Brownian motion of a particle with higher-derivative dynamics

Z. C. Tu

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arXiv · 2303.15157

Brownian motion of a particle with higher-derivative dynamics

Z. C. Tu

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Abstract

The Brownian motion of a particle with higher-derivative dynamics (HDD) coupling with a bath consisting of harmonic oscillators is investigated. The Langevin equation and corresponding Fokker-Planck equation for the Brownian motion of the HDD particle are derived. As a case study, we particularly consider a stochastic Pais-Uhlenbeck oscillator. It is found that the Boltzmann distribution is pathological while this distribution is the steady solution to the Fokker-Planck equation.

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Z. C. Tu. 2023-03-27. Brownian motion of a particle with higher-derivative dynamics. https://arxiv.org/abs/2303.15157

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