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arXiv · 2606.17909

A Lindbladian for holographic Brownian motion

Daichi Takeda
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Abstract

We derive a Lindbladian description of holographic Brownian motion in the high-temperature regime. Starting from the influence functional for a trailing string endpoint, we identify the corresponding quantum master equation and prove that it is completely positive and trace-preserving. We determine the coefficients of the Lindbladian explicitly for two holographic backgrounds: the BTZ black hole and the AdS$_5$ black brane, restricting in the latter case to the endpoint fluctuation along the $x^1$-direction. We then analyze the time evolution of phase-space moments, energy relaxation, and steady states.

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Daichi Takeda. 2026-06-16. A Lindbladian for holographic Brownian motion. https://arxiv.org/abs/2606.17909

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