Physics Letters B 795 (2019) 694–699
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Fluctuation-dissipation and correlation-propagation relations in
(1 +3)D moving detector-quantum field systems
Jen-Tsung Hsiang
a,∗
, B.L. Hu
b
, Shih-Yuin Lin
c
, Kazuhiro Yamamoto
d
a
Center for High Energy and High Field Physics, National Central University, Chungli 32001, Taiwan
b
Maryland Center for Fundamental Physics and Joint Quantum Institute, University of Maryland, College Park, MD 20742-4111, USA
c
Department of Physics, National Changhua University of Education, Changhua 50007, Taiwan
d
Department of Physics, Kyushu University, Fukuoka 819-0395, Japan
a r t i c l e i n f o a b s t r a c t
Article history:
Received
11 June 2019
Received
in revised form 25 June 2019
Accepted
28 June 2019
Available
online 2 July 2019
Editor: M.
Cveti
ˇ
c
The fluctuation-dissipation relations (FDR) are powerful relations which can capture the essence of the
interplay between a system and its environment. Challenging problems of this nature which FDRs aid
in our understanding include the backreaction of quantum field processes like particle creation on the
spacetime dynamics in early universe cosmology or quantum black holes. The less familiar, yet equally
important correlation-propagation relations (CPR) relate the correlations of stochastic forces on different
detectors to the retarded and advanced parts of the radiation propagated in the field. Here, we analyze a
system of N uniformly-accelerated Unruh-DeWitt detectors whose internal degrees of freedom (idf) are
minimally coupled to a real, massless, scalar field in 4D Minkowski space, extending prior work in 2D
with derivative coupling. Using the influence functional formalism, we derive the stochastic equations
describing the nonequilibrium dynamics of the idfs. We show after the detector-field dynamics has
reached equilibration the existence of the FDR and the CPR for the detectors, which combine to form
a generalized fluctuation-dissipation matrix relation. We show explicitly the energy flows between the
constituents of the system of detectors and between the system and the quantum field environment.
This power balance anchors the generalized FDR. We anticipate this matrix relation to provide a useful
guardrail in expounding some basic issues in relativistic quantum information, such as ensuring the self-
consistency
of the energy balance and tracking the quantum information transfer in the detector-field
system.
© 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
Fluctuation-dissipation relations (FDR), though rooted in statis-
tical
mechanics [1–3], has wide-ranging implications and applica-
tions.
For example, it captures the essence of the so-called back-
reaction
problem in particle-field systems and in gravitational and
cosmological physics. Sciama [4]treated black holes with Hawking
radiation [5]as a dissipative system, and, with Candelas, proposed
to view its interaction with a quantum field in the light of a FDR
[6](see also Mottola [7]). Hu & Sinha, Campos & Verdaguer [8–10]
showed
how the backreaction of particle creation on the geometro-
dynamics
of the early universe can be phrased in terms of a FDR.
The
existence of FDR in a thermal field in the context of linear
response theory (LRT) [1,2]is better known than the correlation-
*
Corresponding author.
E-mail
addresses: cosmology@gmail.com (J.-T. Hsiang), blhu@umd.edu (B.L. Hu),
sylin@cc.ncue.edu.tw (S.-Y. Lin), yamamoto@phys.kyushu-u.ac.jp (K. Yamamoto).
propagation relations (CPR), the existence of which in a quantum
field was first discovered by Raval, Hu and Anglin. In Ref. [11]they
showed that there exists 1) a set of FDR relating the fluctuations
of the stochastic forces to the dissipative forces on the detectors,
and 2) a related set of CPR between the correlations of stochastic
forces on different detectors and the retarded and advanced parts
of the radiation mediated by them.
Here
the detector is a physical object with internal degrees of
freedom, like an atom. A uniformly accelerated detector moving in
a quantum field was used by Unruh [12]to illuminate the physics
of Hawking effect. Considering a detector’s motion and interac-
tion
with the quantum field, the detector-field system opens up
accessible channels to probe experimentally into the many prop-
erties
of a moving detector or atom in a quantum field, such as
quantum radiation [11,13–23] and nonequilibrium, non-Markovian
effects [24–28]. It has also become popular in the newly emergent
field of relativistic quantum information [29]for tackling environ-
https://doi.org/10.1016/j.physletb.2019.06.062
0370-2693/
© 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.