The search for the QCD critical point in heavy-ion collision experiments requires dynamical simulations of the bulk evolution of QCD matter as well as of fluctuations. We consider two essential ingredients of such a simulation: a generic extension of hydrodynamics by a parametrically slow mode or modes (``$\mathrm{Hydro}+$'') and a description of fluctuations out of equilibrium. By combining the two ingredients, we are able to describe the bulk evolution and the fluctuations within the same framework. Critical slowing-down means that equilibration of fluctuations could be as slow as hydrodynamic evolution, and thus fluctuations could significantly deviate from equilibrium near the critical point. We generalize hydrodynamics to partial-equilibrium conditions where the state of the system is characterized by the off-equilibrium magnitude of fluctuations in addition to the usual hydrodynamic variables---conserved densities. We find that the key element of the new formalism---the extended entropy taking into account the off-equilibrium fluctuations---is remarkably similar to the 2PI action in the quantum field theory. We show how the new $\mathrm{Hydro}+$ formalism reproduces two major effects of critical fluctuations on the bulk evolution: the strong frequency dependence of the anomalously large bulk viscosity as well as the stiffening of the equation of state with an increasing frequency or wave number. While the agreement with known results confirms its validity, the fact that $\mathrm{Hydro}+$ achieves this within a local and deterministic framework gives it significant advantages for dynamical simulations.

Hydrodynamics with parametric slowing down and fluctuations near the critical point

Quantum simulation of fundamental particles and forces

The nuclear equation of state (EOS) is at the center of numerous theoretical and experimental efforts in nuclear physics. With advances in microscopic theories for nuclear interactions, the availability of experiments probing nuclear matter under conditions not reached before, endeavors to develop sophisticated and reliable transport simulations to interpret these experiments, and the advent of multi-messenger astronomy, the next decade will bring new opportunities for determining the nuclear matter EOS, elucidating its dependence on density, temperature, and isospin asymmetry. Among controlled terrestrial experiments, collisions of heavy nuclei at intermediate beam energies (from a few tens of MeV/nucleon to about 25 GeV/nucleon in the fixed-target frame) probe the widest ranges of baryon density and temperature, enabling studies of nuclear matter from a few tenths to about 5 times the nuclear saturation density and for temperatures from a few to well above a hundred MeV, respectively. Collisions of neutron-rich isotopes further bring the opportunity to probe effects due to the isospin asymmetry. However, capitalizing on the enormous scientific effort aimed at uncovering the dense nuclear matter EOS, both at RHIC and at FRIB as well as at other international facilities, depends on the continued development of state-of-the-art hadronic transport simulations. This white paper highlights the essential role that heavy-ion collision experiments and hadronic transport simulations play in understanding strong interactions in dense nuclear matter, with an emphasis on how these efforts can be used together with microscopic approaches and neutron star studies to uncover the nuclear EOS. 

Dense nuclear matter equation of state from heavy-ion collisions

We present a strangeness-neutral equation of state for QCD that exhibits critical behavior and matches lattice QCD results for the Taylor-expanded thermodynamic variables up to fourth order in $$\mu _B/T$$
 . It is compatible with the SMASH hadronic transport approach and has a range of temperatures and baryonic chemical potentials relevant for phase II of the Beam Energy Scan at RHIC. We provide an updated version of the software BES-EoS, which produces an equation of state for QCD that includes a critical point in the 3D Ising model universality class. This new version also includes isentropic trajectories and the critical contribution to the correlation length. Since heavy-ion collisions have zero global net-strangeness density and a fixed ratio of electric charge to baryon number, the BES-EoS is more suitable to describe this system. Comparison with the previous version of the EoS is thoroughly discussed.

Strangeness-neutral equation of state for QCD with a critical point

A review of the recent progress of relativistic hydrodynamic attractors is presented, with a focus on applications in heavy ion collisions and the quark gluon plasma. Pedagogical introductions to the effective descriptions relevant for attractors in high energy physics, namely hydrodynamics, holography and kinetic theory, are followed by highlights of some recent advances.

Hydrodynamic attractors in heavy ion collisions: a review

Initial conditions for relativistic heavy-ion collisions may be far from equilibrium (i.e., there are large initial contributions from the shear-stress tensor and bulk pressure), but it is expected that on very short timescales the dynamics converge to a universal attractor that defines hydrodynamic behavior. Thus far, studies of this nature have only considered an idealized situation at LHC energies (high temperatures $T$ and vanishing baryon chemical potential ${\ensuremath{\mu}}_{B}=0$), but in this work, we investigate for the first time how far-from-equilibrium effects may influence experimentally driven searches for the quantum chromodynamic critical point at the Relativistic Heavy Ion Collider. We find that the path to the critical point is heavily influenced by far-from-equilibrium initial conditions where viscous effects lead to dramatically different ${T,{\ensuremath{\mu}}_{B}}$ trajectories through the QCD phase diagram. We compare hydrodynamic equations of motion with shear and bulk coupled together at finite ${\ensuremath{\mu}}_{B}$ for both Denicol-Niemi-Molnar-Rischke and phenomenological Israel-Stewart equations of motion and discuss their influence on potential attractors at finite ${\ensuremath{\mu}}_{B}$ and their corresponding ${T,{\ensuremath{\mu}}_{B}}$ trajectories.

Far-from-equilibrium search for the qcd critical point

The speed of sound of the matter within neutron stars may contain non-smooth structure related to first-order phase transitions or or crossovers. Here we investigate what are the observable consequences of structure, such as bumps, spikes, step functions, plateaus, and kinks. One of the main consequences is the possibility of ultra-heavy neutron stars, i.e.~stars with masses significantly heavier than two solar masses. These stars pass all observational and theoretical constraints, including those imposed by recent LIGO/Virgo gravitational-wave observations and NICER X-ray observations. We thoroughly investigate other consequences of this structure in the speed of sound to develop an understanding of how non-smooth features affect astrophysical observables, such as stellar radii, tidal deformability, moment of inertia, and Love number. Our results have important implications to future gravitational wave and X-ray observations of neutron stars and their impact in nuclear astrophysics.

Extreme Matter meets Extreme Gravity: Ultra-heavy neutron stars with crossovers and first-order phase transitions

Current experiments at the Relativistic Heavy Ion Collider (RHIC) are probing finite baryon densities where the shear viscosity to enthalpy ratio $\eta T/w$ of the Quark Gluon Plasma remains unknown. We use the Hadron Resonance Gas (HRG) model with the most up-to-date hadron list to calculate $\eta T/w$ at low temperatures and at finite baryon densities $\rho_B$. We then match $\eta T/w$ to a QCD-based shear viscosity calculation within the deconfined phase to create a table across $\left\{T,\mu_B\right\}$ for different cross-over and critical point scenarios at a specified location. We find that these new $\eta T/w(T,\mu_B)$ values would require initial conditions at significantly larger $\rho_B$, compared to ideal hydrodynamic trajectories, in order to reach the same freeze-out point.

Building a testable shear viscosity across the QCD phase diagram

The existence of hydrodynamic attractors in rapidly expanding relativistic systems has shed light on the success of relativistic hydrodynamics in describing heavy-ion collisions at zero chemical potential. As the search for the QCD critical point continues, it is important to investigate how out of equilibrium effects influence the trajectories on the QCD phase diagram. In this proceedings, we study a Bjorken expanding hydrodynamic system based on DMNR equations of motion with initial out of equilibrium effects and finite chemical potential in a system with a critical point. We find that the initial conditions are not unique for a specific freeze-out point, but rather the system can evolve to the same final state freeze-out point with a wide range of initial baryon chemical potential, $\mu_B$. For the same initial energy density and baryon density, depending on how far out of equilibrium the system begins, the initial $\mu_B$ can vary by $\Delta \mu_B\sim 350$ MeV. Our results indicate that knowledge of the out-of-equilibrium effects in the initial state provide vital information that influences the search for the QCD critical point.

Far From Equilibrium Hydrodynamics and the Beam Energy Scan

The Quark Gluon Plasma produced in heavy-ion collisions has three relevant conserved charges: baryon number (B), strangeness (S), and electric charge (Q). Here we derive the Israel-Stewart framework for BSQ diﬀusion coupled to shear and bulk viscosity and the thermodynamic derivatives needed to couple this to a BSQ equation of state. We reproduce a subset of the J terms in the DNMR approach and propose a technique to derive other terms from the maximum entropy principle. Finally, we preform a stability analysis that can be used to constraint transport coeﬃcients in BSQ hydrodynamics.

Stability of multi-component relativistic viscous hydrodynamics from Israel-Stewart and reproducing DNMR from maximizing the entropy

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

Travis Dore

Author Tools

Chat about Author