### Abstract

We investigate Brownian motions of a particle coupled to vacuum fluctuations of a quantum field. The Unruh effect predicts that an observer in an accelerated motion sees the Minkowski vacuum as thermally excited. This addresses the problem of whether or not a thermal property appears in a perturbative random motion of a particle in an accelerated motion due to the coupling. We revisit this problem by solving the equation of motion of a particle coupled to vacuum fluctuations including the radiation reaction force. We compute a Fourier integral for the variance of the random velocity in a rigorous manner. Similarly, we consider a particle coupled to vacuum fluctuations in de Sitter spacetime motivated by the argument that an observer in de Sitter spacetime sees the Bunch-Davies vacuum as a thermally excited state with the Gibbons-Hawking temperature. Our investigation clarifies the condition that the energy equipartition relation arises in the Brownian motions of a particle.

Original language | English |
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Article number | 124028 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 89 |

Issue number | 12 |

DOIs | |

Publication status | Published - Jun 24 2014 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)

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## Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*89*(12), [124028]. https://doi.org/10.1103/PhysRevD.89.124028