Electromagnetic response in an expanding quark-gluon plasma

2025-05-04 0 0 350.29KB 9 页 10玖币

侵权投诉

Citation: Shovkovy, I. A.

Electromagnetic response in an

expanding quark-gluon plasma.

Preprints 2022,5, 442–450. https://

doi.org/10.3390/particles5040034

Publisher’s Note: MDPI stays neutral

with regard to jurisdictional claims in

published maps and institutional afﬁl-

iations.

Licensee MDPI, Basel, Switzerland.

This article is an open access article

distributed under the terms and

conditions of the Creative Commons

Attribution (CC BY) license (https://

creativecommons.org/licenses/by/

4.0/).

Article

Electromagnetic response in an expanding quark-gluon plasma

Igor A. Shovkovy 1,2

1College of Integrative Sciences and Arts, Arizona State University, Mesa, Arizona 85212, USA;

igor.shovkovy@asu.edu

2Department of Physics, Arizona State University, Tempe, Arizona 85287, USA

Abstract:

The validity of conventional Ohm’s law is tested in the context of a rapidly evolving quark-

gluon plasma produced in heavy-ion collisions. Here we discuss the electromagnetic response using

an analytical solution in kinetic theory. As conjectured previously, after switching on an electric ﬁeld

in a nonexpanding plasma, the time-dependent current is given by

J(t) = (

−e−t/τ0)σ0E

, where

τ0

is the transport relaxation time and

σ0

is the steady-state electrical conductivity. Such an incomplete

electromagnetic response reduces the efﬁciency of the magnetic ﬂux trapping in the quark-gluon plasma

and may prevent the observation of the chiral magnetic effect. Here we extend the study to the case

of a rapidly expanding plasma. We ﬁnd that the decreasing temperature and the increasing transport

relaxation time have opposite effects on the electromagnetic response. While the former suppresses the

time-dependent conductivity, the latter enhances it.

Keywords: quark-gluon plasma; heavy-ion collisions; kinetic theory; transport; electrical conductivity

1. Introduction

The relativistic heavy-ion collision experiments in Brookhaven and CERN produce the

hottest state of matter ever created in experiments [

]. It is so hot that not only nuclei but

also their constituent protons and neutrons melt away. The corresponding state of matter is

the quark-gluon plasma (QGP) [

]. Over the last two decades, we learned much about its

physical properties. The QGP produced by relativistic heavy-ion collisions has a rather high

temperature of several hundred megaelectronvolts. While composed of deconﬁned quarks and

gluons, it remains surprisingly strongly interacting. The strong interaction is responsible for a

quick equilibration of the plasma, its high opacity to passing relativistic jets [

], low viscosity

[

], and a well-pronounced hydrodynamic ﬂow [

]. Theoretical studies also predict that the

QGP may reveal unusual features connected with the chiral magnetic and chiral separation

effects [9–12] that have roots in the quantum chiral anomaly [13,14].

The presence of background magnetic ﬁelds is one of the prerequisites for the chiral

anomalous effects [

–

]. Strong magnetic ﬁelds are indeed natural to expect in relativistic

heavy-ion collisions. Since the colliding ions carry positive charges, they produce large electric

currents while moving past each other at speeds close to the speed of light in opposite directions.

According to theoretical estimates, the corresponding currents induce magnetic ﬁelds with the

strengths of the order of |eB| ∼ m2

π[15–18].

The detailed description of QGP is intricate because the magnetic ﬁelds in heavy-ion

collisions are so short-lived. Moreover, while the ﬁelds spike to large values at the moment

of the closest approach of colliding ions, they may become negligible when the proper QGP

forms and becomes equilibrated [

]. If it is the case, the chiral effects would not have enough

time to build up. Then, in turn, their observable signatures will be suppressed or non-existent.

One may suggest that the magnetic ﬂux can be trapped and sustained by the QGP because

the latter has a substantial electrical conductivity [

–

]. If true, the ﬁeld strength would

decrease relatively slowly with time and, thus, remain sufﬁciently large to yield discernible

effects due to the chiral anomaly. For a while, this scenario seemed plausible although, perhaps,

arXiv:2210.00691v2 [nucl-th] 22 Oct 2022

443

only marginally so [

]. On the other hand, it was even suggested that the electromagnetic

response is too weak for applicability of the classical treatment [

]. A recent study in Ref. [

]

subjected the underlying mechanism to another scrutiny. It claimed that the incomplete

electromagnetic response in heavy-ion collisions, termed colloquially as the "violation of the

conventional Ohm’s law," would reduce trapping of the magnetic ﬂux and, thus, strongly

suppress possible observables due to the chiral anomalous effects. A similar conclusion follows

also from other considerations in Ref. [27].

In retrospect, it should not be surprising that the conventional Ohm’s law is violated on

time scales shorter than the transport relaxation time. However, one needs to clarify why the

electrical conductivity should be suppressed compared to the conventional Ohm’s law in the

steady state. Recall that the electrical conductivity quantiﬁes the electromagnetic response to

an electric ﬁeld, which is a dissipative process. The dissipation comes from the momentum

relaxation of charges scattering on one another. On times shorter than the relaxation time, the

probability of scattering is negligible, no momentum relaxation occurs, and no dissipation is

expected. In other words, the transport is effectively ballistic. Nevertheless, on short times

scales, the electromagnetic response is indeed incomplete. Below we reconﬁrm the result by

using analytical solutions within the framework of kinetic theory. We also extend the study to

the case of QGP with a rapid expansion.

The paper is organized as follows. In Sec. 2, we discuss the electromagnetic response in

the simplest model of a plasma without expansion. The effects of expansion are studied in

Sec. 3, where we address the effects of changing temperature, electric ﬁeld, and collision rate.

Discussion of the main results and the summary of ﬁndings are given in Sec. 4

2. Electromagnetic response in a plasma without expansion

Kinetic theory is a convenient tool for describing the electromagnetic response in a plasma.

Within such a framework, a state of QGP is described by distribution functions for every

particle type. For simplicity, we will restrict our consideration below to a single species of

charged particles. Conceptually, such a model will capture the main qualitative features

of the electromagnetic response. Also, the generalization to the case of multiple species is

straightforward.

To study the electromagnetic response, we will perturb the plasma by applying a back-

ground electric ﬁeld

, which turns on suddenly at

0. Without loss of generality, we will

assume that the electric ﬁeld points in the

direction. Such a ﬁeld will induce a nonzero electric

current in the plasma,

Jx(t) = 4eZd3p

(2π)3vxf(px,t), (1)

where

f(px

is a time-dependent distribution function in the perturbed plasma. By deﬁnition,

the particle velocity is given by

vx≡∂ep/∂px

, where

ep=qp2

x+p2

⊥+m2

. Note that the extra

overall factor 4 accounts for the contributions from both particles and antiparticles, as well as

from the two spin degrees of freedom.

The out-of-equilibrium distribution function

f(px

satisﬁes the following kinetic equa-

tion: ∂f(px,t)

∂t+eEx∂f(px,t)

∂px

=−f(px,t)−f0(px)

τ0

, (2)

where

is the

-component of the electric ﬁeld,

τ0

is the transport relaxation time, and

f0(px) =

/(e√p2

x+p2

⊥+m2/T0+

)

is the Fermi-Dirac distribution function of the plasma in

equilibrium at temperature

. It is appropriate to mention that, in heavy-ion collisions, the

distribution function may differ considerably from the Fermi-Dirac one, especially during

the early stages of plasma evolution. Thus, one might be tempted to complicate the analysis

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

Citation:Shovkovy,I.A.Electromagneticresponseinanexpandingquark-gluonplasma.Preprints2022,5,442450.https://doi.org/10.3390/particles5040034Publisher'sNote:MDPIstaysneutralwithregardtojurisdictionalclaimsinpublishedmapsandinstitutionalafl-iations.Copyright:©2022bytheauthor.LicenseeMDPI,Basel,Switze...

展开>> 收起<<

Electromagnetic response in an expanding quark-gluon plasma.pdf

共9页,预览2页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Electromagnetic response in an expanding quark-gluon plasma

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: