Diffusing diffusivity model with dichotomous noise

Abstract

We study Langevin dynamics with stochastic diffusivity arising from fluctuations of the surrounding medium. The diffusivity is modeled as an Ornstein–Uhlenbeck process driven by symmetric dichotomous noise, which confines it to a finite interval. We derive analytical expressions for the short-time probability density function (PDF) of the particle displacement and analyze its asymptotic behavior. While the PDF retains the characteristic logarithmic divergence at the origin, its tails differ from the Gaussian white-noise case: exponential tails are replaced by Gaussian ones modulated by a power-law with a switching-rate-dependent exponent. At long times, the dynamics converges to ordinary Gaussian diffusion. We determine the variance and covariance of the time-averaged stochastic diffusivity and show that it is self-averaging. The model provides a minimal analytically tractable framework for stochastic transport in environments with bounded or switching fluctuations.

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BibTeX RIS

BibTeX

@article{lee2026diffusing,
  title = {{Diffusing diffusivity model with dichotomous noise}},
  author = {Dongho Lee and Jae-Hyung Jeon and Pascal Viot and Gleb Oshanin},
  journal = {Journal of Physics A: Mathematical and Theoretical},
  year = {2026},
  month = sep,
  doi = {10.1088/1751-8121/aea1ad},
  url = {https://hal.science/hal-05750051v1},
  note = {CC BY},
}

RIS

TY  - JOUR
TI  - Diffusing diffusivity model with dichotomous noise
AU  - Dongho Lee
AU  - Jae-Hyung Jeon
AU  - Pascal Viot
AU  - Gleb Oshanin
PY  - 2026
DA  - 2026/09/15
JO  - Journal of Physics A: Mathematical and Theoretical
DO  - 10.1088/1751-8121/aea1ad
UR  - https://hal.science/hal-05750051v1
AB  - We study Langevin dynamics with stochastic diffusivity arising from fluctuations of the surrounding medium. The diffusivity is modeled as an Ornstein–Uhlenbeck process driven by symmetric dichotomous noise, which confines it to a finite interval. We derive analytical expressions for the short-time probability density function (PDF) of the particle displacement and analyze its asymptotic behavior. While the PDF retains the characteristic logarithmic divergence at the origin, its tails differ from the Gaussian white-noise case: exponential tails are replaced by Gaussian ones modulated by a power-law with a switching-rate-dependent exponent. At long times, the dynamics converges to ordinary Gaussian diffusion. We determine the variance and covariance of the time-averaged stochastic diffusivity and show that it is self-averaging. The model provides a minimal analytically tractable framework for stochastic transport in environments with bounded or switching fluctuations.
SN  - 1751-8113
SN  - 1751-8121
ER  -

Abstract

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