arXiv subjects

Mikhail Stephanov

Publications and source records attributed to Mikhail Stephanov.

32 records · Page 2Linked to original sources

arXiv2022

Spin relaxation rate for heavy quarks in weakly coupled QCD plasma

We compute the relaxation rate of the spin density of heavy quarks in a perturbative QCD plasma to leading-log order in the coupling constant $g$. The spin relaxation rate $Γ_s$ in spin hydrodynamics is shown to be $Γ_s\sim g^4\log(1/g)T (T/M)^2$ in the heavy-quark limit $T/M\ll 1$, which is smaller than the relaxation rate of other non-hydrodynamic modes by additional powers of $T/M$. We demonstrate three different methods to evaluate the spin relaxation rate: 1) the Green-Kubo formula in the spin hydrodynamic regime, 2) the spin density correlation function in the strict hydrodynamic limit, and 3) quantum kinetic theory of the spin distribution function in momentum space. We highlight the interesting differences between these methods, while they are ultimately connected to each other by the underlying Ward-Takahashi identity for the non-conserved spin density.

hep-th↗

arXiv2022

Relativistic spin hydrodynamics with torsion and linear response theory for spin relaxation

Using the second law of local thermodynamics and the first-order Palatini formalism, we formulate relativistic spin hydrodynamics for quantum field theories with Dirac fermions, such as QED and QCD, in a torsionful curved background. We work in a regime where spin density, which is assumed to relax much slower than other non-hydrodynamic modes, is treated as an independent degree of freedom in an extended hydrodynamic description. Spin hydrodynamics in our approach contains only three non-hydrodynamic modes corresponding to a spin vector, whose relaxation time is controlled by a new transport coefficient: the rotational viscosity. We study linear response theory and observe an interesting mode mixing phenomenon between the transverse shear and the spin density modes. We propose several field-theoretical ways to compute the spin relaxation time and the rotational viscosity, via the Green-Kubo formula based on retarded correlation functions.

hep-th↗

arXiv2021

Fate of Multiparticle Resonances: From $Q$-Balls to $^3$He Droplets

We consider a system of $N$ nonrelativistic particles which form a near-threshold resonance. Assuming no subset of these particles can form a bound state, the resonance can only decay through an "explosion" into $N$ particles. We show that the decay width of the resonance scales as $E^{Δ-5/2}$ in the limit when the energy $E$ of the resonance goes to zero, where $Δ$ is the ground state energy of a system of $N$ particles in a spherical harmonic trap with unit frequency. The formula remains valid when some pairs of final particles have zero-energy $s$-wave resonance, but the Efimov effect is not present. In the limit of large $N$, we show that the final particles follow a Maxwell-Boltzmann distribution if they are bosons, and a semicircle-like law if they are fermions. We argue that metastable $^3$He droplets exist with the lifetime varying over many orders of magnitudes ranging from a fraction of a nanosecond to values greatly exceeding the age of the Universe.

nucl-th↗

arXiv2021

The BEST framework for the search for the QCD critical point and the chiral magnetic effect

The Beam Energy Scan Theory (BEST) Collaboration was formed with the goal of providing a theoretical framework for analyzing data from the Beam Energy Scan (BES) program at the relativistic heavy ion collider (RHIC) at Brookhaven National Laboratory. The physics goal of the BES program is the search for a conjectured QCD critical point as well as for manifestations of the chiral magnetic effect. We describe progress that has been made over the previous five years. This includes studies of the equation of state and equilibrium susceptibilities, the development of suitable initial state models, progress in constructing a hydrodynamic framework that includes fluctuations and anomalous transport effects, as well as the development of freezeout prescriptions and hadronic transport models. Finally, we address the challenge of integrating these components into a complete analysis framework. This document describes the collective effort of the BEST Collaboration and its collaborators around the world.

nucl-th↗

arXiv2021

Evolution of Non-Gaussian Hydrodynamic Fluctuations

In the context of the search for the QCD critical point using non-Gaussian fluctuations, we obtain the evolution equations for non-Gaussian cumulants to the leading order of the systematic expansion in the magnitude of thermal fluctuations. We develop a diagrammatic technique in which the leading order contributions are given by tree diagrams. We introduce a Wigner transform for multipoint correlators and derive the evolution equations for three- and four-point Wigner functions for the problem of nonlinear stochastic diffusion with multiplicative noise.

hep-th↗

arXiv2020

The phase diagram of ultra quantum liquids

We discuss the dependence of the phase diagram of a hypothetical isotope of helium with nuclear mass less than 4 atomic mass units. We argue that with decreasing nucleus mass, the temperature of the superfluid phase transition (about 2.2 K in real He-4) increases, while that of the liquid-gas critical point (about 5.2 K in real He-4) decreases. We discuss various scenarios that may occur when the two temperatures approach each other and the order parameters of the superfluid and the liquid-gas phase transitions interact with each other. The simplest scenario, in which both order parameters become critical at particular values of the nuclear mass, temperature, and pressure, can be ruled out through on an analysis of the Landau theory. We argue that in the most likely scenario, as the nuclear mass decreases, first, a tricritical point appears on the line separating the superfluid and the normal fluid phase, then the critical point disappears under the first-order part of superfluid phase transition line, and in the end the tricritical point disappears. The last change in the phase diagram occurs when the two-body scattering length crosses zero, which corresponds to the nuclear mass of about 1.55 u. We develop a quantitative theory that allows one to determine the phase diagram in the vicinity of this point. Finally, we discuss several ways to physically realize such liquids.

cond-mat.quant-gas↗

arXiv2020

Mapping the Phases of Quantum Chromodynamics with Beam Energy Scan

We review the present status of the search for a phase transition and critical point as well as anomalous transport phenomena in Quantum Chromodynamics (QCD), with an emphasis on the Beam Energy Scan program at the Relativistic Heavy Ion Collider at Brookhaven National Laboratory. We present the conceptual framework and discuss the observables deemed most sensitive to a phase transition, QCD critical point, and anomalous transport, focusing on fluctuation and correlation measurements. Selected experimental results for these observables together with those characterizing the global properties of the systems created in heavy ion collisions are presented. We then discuss what can be already learned from the currently available data about the QCD critical point and anomalous transport as well as what additional measurements and theoretical developments are needed in order to discover these phenomena.

nucl-th↗

arXiv2020

QCD equation of state matched to lattice data and exhibiting a critical point singularity

We construct a family of equations of state for QCD in the temperature range 30 MeV $\leq T\leq$ 800 MeV and in the chemical potential range $0\leq μ_B \leq$ 450 MeV. These equations of state match available lattice QCD results up to $\mathcal{O}(μ_B^4)$ and in each of them we place a critical point in the 3D Ising model universality class. The position of this critical point can be chosen in the range of chemical potentials covered by the second Beam Energy Scan at RHIC. We discuss possible choices for the free parameters, which arise from mapping the Ising model onto QCD. Our results for the pressure, entropy density, baryon density, energy density and speed of sound can be used as inputs in the hydrodynamical simulations of the fireball created in heavy ion collisions. We also show our result for the second cumulant of the baryon number in thermal equilibrium, displaying its divergence at the critical point. In the future, comparisons between RHIC data and the output of the hydrodynamic simulations, including calculations of fluctuation observables, built upon the model equations of state that we have constructed may be used to locate the critical point in the QCD phase diagram, if there is one to be found.

hep-ph↗

arXiv2019

Fluctuation dynamics in a relativistic fluid with a critical point

To describe dynamics of bulk and fluctuations near the QCD critical point we develop general relativistic fluctuation formalism for a fluid carrying baryon charge. Feedback of fluctuations modifies hydrodynamic coefficients including bulk viscosity and conductivity and introduces nonlocal and non-instantaneous terms in constitutive equations. We perform necessary ultraviolet (short-distance) renormalization to obtain cutoff independent deterministic equations suitable for numerical implementation. We use the equations to calculate the universal non-analytic small-frequency dependence of transport coefficients due to fluctuations (long-time tails). Focusing on the critical mode we show how this general formalism matches existing Hydro+ description of fluctuations near the QCD critical point and nontrivially extends it inside and outside of the critical region.

hep-th↗

arXiv2019

Universality of the critical point mapping between Ising model and QCD at small quark mass

The universality of the QCD equation of state near the critical point is expressed by mapping pressure as a function of temperature $T$ and baryon chemical potential $μ$ in QCD to Gibbs free energy as a function of reduced temperature $r$ and magnetic field $h$ in the Ising model. The mapping parameters are, in general, not universal, i.e., determined by details of the microscopic dynamics, rather than by symmetries and long-distance dynamics. In this paper we point out that in the limit of small quark masses, when the critical point is close to the tricritical point, the mapping parameters show universal dependence on the quark mass $m_q$. In particular, the angle between the $r=0$ and $h=0$ lines in the $(μ,T)$ plane vanishes as $m_q^{2/5}$. We discuss possible phenomenological consequences of these findings.

hep-ph↗

arXiv2019

Relativistic Hydrodynamic Fluctuations

We present a general systematic formalism for describing dynamics of fluctuations in an arbitrary relativistic hydrodynamic flow, including their feedback (known as long-time hydrodynamic tails). The fluctuations are described by two-point equal-time correlation functions. We introduce a definition of equal time in a situation where the local rest frame is determined by the local flow velocity, and a method of taking derivatives and Wigner transforms of such equal-time correlation functions, which we call confluent. We find that the equations for confluent Wigner functions not only resemble kinetic equations, but that the kinetic equation for phonons propagating on an arbitrary background nontrivially matches the equations for Wigner functions, including relativistic inertial and Coriolis forces due to acceleration and vorticity of the flow. We also describe the procedure of renormalization of short-distance singularities which eliminates cutoff dependence, allowing efficient numerical implementation of these equations.

hep-th↗

arXiv2014

Collective Modes of Chiral Kinetic Theory in Magnetic Field

We study collective excitations in systems described by chiral kinetic theory in external magnetic field. We consider high-temperature weak-coupling plasma, as well as high-density Landau Fermi liquid with interaction not restricted to be weak. We show that chiral magnetic wave (CMW) emerges in hydrodynamic regime (at frequencies smaller than collision relaxation rate) and the CMW velocity is determined by thermodynamic properties only. We find that in a plasma of opposite chiralities, at frequencies smaller than the chirality-flipping rate, the CMW excitation turns into a vector-like diffusion mode. In the interacting Fermi liquid, the CMW turns into the Landau zero sound mode in the high-frequency collisionless regime.

hep-th↗

arXiv2014

Reversing a heavy-ion collision

We introduce a novel approach to study the longitudinal hydrodynamic expansion of the quark-gluon fluid created in heavy-ion collisions. It consists of two steps: First, we apply the maximum entropy method to reconstruct the freeze-out surface from experimentally measured particle distribution. We then take the output of the reconstruction as the "initial" condition to evolve the system back in time by solving the 1+1 ideal hydrodynamic equations analytically, using the method of Khalatnikov and Landau. We find an approximate Bjorken-like plateau in the energy density vs rapidity profile at the early times, which shrinks with time as the boundary shocks propagate inward. In Bjorken frame, the fluid velocity is close to zero within the plateau, as in the Bjorken solution, but increases outside the plateau. The results carry implications for fully numerical hydrodynamic simulations as well as models of heavy-ion collisions based on gauge-gravity duality.

nucl-th↗

arXiv2012

Hydrodynamic fluctuations and two-point correlations

We examine correlations of energy density induced by initial state fluctuations, which are localized in both transverse and longitudinal extent. The hotspots are evolved according to hydrodynamics in a background which includes radial flow. Two-point energy density correlations from these hotspots are computed as a function of the difference in azimuthal angle and rapidity. Such localized perturbations occur naturally in the theory of hydrodynamic fluctuations and may provide insight into some features of the two-particle correlation data from RHIC and the LHC.

nucl-th↗