TY - JOUR

T1 - Fluctuation-dissipation and correlation-propagation relations in (1 + 3)D moving detector-quantum field systems

AU - Hsiang, Jen Tsung

AU - Hu, B. L.

AU - Lin, Shih Yuin

AU - Yamamoto, Kazuhiro

N1 - Funding Information:
The authors thank Prof. Chong-Sun Chu, Director of the National Center for Theoretical Sciences in Hsinchu, Taiwan for his hospitality where many discussions in this paper took place. SYL is supported by the Ministry of Science and Technology of Taiwan under Grant No. MOST 106-2112-M-018-002-MY3 and in part by the National Center for Theoretical Sciences , Taiwan. KY is supported by MEXT/JSPS KAKENHI Grant No. 15H05895 , No. 16H03977 , No. 17K05444 , No. 17H06359 .
Publisher Copyright:
© 2019 The Authors

PY - 2019/8/10

Y1 - 2019/8/10

N2 - 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.

AB - 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.

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U2 - 10.1016/j.physletb.2019.06.062

DO - 10.1016/j.physletb.2019.06.062

M3 - Article

AN - SCOPUS:85068784334

VL - 795

SP - 694

EP - 699

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

ER -