光标量场影响下的开放量子动力学研究

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"光标量场引起的开放量子动力学" 本文探讨了一个涉及光标量场的开放量子系统动力学问题，主要研究了弱耦合的光标量场如何影响量子探测场的动力学行为。在这个模型中，光标量场可以是通过非最小耦合与重力相互作用，或者通过希格斯门户与物质粒子发生耦合。研究的背景和潜在应用主要是针对原子干涉实验。作者首先假设探测场能够在非光标量场-探针系统的本征态下被初始化，这通常需要外部驱动来实现。他们得到了一个主方程，该方程描述了探测场的相干动态、退相干和动量扩散的修正项。为了推导这个主方程，研究者运用了非平衡量子场论的方法，包括费因曼-弗农影响泛函和热场动力学，这些都是用来实现类似莱曼-席曼齐克-齐默尔曼的还原方法的关键工具。在处理过程中，他们发现为了得到与探针场动力学无关的截止值独立结果，需要采用时间相关的重新归一化程序。这个程序揭示了一个重要的现象，即淬灭后的非马尔可夫效应，它由有限时间效应导致时间平移不变性的破坏，进而影响了通常真空反条件项的时间依赖性调制。此外，作者还讨论了实验检测这些效应的可能性以及面临的挑战，并指出了一些可能的改进方向。他们的工作对于理解和模拟量子系统在复杂环境中，特别是存在光标量场时的行为，提供了重要的理论框架。对于未来原子干涉和其他精密测量实验的设计和解释，这一研究将有深远影响。 * Clare Burrage, Christian Käding, Peter Millington, Jiří Minář 1 University of Nottingham, School of Physics and Astronomy 2 University of Amsterdam, Institute for Theoretical Physics 3 Lancaster University, Department of Physics 4 University of Nottingham, Centrefor the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems 文章接收日期：2019年2月25日，修订稿接收日期：2019年6月13日，发表日期：2019年10月9日

int

½ϕ; χ¼

x∈Ω



−

mχϕ

−



; ð15dÞ

where we omit the term arising from V

eff

ðhXiÞ

[cf. Eq. (46)] and use the shorthand notation

≡

x: ð16Þ

The terms in S

int

½ϕ; χ should be compared with Eq. (1),

illustrating the connection with portal couplings discussed

earlier.

In Eqs. (15c) and (15d), we have accounted for the

fact that we will later restrict the interactions to take place

over a finite period of time between the quench of the initial

state of the system and its subsequent measurement. The

spacetime integrals in the interaction parts of the action are

therefore restricted to the hypervolume Ω

¼½0;t × R

We emphasize that the free parts nevertheless have support

for all times (see Refs. [113,114]).

In order to make the quench manifest, one could instead

extend the limits of the time integrals to the full real line

and replace the coupling constants α

, α

, and λ by time-

dependent couplings, which then parametrize the effective

switching on and off of the interactions by the experimental

apparatus. (We might imagine preparing the system

in a screened environment, before allowing it to evolve

unscreened.) While we consider instantaneous switching

here, we might more generally introduce a switching

function that reflects the realistic preparation and quench-

ing of the system over some finite timescale.

B. Chameleons

The scalar field theory described by Eq. (2) is a

chameleon model if, in the presence of a nonrelativistic

matter distribution, the scalar field X is stabilized at the

minimum of its effective potential and the mass of small

fluctuations about this minimum depends on the local

energy density. It is this variation in the mass which allows

the scalar fifth force to be suppressed, or screened, from

local tests of gravity. Specifically, near dense sources of

matter, the minimum of the effective potential V

eff

ðXÞ [see

Eq. (9)] lies at a finite value hXi¼X

min

and the mass

becomes large, such that the fifth force is Yukawa sup-

pressed. Instead, in the cosmological vacuum, the fluctua-

tions are essentially massless, allowing them to propagate a

long-range force of a strength comparable to gravity. It is

common to consider polynomial potentials of the form

eff

ðXÞ¼Λ

ðΛ=XÞ

þ AðXÞρ

ext

, with integer n, giving a

chameleon model if n>0 or if n is a negative even integer

strictly less than −2.

In this work, we consider the case n ¼ −4, in which a

factor λ=4! is usually introduced by hand in the self-

coupling term, giving the effective potential

eff

ðXÞ¼

þ AðXÞρ

ext

; ð17Þ

with

AðXÞ¼e

X=M

: ð18Þ

This corresponds to taking a ¼ 1, b ¼ c ¼ 2, and μ ¼ 0 in

the results of the preceding subsection, giving, for instance,

the coupling constants

¼ 2

; α

¼ α

: ð19Þ

The quartic chameleon model, with the potential given by

Eq. (17), is currently under pressure from atom-interferom-

etry and torsion-balance experiments, with only a small

window of parameter space remaining for λ close to one and

M close to the Planck scale [21]. However, we shall

consider this model with screening, since it is a particularly

useful prototype for evaluating the effect of the chameleon

fluctuations on the dynamics of the matter fields.

In a constant-density environment, the expectation

value of the chameleon field is given (to leading order

in ρ

ext

=M)by

min

ðρ

ext

Þ¼−



6ρ

ext

λM



1=3

; ð20Þ

and the corresponding squared mass of small fluctuations

around the minimum is

min

ðρ

ext

Þ¼





1=3



3ρ

ext



2=3

: ð21Þ

The situation is summarized in Fig. 1. The solid blue, solid

red, and black dashed lines correspond to the effective

potential V

eff

ðXÞ at zero external density ρ

ext

¼ 0, the

contribution from the linear coupling to matter at nonzero

density, and the effective potential at nonzero density,

respectively. The panes (a) and (b) correspond to the

potential in regions with lower and higher matter densities,

respectively. In higher-density environments, the chame-

leon is more massive; in lower-density environments, it is

less massive.

To see how this variation in the mass of the scalar leads

to a suppression of the scalar fifth force, we now consider

situations where the background matter density is not

uniform. Specifically, we consider a uniform sphere of

constant density ρ

ext

and radius R embedded in a back-

ground of lower density ρ

. For sufficiently large spheres,

the scalar field can reach the value X

min

that minimizes its

effective potential at the center of the sphere. It therefore

has a large mass in the interior of the sphere and does not

roll from X

min

apart from in a thin shell near the surface.

It is only matter in this thin shell (whose thickness is

OPEN QUANTUM DYNAMICS INDUCED BY LIGHT … PHYS. REV. D 100, 076003 (2019)

076003-5

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