arXiv subjects

Todd Mendenhall

Publications and source records attributed to Todd Mendenhall.

5 recordsLinked to original sources

arXiv2025

Effectiveness of parton cascade in solving the relativistic Boltzmann equation in a box

We benchmark the ZPC parton cascade with an exact analytical solution of the relativistic Boltzmann equation for a homogeneous and massless gas with a constant and isotropic elastic cross section. We measure the accuracy of ZPC with the relative mean deviation between its momentum distribution and the exact solution. We use two generalized collision schemes to further improve the accuracy of ZPC over the recent $t$-minimum collision scheme. We find that ZPC can reproduce very well the time evolution of the single-particle distribution function for the exact solution's initial condition, with one generalized collision scheme giving an accuracy better than $1\%$ for the momentum distribution at any time in all studied cases, including very high opacities where naively the parton cascade approach is expected to fail.

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arXiv2023

Semi-analytical calculation of the trajectory of relativistic nuclear collisions in the QCD phase diagram

We extend a semi-analytical model that includes the finite nuclear thickness to calculate the energy density $ε(t)$ and conserved-charge densities including the net-baryon density $n_{\rm _B}(t)$ produced at mid-spacetime-rapidity in central Au+Au collisions. Assuming the formation of a quark-gluon plasma with an ideal gas equation of state of either quantum or Boltzmann statistics or with a lattice QCD-based equation of state, we extract the temperature $T$ and chemical potentials $μ_{\rm _B}$, $μ_{\rm _Q}$ and $μ_{\rm _S}$ as functions of time. This then allows us to semi-analytically calculate the $T-μ_{\rm _B}$ trajectory of relativistic nuclear collisions in the QCD phase diagram, which should benefit the studies of high density physics including the search for the critical end point. This model is also useful for exploring the trajectories in the more general $T-μ_{\rm _B}-μ_{\rm _Q}-μ_{\rm _S}$ QCD phase space.

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arXiv2022

Calculating QCD Phase Diagram Trajectories of Nuclear Collisions using a Semi-analytical Model

At low to moderate collision energies where the parton formation time $τ_F$ is not small compared to the nuclear crossing time, the finite nuclear thickness significantly affects the energy density $ε(t)$ and net conserved-charge densities such as the net-baryon density $n_B(t)$ produced in heavy ion collisions. As a result, at low to moderate energies the trajectory in the QCD phase diagram is also affected by the finite nuclear thickness. Here, we first discuss our semi-analytical model and its results on $ε(t)$, $n_B(t)$, $n_Q(t)$, and $n_S(t)$ in central Au+Au collisions. We then compare the $T(t)$, $μ_B(t)$, $μ_Q(t)$, and $μ_S(t)$ extracted with the ideal gas equation of state (EoS) with quantum statistics to those extracted with a lattice QCD-based EoS. We also compare the $T-μ_B$ trajectories with the RHIC chemical freezeout data. Finally, we discuss the effect of transverse flow on the trajectories.

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arXiv2022

A Semi-analytical Method of Calculating Nuclear Collision Trajectory in the QCD Phase Diagram

The finite nuclear thickness affects the energy density $ε(t)$ and conserved-charge densities such as the net-baryon density $n_B(t)$ produced in heavy ion collisions. While the effect is small at high collision energies where the Bjorken energy density formula for the initial state is valid, the effect is large at low collision energies, where the nuclear crossing time is not small compared to the parton formation time. The temperature $T(t)$ and chemical potentials $μ(t)$ of the dense matter can be extracted from the densities for a given equation of state (EOS). Therefore, including the nuclear thickness is essential for the determination of the $T$-$μ_B$ trajectory in the QCD phase diagram for relativistic nuclear collisions at low to moderate energies such as the RHIC-BES energies. In this proceeding, we will first discuss our semi-analytical method that includes the nuclear thickness effect and its results on the densities $ε(t), n_B(t), n_Q(t)$, and $n_S(t)$. Then, we will show the extracted $T(t), μ_B(t), μ_Q(t)$, and $μ_S(t)$ for a quark-gluon plasma using the ideal gas EOS with quantum or Boltzmann statistics. Finally, we will show the results on the $T$-$μ_B$ trajectories in relation to the possible location of the QCD critical end point. This semi-analytical model provides a convenient tool for exploring the trajectories of nuclear collisions in the QCD phase diagram.

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arXiv2021

Calculating the initial energy density in heavy ion collisions by including the finite nuclear thickness

The initial energy density produced in heavy ion collisions can be estimated with the Bjorken energy density formula after choosing a proper formation time $τ{_{\rm F}}$. However, the Bjorken formula breaks down at low energies because it neglects the finite nuclear thickness. Here we include both the finite time duration and finite longitudinal extension of the initial energy production. When $τ{_{\rm F}}$ is not too much smaller than the crossing time of the two nuclei, our results are similar to those from a previous study that only considers the finite time duration. In particular, we find that at low energies the initial energy density has a much lower maximum value but evolves much longer than the Bjorken formula, while at large-enough $τ{_{\rm F}}$ and/or high-enough energies our result approaches the Bjorken formula. We also find a qualitative difference in that our maximum energy density $ε^{\rm max}$ at $τ{_{\rm F}}=0$ is finite, while the Bjorken formula diverges as $1/τ{_{\rm F}}$ and the previous result diverges as $\ln (1/τ{_{\rm F}})$ at low energies but as $1/τ{_{\rm F}}$ at high energies. Furthermore, our solution of the energy density approximately satisfies a scaling relation. As a result, the $τ{_{\rm F}}$-dependence of $ε^{\rm max}$ determines the $A$-dependence, and the weaker $τ{_{\rm F}}$-dependence of $ε^{\rm max}$ in our results at low energies means a slower increase of $ε^{\rm max}$ with $A$.

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