Anomalous scalings of fluctuations of the area swept by a Brownian particle trapped in a |x| potential

Naftali R. Smith

Physica A: Statistical Mechanics and its Applications, 2024, vol. 650, issue C

Abstract: We study the fluctuations of the area A=∫0Tx(t)dt under a one-dimensional Brownian motion x(t) in a trapping potential ∼|x|, at long times T→∞. We find that typical fluctuations of A follow a Gaussian distribution with a variance that grows linearly in time (at large T), as do all higher cumulants of the distribution. However, large deviations of A are not described by the “usual” scaling (i.e., the large deviations principle), and are instead described by two different anomalous scaling behaviors: Moderately-large deviations of A, obey the anomalous scaling PA;T∼e−T1/3fA/T2/3 while very large deviations behave as PA;T∼e−TΨA/T2. We find the associated rate functions f and Ψ exactly. Each of the two functions contains a singularity, which we interpret as dynamical phase transitions of the first and third order, respectively. We uncover the origin of these striking behaviors by characterizing the most likely scenario(s) for the system to reach a given atypical value of A. We extend our analysis by studying the absolute area B=∫0T|x(t)|dt and also by generalizing to higher spatial dimension, focusing on the particular case of three dimensions.

Keywords: Large deviation theory; Brownian motion; Dynamical phase transitions (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437124004965
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:650:y:2024:i:c:s0378437124004965

DOI: 10.1016/j.physa.2024.129987

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().