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Mikhail Stephanov

Publications and source records attributed to Mikhail Stephanov.

At least 19 recordsLinked to original sources
arXiv2026

Non-Gaussian fluctuations in relativistic hydrodynamics: Confluent equations for three-point correlations

We derive deterministic equations for the evolution of non-Gaussian fluctuations in relativistic stochastic hydrodynamics. This is achieved by defining the average local Landau frame and corresponding fluctuating hydrodynamic variables. Fully nonlinear stochastic hydrodynamics is expressed in a unified multi-component matrix form. A novel relativistic formalism, also manifestly covariant under SO(3) rotations of the local spatial basis in the average local Landau frame, is introduced. The equations describe correlators of all hydrodynamic variables, including fluctuating velocity (or momentum density) -- a nontrivial problem in relativistic hydrodynamics.

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arXiv2026

Equation of state and cumulants of proton multiplicity in equilibrium near critical point from Pade estimates

The fluctuations of proton multiplicity in heavy-ion collisions are the key observables in the search for the QCD critical point. In this work we present an approach to constraining the cumulants of proton number based on the analytical properties of the QCD equation of state in the vicinity of the critical point. We show that, under the assumption of local equilibrium, the features of the collision energy dependence, such as the peaks and the dips of the cumulants, are significantly constrained by the data on the Lee-Yang singularity structure available via Pade resummation of the lattice QCD data. Furthermore, we identify four topologically distinct scenarios, all within the uncertainty range of the Pade estimates for the non-universal mapping parameters, classified based on the location of the critical point and the slope of the chiral crossover curve with respect to the freeze-out curve. These different scenarios result in qualitatively different critical signatures, especially for the third factorial cumulant and thus could be potentially discriminated using the experimental data.

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arXiv2025

Factorial cumulants of proton multiplicity near a critical point using maximum entropy freeze-out prescription

We present the first application of the maximum-entropy freeze-out prescription to calculate factorial cumulants of proton multiplicities near the conjectured QCD critical point in thermal equilibrium. We map the Gibbs free energy of the 3D Ising model to a parameterized class of possible EoS near QCD critical point. This equilibrium baseline highlights how factorial cumulants isolate critical fluctuations by subtracting trivial self-correlations, setting the stage for future out-of-equilibrium analyses. We identify the key non-universal aspects of the mapping to the Ising model that strongly control the characteristic properties, such as magnitude and location of the peaks of the factorial cumulants along the freeze-out curve.

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arXiv2025

Quantifying fluctuation signatures of the QCD critical point using maximum entropy freeze-out

A key question about the QCD phase diagram is whether there is a critical point somewhere on the boundary between the hadronic and quark-gluon plasma phases, and if so where. Heavy-ion collisions offer a unique opportunity to search for signatures of such a critical point by analyzing event-by-event fluctuations in particle multiplicities. To draw meaningful conclusions from experimental data, a theoretical framework is needed to link QCD thermodynamics with the particle spectra and correlations observed in detectors. The Equation of State (EoS) of QCD near a critical point can be related to the universal Gibbs free energy of the 3D Ising model using four currently unknown non-universal mapping parameters whose values are determined by the microscopic details of QCD. We utilize the maximum entropy approach to freeze-out the fluctuations in order to make estimates for factorial cumulants of proton multiplicities, assuming thermal equilibrium, for a family of EoS with a 3D Ising-like critical point, varying the microscopic inputs that determine the strength and structure of the critical features. We quantify the effect of the non-universal mapping parameters, and the distance between the critical point and the freeze-out curve, on the factorial cumulants of proton multiplicities.

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arXiv2025

Enhancement of photon emission rate near QCD critical point

We compute photon emission rate enhancement near the QCD critical point using an effective theory of dynamic critical phenomena and derive a universal photon spectrum. The emission rate scales similarly to conductivity, increasing with the correlation length ($\xi$), diverging at the critical point. The spectrum exhibits $\omega dN_{\gamma}/d^3k \propto \omega^{-1/2}$ in the scaling regime, with the transition occurring at a frequency comparable to shear damping rate $\omega \sim \gamma_{\eta}/\xi^2$, reflecting the nonequilibrium properties of the near-critical liquid.

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arXiv2024

Equilibrium expectations for non-Gaussian fluctuations near a QCD critical point

With the highly anticipated results from the Beam Energy Scan II program at RHIC being recently revealed, an understanding of particle-number fluctuations and their significance as a potential signature of a possible QCD critical point is crucial. Early works that embarked on this endeavor sought to estimate the fluctuations due to the presence of a critical point assuming they stay in equilibrium. From these results came the proposal to focus efforts on higher, non-Gaussian, moments of the event-by-event distributions, in particular of the number of protons. These non-Gaussian moments are especially sensitive to critical fluctuations, as their magnitudes are proportional to high powers of the critical correlation length. As the equation of state provides key input for hydrodynamical simulations of heavy-ion collisions, we estimate equilibrium fluctuations from the BEST equation of state (EoS) that includes critical features from the 3D Ising Model. In particular, the proton factorial cumulants and their dependence on non-universal mapping parameters is investigated within the BEST EoS. Furthermore, the correlation length, as a central quantity for the assessment of fluctuations in the vicinity of a critical point, is also calculated in a consistent manner with the scaling equation of state. An understanding of the equilibrium estimates of proton factorial cumulants will be useful for further comparison to estimates of out-of-equilibrium fluctuations in order to determine the magnitude of the observable fluctuations to be expected in heavy-ion collision experiments, in which the time spent near a critical point is short.

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arXiv2024

Relativistic Guiding-Center Motion: Action Principle, Kinetic Theory, and Hydrodynamics

We treat the guiding-center dynamics in a varying external Maxwell field using a relativistically covariant action principle which reproduces the known Vandervoort expression for the drift velocity and extends it to curved spacetime. We derive the corresponding kinetic theory and ideal hydrodynamic theory. In contrast to conventional five-equation hydrodynamics, the guiding-center hydrodynamics needs only three equations due to a constraint on the motion across magnetic field. We argue that such a hydrodynamics is applicable to strongly coupled plasmas where kinetic theory fails.

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arXiv2024

QCD critical point and hydrodynamic fluctuations in relativistic fluids

These lecture notes consist of two major connected parts. The first part (Sections 1, 2), after a brief historical introduction, deals with the physics of critical points in thermodynamic equilibrium. The features of the fluctuations relevant for the QCD critical point search are highlighted. The second part (Sections 3, 4) focuses on the recent developments in the description of the fluctuation dynamics especially relevant for the QCD critical point search in heavy-ion collisions.

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arXiv2024

The QCD phase diagram and Beam Energy Scan physics: a theory overview

We review recent theoretical developments relevant to heavy-ion experiments carried out within the Beam Energy Scan program at the Relativistic Heavy Ion Collider. Our main focus is on the description of the dynamics of systems created in heavy-ion collisions and establishing the necessary connection between the experimental observables and the QCD phase diagram.

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arXiv2024

Nonmonotonic specific entropy on the transition line near the QCD critical point

We investigate the effect of the quantum chromodynamics (QCD) critical point on the isentropic trajectories in the QCD phase diagram. We point out that the universality of the critical equation of state and the third law of thermodynamics require the specific entropy (per baryon) along the coexistence (first-order transition) line to be nonmonotonic at least on one side of that line. Specifically, a maximum must occur. We show how the location of the maximum relative to the QCD critical point depends on the parameters of the critical equation of state commonly used in the literature. We then examine how the isentropic trajectories followed by adiabatically expanding heavy-ion collision fireballs behave near the critical point. We find that a crucial role is played by the sign of the isochoric temperature derivative of pressure at the critical point; this sign determines on which side of the coexistence curve the specific entropy must be nonmonotonic (i.e., has a maximum). We classify different scenarios of the adiabatic expansion that arise depending on the value of the discriminant parameter and the proximity of the trajectory to the critical point.

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arXiv2024

Finite density QCD equation of state: critical point and lattice-based $T'$-expansion

We present a novel construction of the QCD equation of state (EoS) at finite baryon density. Our work combines a recently proposed resummation scheme for lattice QCD results with the universal critical behavior at the QCD critical point. This allows us to obtain a family of equations of state in the range $0 \leq \mu_B \leq 700$ MeV and 25 MeV $\leq T \leq 800$ MeV, which match lattice QCD results near $\mu_B=0$ while featuring a critical point in the 3D Ising model universality class. The position of the critical point can be chosen within the range accessible to beam-energy scan heavy-ion collision experiments. The strength of the singularity and the shape of the critical region are parameterized using a standard parameter set. We impose stability and causality constraints and discuss the available ranges of critical point parameter choices, finding that they extend beyond earlier parametric QCD EoS proposals. We present thermodynamic observables, including baryon density, pressure, entropy density, energy density, baryon susceptibility and speed of sound, that cover a wide range in the QCD phase diagram relevant for experimental exploration.

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arXiv2023

Spin relaxation rate for baryons in thermal pion gas

We study the relaxation dynamics of the spin polarization of baryons (nucleon and $\Lambda$-baryon), in a thermal pion gas as a simple model of the hadronic phase of the QCD plasma produced in relativistic heavy-ion collisions. For this purpose, we formulate the quantum kinetic theory for the spin density matrix of baryons in the leading order of the gradient expansion. Considering the baryon-pion elastic scattering processes as the dominant interaction between baryons and thermal pions, we compute the spin relaxation rate of nucleons and $\Lambda$-baryons in a pion gas up to temperature 200 MeV. In the case of nucleons, we evaluate the spin relaxation rate in the $s$-channel resonance approximation, based on the known experimental data on $\Delta$-resonances. We also estimate the spin relaxation rate for $\Lambda$-baryons, based on experimental inputs and theoretical models for the low-energy $\Lambda$$\pi$ scattering, including the chiral perturbation theory.

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arXiv2022

Non-Gaussian fluctuation dynamics in relativistic fluids

We consider non-equilibrium evolution of non-Gaussian fluctuations within relativistic hydrodynamics relevant for the QCD critical point search in heavy-ion collision experiments. We rely on the hierarchy of relaxation time scales, which emerges in the hydrodynamic regime near the critical point, to focus on the slowest mode such as the fluctuations of specific entropy, whose equilibrium magnitude, non-Gaussianity and typical relaxation time are increasing as the critical point is approached. We derive evolution equations for the non-Gaussian correlators of this diffusive mode in an arbitrary relativistic hydrodynamic flow. We compare with the simpler case of the stochastic diffusion on a static homogeneous background and identify terms which are specific to the case of the full hydrodynamics with pressure fluctuations and flow.

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arXiv2022

Maximum entropy freezeout of hydrodynamic fluctuations

We propose a general approach to freezing out fluctuations in heavy-ion collisions using the principle of maximum entropy. We find the results naturally expressed as a direct relationship between the irreducible relative correlators quantifying the deviations of hydrodynamic as well as hadron gas fluctuations from the ideal hadron gas baseline. The method also allows us to determine heretofore unknown parameters crucial for the freezeout of fluctuations near the QCD critical point in terms of the QCD equation of state.

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arXiv2022

Long Range Plan: Dense matter theory for heavy-ion collisions and neutron stars

Since the release of the 2015 Long Range Plan in Nuclear Physics, major events have occurred that reshaped our understanding of quantum chromodynamics (QCD) and nuclear matter at large densities, in and out of equilibrium. The US nuclear community has an opportunity to capitalize on advances in astrophysical observations and nuclear experiments and engage in an interdisciplinary effort in the theory of dense baryonic matter that connects low- and high-energy nuclear physics, astrophysics, gravitational waves physics, and data science

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arXiv2022

Freezing Out Fluctuations in Hydro+ Near the QCD Critical Point

We introduce a freeze-out procedure to convert the critical fluctuations in a droplet of quark-gluon plasma (QGP) that has, as it expanded and cooled, passed close to a posited critical point on the phase diagram into cumulants of hadron multiplicities that can subsequently be measured. The procedure connects the out-of-equilibrium critical fluctuations described in concert with the hydrodynamic evolution of the droplet of QGP by extended hydrodynamics, known as Hydro+, with the subsequent kinetic description in terms of observable hadrons. We introduce a critical scalar isoscalar field sigma whose fluctuations cause correlations between observed hadrons due to the couplings of the sigma field to the hadrons via their masses. We match the QGP fluctuations obtained by solving the Hydro+ equations describing the evolution of critical fluctuations before freeze-out to the correlations of the sigma field. In turn, these are imprinted onto correlations and fluctuations in the multiplicity of hadrons, most importantly protons, after freeze-out via the generalization of the familiar half-century-old Cooper-Frye freeze-out prescription which we introduce. The proposed framework allows us to study the effects of critical slowing down and the consequent deviation of the observable predictions from equilibrium expectations quantitatively. We also quantify the suppression of cumulants due to conservation of baryon number. We demonstrate the procedure in practice by freezing out a Hydro+ simulation in an azimuthally symmetric and boost invariant background that includes radial flow discussed in arXiv:1908.08539.

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