Brownian Motion in AdS/CFT
By J. Boer, V. Hubeny, M. Rangamani, M. Shigemori. 2008
156 citations recorded by the source corpus.
We study Brownian motion and the associated Langevin equation in AdS/CFT. The Brownian particle is realized in the bulk spacetime as a probe fundamental string in an asymptotically AdS black hole background, stretching between the AdS boundary and the horizon. The modes on the string are excited by the thermal black hole environment and consequently the string endpoint at the boundary undergoes an erratic motion, which is identified with an external quark in the boundary CFT exhibiting Brownian motion. Semiclassically, the modes on the string are thermally excited due to Hawking radiation, which translates into the random force appearing in the boundary Langevin equation, while the friction in the Langevin equation corresponds to the excitation on the string being absorbed by the black hole. We give a bulk proof of the fluctuation-dissipation theorem relating the random force and friction. This work can be regarded as a step toward understanding the quantum microphysics underlying the fluid-gravity correspondence. We also initiate a study of the properties of the effective membrane or stretched horizon picture of black holes using our bulk description of Brownian motion.
Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/060b8a1f6c7ed8daecc5741fb2cbcc8ee8ce0241
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Citations in the corpus
- Probe branes, time-dependent couplings and thermalization in AdS/CFT (2010, methodology): “t N= 4 gauge theory. In this case the bulk black brane metric induces a worldsheet metric which has a horizon. The uctuations then re ect Hawking radiation from the worldsheet horizon. The results in [47] and [48] are consistent with the uctuation-dissipation theorem. 22 In the D-brane solutions con”
- Gauge/String Duality, Hot QCD and Heavy Ion Collisions (2011, result): “[477, 484], and these results nicely reproduce those we have obtained within a Langevin formalism.”
- Heavy ions and string theory (2013, methodology): “While the spectral density (which describes classical absorption) is easily computed using the classical methods of the correspondence, the symmetrized correlation function (which describes the quantum-statistical fluctuations) can only be computed through an analysis of the Hawking flux [114, 115, ”
- A Holographic View on Physics out of Equilibrium (2010, methodology): “There are some essential differences in the derivation, since the real time formalism employed in [127] is intrinsically tied to the Lorentzian geometry, whereas the Hartle-Hawking state used in the derivation of [95] is essentially an equilibrium thermal computation (which therefore can be carried ”