相对论重离子碰撞中守恒电荷的扩散
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Diffusion of Conserved Charges in Relativistic Heavy Ion Collisions
Moritz Greif,
1,*
Jan. A. Fotakis,
1
Gabriel S. Denicol,
2
and Carsten Greiner
1
1
Institut für Theoretische Physik, Johann Wolfgang Goethe-Universität, Max-von-Laue-Straße 1,
D-60438 Frankfurt am Main, Germany
2
Instituto de Física, Universidade Federal Fluminense, UFF, Niterói 24210-346, Rio de Janeiro, Brazil
(Received 1 December 2017; published 12 June 2018)
We demonstrate that the diffusion currents do not depend only on gradients of their corresponding
charge density, but that the different diffusion charge currents are coupled. This happens in such a way that
it is possible for density gradients of a given charge to generate dissipative currents of another charge.
Within this scheme, the charge diffusion coefficient is best viewed as a matrix, in which the diagonal terms
correspond to the usual charge diffusion coefficients, while the off-diagonal terms describe the coupling
between the different currents. In this Letter, we calculate for the first time the complete diffusion matrix for
hot and dense nuclear matter, including baryon, electric, and strangeness charges. We find that the baryon
diffusion current is strongly affected by baryon charge gradients but also by its coupling to gradients in
strangeness. The electric charge diffusion current is found to be strongly affected by electric and
strangeness gradients, whereas strangeness currents depend mostly on strange and baryon gradients.
DOI: 10.1103/PhysRevLett.120.242301
Introduction.—Ultrarelativistic hadronic collisions, per-
formed in the largest particle accelerators, allow us to study
the properties of hot and dense hadronic and quark matter.
These experiments have played a crucial role in uncovering
novel transport properties of the quark-gluon plasma
(QGP), the state of nuclear matter in which quarks and
gluons are no longer confined inside hadrons. In particular,
several phenomenological studies [1–8] demonstrated that
the QGP has one of the smallest shear viscosity to entropy
density ratios in nature—a surprising result that is still not
well understood from first principles. Additional studies
[4,9–14] have also improved our understanding of the bulk
viscosity, unravelling novel behavior near the deconfine-
ment transition of nuclear matter. Recently, much attention
was paid to the electric conductivity; several studies on the
lattice [15–17], in perturbative QCD [18–20] and effective
theories [21–23] have been carried out.
On the other hand, at this stage, very little is known about
net-charge diffusion in hot and dense nuclear matter. This is
due to the fact that in high energy heavy ion collisions the
net-charge density of the matter produced is extremely
small in almost all space-time points, and it becomes very
difficult to observe any dissipative effects due to diffusion
[24]. Recently, the Relativistic Heavy-Ion Collider (RHIC)
started to perform hadronic collisions at lower energies
within the beam energy scan (BES) program in order to
investigate the phase diagram and transport properties of
nuclear matter at finite net-baryon (and net-electric charge)
density [25–27]. At beam energies down to, e.g.,
ffiffiffiffiffiffiffiffi
s
NN
p
¼
7.7 GeV in the RHIC BES, the baryon chemical potential
can reach values up to μ
B
∼ 400 MeV which is significant
compared to the temperatures that are reached [28,29], and
strong gradients in the chemical potential of conserved
charges are expected. Therefore, one can expect that low
energy collisions are particularly useful to explore the
properties of net-charge diffusion of nuclear matter that
were out of reach in higher energy collisions.
In relativistic Navier-Stokes-Fourier theory, a net-charge
(q) diffusion 4-current, j
μ
q
, is determined by the following
constitutive relation,
j
μ
q
¼ κ
q
∇
μ
α
q
; ð1Þ
where α
q
≡ μ
q
=T is the thermal potential, with μ
q
being the
charge chemical potential, T the temperature, and κ
q
the
corresponding net-charge diffusion coefficient. We further
defined the transverse gradient ∇
μ
≡ Δ
μν
∂
ν
and the pro-
jection operator Δ
μν
≡ g
μν
− u
μ
u
ν
, where u
μ
is the local
fluid velocity and g
μν
the space-time metric. We remark that
this relativistic constitutive relation also includes the effects
of heat flow.
However, we emphasize that Eq. (1) cannot be employed
to describe diffusion processes in the presence of more than
one conserved charge. This is exactly what happens in matter
produced in heavy ion collisions, in which we must always
consider at least three conserved charges: baryon number
(B), electric charge (Q), and strangeness (S). Since several
Published by the American Physical Society under the terms of
the Creative Commons Attribution 4.0 International license.
Further distribution of this work must maintain attribution to
the author(s) and the published article’s title, journal citation,
and DOI . Funded by SCOAP
3
.
PHYSICAL REVIEW LETTERS 120, 242301 (2018)
0031-9007=18=120(24)=242301(6) 242301-1 Published by the American Physical Society
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