Holographic Brownian Motion in 1+1 Dimensions

Abstract

We study the motion of a stochastic string in the background of a BTZ black hole. In the 1+1 dimensional boundary theory this corresponds to a very heavy external particle (e.g, a quark), interacting with the fields of a CFT at finite temperature, and describing Brownian motion. The equations of motion for a string in the BTZ background can be solved exactly. Thus we can use holographic techniques to obtain the Schwinger-Keldysh Green function for the boundary theory for the force acting on the quark. We write down the generalized Langevin equation describing the motion of the external particle and calculate the drag and the thermal mass shift. Interestingly we obtain dissipation even at zero temperature for this 1+1 system. Even so, this does not violate boost (Lorentz) invariance because the drag force on a constant velocity quark continues to be zero. Furthermore since the Green function is exact, it is possible to write down an effective membrane action, and thus a Langevin equation, located at a "stretched horizon" at an arbitrary finite distance from the horizon.

39 pages, 4 figures; New discussion on holographic RG in subsection 5.1 and new section 6 on different time scales. Modified discussion on zero temperature dissipation in section 3. Typos corrected , references added. Revised version to appear in Nucl. Phys. B

References in corpus (16)

• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• Energy loss of a heavy quark moving through N=4 supersymmetric Yang-Mills plasma
• Drag force in AdS/CFT
• Schwinger-Keldysh Propagators from AdS/CFT Correspondence
• Heavy Quark Diffusion in Strongly Coupled $\mathbb{N}=4$ Yang Mills
• Momentum fluctuations of heavy quarks in the gauge-string duality
• On the exact solution of the accelerating string in $Ad{S}_5$ space
• Real-time gauge/gravity duality and ingoing boundary conditions
• Nonlinear waves in AdS/CFT correspondence
• Quantum Fluctuations in Holographic Theories with Hyperscaling Violation
• Generalized Lorentz-Dirac Equation for a Strongly-Coupled Gauge Theory
• Fluctuation and Dissipation at a Quantum Critical Point
• Coulomb drag at zero temperature
• Effective potential renormalization and polaronic mass shift in a trapped dynamical impurity-luttinger liquid system
• Non-equilibrium fluctuation-dissipation relation from holography
• Effective Mass of Holographic Brownian Particle in Rotating Plasma

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• Entanglement from Dissipation and Holographic Interpretation
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• Holographic Brownian motion at finite density
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• Out of time ordered effective dynamics of a quartic oscillator
• Holographic influence functional and its application to decoherence induced by quantum critical theories
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• Zero Temperature Dissipation and Holography
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• Back reaction effects on the dynamics of heavy probes in heavy quark cloud
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• Strongly Coupled Heavy and Light Quark Thermal Motion from AdS/CFT