量子弦热激发光谱：扩展与纠缠的解析

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"纠缠在扩展量子串中的热激发光谱" 这篇研究文章发表在Physics Letters B778(2018)442–446，主要探讨了在扩展量子串中发现的热激发光谱现象。作者Jürgen Berges, Stefan Floerchinger和Raju Venugopalan分别来自德国海德堡大学理论物理研究所和美国布鲁克海文国家实验室。文章在2017年10月11日提交，经过修订后于2018年1月24日被接受，并在同年的xxxx日期在线发布，编辑为A. Ringwald。文章的核心问题源自于电子-正电子(e+e-)碰撞实验中一个令人费解的现象：尽管散射事件似乎不足以解释，但由散射的夸克-反夸克对形成的量子弦所产生的粒子光谱却呈现出热力学特性。为了解决这一问题，研究人员采用了一种新的方法，即考虑量子串的有限可观测区间，通过追踪互补区域来处理相对密度算子。这种方法揭示了量子纠缠在扩展量子串中起到的关键作用。量子纠缠是量子力学中的一个基本概念，指的是两个或多个量子系统间的一种非经典关联状态，即使它们在空间上分离，也无法独立描述各自的状态。在这种情况下，量子纠缠与扩展量子串的时空背景相结合，尤其是在存在类时或类空边界（如黑洞视界）的情况下，会显著影响系统的动力学行为。研究者指出，量子纠缠可以解释即使散射频率不足，粒子光谱仍然具有热性质的原因。这是因为量子纠缠能导致信息在系统不同部分之间以非局域的方式分布，这可能在一定程度上模拟了热化过程。换句话说，量子纠缠使得量子串内部的态变得相互依赖，即便它们没有直接相互作用，也能表现出类似热平衡的统计特征。这项工作对于理解高能物理中的复杂现象，特别是在强相互作用系统的热化过程和量子信息的非局域传播方面有重要贡献。它还可能对量子重力理论和黑洞物理学产生深远影响，因为黑洞边界附近的量子效应同样涉及到纠缠和信息丢失的问题。这篇论文揭示了量子纠缠在扩展量子串中的独特作用，以及这种纠缠如何解释看似不匹配的热激发光谱现象。这不仅深化了我们对基本粒子相互作用的理解，也为量子信息科学和宇宙学提供了新的研究视角。

Physics Letters B 778 (2018) 442–446

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Thermal excitation spectrum from entanglement in an expanding

quantum string

Jürgen Berges

, Stefan Floerchinger

a,∗

, Raju Venugopalan

Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany

Physics Department, Brookhaven National Laboratory, Bldg. 510A, Upton, NY 11973, USA

a r t i c l e i n f o a b s t r a c t

Article history:

Received

11 October 2017

Received

in revised form 13 December 2017

Accepted

24 January 2018

Available

online xxxx

Editor:

A. Ringwald

A surprising result in e

−

collisions is that the particle spectra from the string formed between

the expanding quark–antiquark pair have thermal properties even though scatterings appear not to

be frequent enough to explain this. We address this problem by considering the ﬁnite observable

interval of a relativistic quantum string in terms of its reduced density operator by tracing over the

complement region. We show how quantum entanglement in the presence of a horizon in spacetime for

the causal transfer of information leads locally to a reduced mixed-state density operator. For very early

proper time τ , we show that the entanglement entropy becomes extensive and scales with the rapidity.

At these early times, the reduced density operator is of thermal form, with an entanglement temperature

h/(2πk

τ ), even in the absence of any scatterings.

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

1. Introduction

A longstanding puzzle in e

−

collisions is that the hadron

spectra measured appear thermal with features that can be char-

acterized

in terms of a common temperature [1–6]. The apparent

thermal origin of the multiparticle production is surprising because

scatterings appear not to be frequent enough for thermalization to

occur and therefore demands an alternative explanation [2,7–10].

argue in this letter that this apparent thermalization is an

intrinsically quantum phenomenon arising from the entanglement

between observable and unobservable regions in an expanding

string. The observable region is described in terms of a reduced

density operator by tracing over the complement region, which is

bounded by the Minkowski spacetime horizon for the causal trans-

fer

of information. We show that the entanglement of the quantum

vacuum accross this horizon leads to dramatic macroscopic quan-

tum

effects. In particular, for very early proper time τ , we discover

that the entanglement entropy is extensive and scales with the ra-

pidity.

At these early times, a conformal symmetry emerges for the

Corresponding author.

E-mail

addresses: berges@thphys.uni-heidelberg.de (J. Berges),

ﬂoerchinger@thphys.uni-heidelberg.de (S. Floerchinger), raju@bnl.gov

(R. Venugopalan).

expanding system and the entanglement generates a reduced den-

sity

matrix of thermal form, with the temperature

2πk

, (1)

even in the absence of any scatterings.

Our

results establish a novel class of horizon phenomena in

quantum ﬁeld theory, featuring an instantaneous thermal excita-

tion

spectrum from a vacuum pure state. In contrast to the well-

known

example of an event horizon in the vicinity of a black

hole, which leads to Hawking radiation, or the related Unruh tem-

perature

for a class of accelerated observers, our setting does

not involve acceleration and it is non-stationary [11]. Speciﬁcally,

the Unruh acceleration a of an observer in the Rindler-wedge of

Minkowski spacetime at a spatial position x = c

/a generates a

space-dependent temperature T

hc/(2πk

x), while the time-

dependent

temperature (1) applies to the initial stages in the for-

ward

light cone with crucial applications to e

−

but also hadron–

hadron

collisions.

2. Model of expanding strings

Models that describe e

−

collisions successfully [12,13] rely

on the Schwinger mechanism of particle production in 1 +1-

dimensional

quantum electrodynamics (QED); a recent compre-

hensive

discussion of the diﬃculties presented by thermal-like

https://doi.org/10.1016/j.physletb.2018.01.068

0370-2693/

SCOAP

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