising from the Gubser flow, the radial domain of validity of the magnetic field arising from the self-similar flow is highly restricted. A comparison of the results suggests that the (conformal) Gubser MHD may give a more appropriate qualitative picture of the magnetic field decay in the plasma of quarks and gluons created in heavy ion collisions.

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