English

Brownian motion of a particle with higher-derivative dynamics

Statistical Mechanics 2023-11-14 v3 Classical Physics

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.

Keywords

Cite

@article{arxiv.2303.15157,
  title  = {Brownian motion of a particle with higher-derivative dynamics},
  author = {Z. C. Tu},
  journal= {arXiv preprint arXiv:2303.15157},
  year   = {2023}
}

Comments

This manuscript is a translation of a Chinese paper contributing for 100 anniversary of Department of Physics, Beijing Normal University