Dichotomous acceleration process in one dimension: Position fluctuations
| Autor: | Santra, Ion, Ajgaonkar, Durgesh, Basu, Urna |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | J. Stat. Mech. (2023) 083201 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1742-5468/ace3b5 |
| Popis: | We study the motion of a one-dimensional particle which reverses its direction of acceleration stochastically. We focus on two contrasting scenarios, where the waiting-times between two consecutive acceleration reversals are drawn from (i) an exponential distribution and (ii) a power-law distribution $\rho(\tau)\sim \tau^{-(1+\alpha)}$. We compute the mean, variance and short-time distribution of the position $x(t)$ using a trajectory-based approach. We show that, while for the exponential waiting-time, $\langle x^2(t)\rangle\sim t^3$ at long times, for the power-law case, a non-trivial algebraic growth $\langle x^2(t)\rangle \sim t^{2\phi(\alpha)}$ emerges, where $\phi(\alpha)=2$, $(5-\alpha)/2,$ and $3/2$ for $\alpha<1,~1<\alpha\leq 2$ and $\alpha>2$, respectively. Interestingly, we find that the long-time position distribution in case (ii) is a function of the scaled variable $x/t^{\phi(\alpha)}$ with an $\alpha$-dependent scaling function, which has qualitatively very different shapes for $\alpha<1$ and $\alpha>1$. In contrast, for case (i), the typical long-time fluctuations of position are Gaussian. Comment: 25 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|