Second Talk at the “Gravity and Quantum” Workshop, Kyushu University, May 2023

Backreaction of Quantum Fields on Moving Atoms, Black Holes and theEarly Universe
Bei-Lok Hu !"#Maryland Center for Fundamental Physics & Joint Quantum Institute,
University of Maryland, College Park, U.S.A“Backreaction” in gravitation and cosmology is a difficult yet important class of problems imbued with many
challenging issues of theoretical physics. It studies how quantum field processes like cosmological particle
creation affect the dynamics of the early universe, how Hawking radiation back-reacts and changes the fateof a black hole. Research in this field began in the late 70’s, with tools from quantum field theory in curved
spacetime and its higher level extensions, semiclassical gravity of the 80’s and stochastic gravity of the 90’s[1]. New insights were added since then from nonequilibrium quantum field theory [2] using open quantum
system ideas and techniques. An interesting theme is the use of fluctuation-dissipation relations (FDR) tocapture the backreaction of quantum fields and their fluctuations on the dynamics of the backgroundspacetime and its fluctuations, known as metric fluctuations or spacetime foams. In this talk I first mention
samples of important work on this topic, exposing the insufficiency of linear response theory [3] and themismatches in earlier proposals [4], then summarize the results of Raval, Hu and Anglin [5] based onstochastic field theory methods. While studying N moving Unruh-DeWitt detectors or harmonic atoms in aquantum field, these authors showed the existence of FDR between any one detector and the quantum field.
They also discovered a new set of relations called the correlation-propagation relations (CPR) between two
moving detectors via the quantum field. They are combined into a set of generalized FDR by Hsiang et al[6][7] recently. This matrix relation ensures the self-consistency in the backreaction of quantum fieldprocesses on the detectors. In the open quantum system perspective these relations provide deeper physicalinsights into the backreaction problems of quantum field processes in moving atoms, radiating black holes
and the early universe. For latest results on FDRs in the context of quantum thermodynamics, see, e.g., [8].
--------------[1] See, e.g., B. L. Hu and E. Verdaguer, Semiclassical and Stochastic Gravity (Cambridge University Press 2020)[2] See, e.g., E. Calzetta and B. L. Hu, Nonequilibrium Quantum Field Theory (Cambridge University Press 2008)[3] E. Mottola, Phys. Rev. D33, 2136 (1986).

[4] P. Candelas and D. W. Sciama, Phys. Rev. Lett. 38, 1372 (1977)[5] A. Raval, B. L. Hu and J. Anglin, Phys. Rev. D 53, 7003 (1996).
[6] J.-T. Hsiang, B. L. Hu, and S.-Y. Lin, Fluctuation-Dissipation and Correlation-Propagation Relations from theNonequilibrium Dynamics of Detector-Quantum Field Systems Phys. Rev. D100, 025019 (2019)[7] J.-T. Hsiang, B. L. Hu, S.-Y. Lin and K. Yamamoto, Fluctuation-Dissipation and Correlation-Propagation Relations in 4D
for Uniformly-Accelerated Detectors in a Quantum Field Phys. Lett. B795, 694 (2019)[8] J.-T. Hsiang and B. L. Hu, Fluctuation-Dissipation Relation for a Quantum Brownian Oscillator in a Parametrically
Squeezed Thermal Field, Ann. Phys. 433, (2021) 168594