Isotropization of a rotating and longitudinally expanding 4scalar system Margaret E. Carrington1 2Gabor Kunstatter3 4 2

2025-04-24 0 0 1.12MB 15 页 10玖币

侵权投诉

Isotropization of a rotating and longitudinally expanding φ4scalar

system

Margaret E. Carrington,1, 2 Gabor Kunstatter,3, 4, 2

Christopher D. Phillips,1, 5 and Marcelo E. Rubio1, 2, 6

1Department of Physics, Brandon University,

Brandon, Manitoba R7A 6A9, Canada

2Winnipeg Institute for Theoretical Physics, Winnipeg, Manitoba, Canada

3Department of Physics, University of Winnipeg,

Winnipeg, Manitoba, R3M 2E9 Canada

4Department of Physics, Simon Fraser University,

Burnaby, British Columbia, V5A 1S6 Canada

5current address: Department of Electrical and Computer Engineering,

University of Waterloo, Ontario, Canada

6SISSA, 34136 Trieste, Italy and INFN (Sezione di Trieste)

(Dated: October 08, 2022)

Abstract

We present numerical simulations for the evolution of an expanding system of massless scalar

ﬁelds with quartic coupling. By setting a rotating, non-isotropic initial conﬁguration, we compute

the energy density, the transverse and longitudinal pressures and the angular momentum of the

system. We compare the time scales associated with the isotropization and the decay of the

initial angular momentum due to the expansion, and show that even for fairly large initial angular

momentum, it decays signiﬁcantly faster than the pressure anistropy.

arXiv:2210.05504v1 [hep-th] 11 Oct 2022

I. INTRODUCTION

In this paper we study the time evolution of an expanding system of rotating massless real

scalar ﬁelds with quartic coupling. Our calculation is based on the method developed in

[1, 2]. Observables calculated in a loop expansion exhibit divergences at next-to-leading

order, which originate from instabilities in the classical solutions. The eﬀect is seen in

a calculation of the energy-momentum tensor at next-to-leading order, where the energy

density and pressures of the system diverge rapidly with increasing time. Gelis et al. have

shown that this problem can be cured using a resummation scheme that collects the leading

secular terms at each order of an expansion in the coupling constant. This resummation can

be done by allowing the initial condition for the classical ﬁeld to ﬂuctuate, and averaging

over these ﬂuctuations. They have shown that a system of scalar ﬁelds isotropizes when this

resummation is performed [2].

The motivation behind the development of this approach is to study the thermalization

of the glasma phase of the matter created in a relativistic heavy ion collision. It is known

that a hydrodynamic description, which is valid when the system is fairly close to thermal

equilibrium, works well at very early times (∼1fm/c). Approaches that are based on

kinetic theory descriptions of the scattering of quasi-particles cannot explain this rapid

thermalization. Another possibility that has been studied extensively is that the system

is strongly coupled, even at very high energies. The proposal of Gelis et al. is that rapid

thermalization could be achieved by a resummation of quantum ﬂuctuations. The Colour

Glass Condensate (CGC) eﬀective theory provides a natural framework for this formulation

[3–5]. At very early times the system is best described as a system of strong classical ﬁelds,

that can be obtained from solutions of the Yang-Mills equation using a CGC approach.

The spectrum of quantum ﬂuctuations was derived in [6]. The success of the resummation

method was demonstrated in [7], where the authors showed that pressure isotropiztion occurs

in an SU(2) analogue of QCD.

Our ultimate goal is to use the Gelis et al. approach to study the creation and evolution

of angular momentum in a glasma. This is interesting in the context of recent proposals

that the glasma is produced in a rapidly rotating state, which could be detected by looking

for the polarization of produced hyperons. There have been calculations that predict very

large values for the initial angular momentum of the system [8–10], but signiﬁcant ﬁnal state

polarization eﬀects have not been observed [11, 12]. In this paper we develop a formulation

to calculate the angular momentum of a system of real scalar ﬁelds. We present preliminary

results that indicate the angular momentum relaxes to a small value on a time scale signiﬁ-

cantly smaller than the time scale for pressure isotropization. If a similar result is obtained

in a QCD glasma, it would be consistent with the observations in [11, 12]. We also comment

that a calculation of angular momentum in glasma was done in [13], using a CGC approach

with a proper time expansion, and found also that large amounts of angular momentum was

not produced.

Since computations in a gauge theory are considerably more complicated, we will work with

a scalar theory. While it is true that QCD and scalar φ4theory are diﬀerent in many ways,

they have important similarities in the context of this calculation because they both have

unstable modes and are scale invariant at the classical level. In addition, we will minic the

kinematics of a relativistic nuclear collision by working in Milne coordinates with a rapidity

independent background ﬁeld. Milne coordinates are suitable because in a nuclear collision,

there is a preferred spatial direction provided by the collision axis, and in the high energy

limit one expects invariance under Lorentz boosts in the z-direction.

This paper is organized as follows. In section II we describe the method, and in section

III we formulate the calculation of the energy-momentum tensor and angular momentum.

Some details of our numerical procecure are discussed in section IV. In section V we present

our results, and in section VI we make some concluding remarks.

Throughout this paper, the spacetime is always taken to be Minkowski, with the signature

(+,−,−,−). In addition to standard inertial coordinates (t, x, y, z), we will also use Milne

coordinates (τ, x, y, η), where τis proper time and ηis spacetime rapidity. Finally, we choose

units such that c=kB=~= 1, where cis the speed of light in vacuum, kBis the Boltzmann

constant, and ~is the Planck constant divided by 2π.

II. FORMALISM

A. Preliminaries

We consider a massless self-interacting real scalar ﬁeld φwith quartic coupling. The La-

grangian density is given by

L=1

2∂µφ∂µφ−g2

4! φ4(1)

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：

Isotropizationofarotatingandlongitudinallyexpanding4scalarsystemMargaretE.Carrington,1,2GaborKunstatter,3,4,2ChristopherD.Phillips,1,5andMarceloE.Rubio1,2,61DepartmentofPhysics,BrandonUniversity,Brandon,ManitobaR7A6A9,Canada2WinnipegInstituteforTheoreticalPhysics,Winnipeg,Manitoba,Canada3Department...

展开>> 收起<<

Isotropization of a rotating and longitudinally expanding 4scalar system Margaret E. Carrington1 2Gabor Kunstatter3 4 2.pdf

共15页,预览3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！

Isotropization of a rotating and longitudinally expanding 4scalar system Margaret E. Carrington1 2Gabor Kunstatter3 4 2

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: