Dynamical phase transition in drifted Brownian motion
Date
2018
Journal Title
Journal ISSN
Volume Title
Publisher
American Physical Society
Abstract
We study the occupation fluctuations of drifted Brownian motion in a closed interval and show that they undergo a dynamical phase transition in the long-time limit without an additional low-noise limit. This phase transition is similar to wetting and depinning transitions, and arises here as a switching between paths of the random motion leading to different occupations. For low occupations, the motion essentially stays in the interval for some fraction of time before escaping, while for high occupations the motion is confined in an ergodic way in the interval. This is confirmed by studying a confined version of the model, which points to a further link between the dynamical phase transition and quantum phase transitions. Other variations of the model, including the geometric Brownian motion used in finance, are considered to discuss the role of recurrent and transient motion in dynamical phase transitions.
Description
CITATION: Nyawo, P. T. & Touchette, H. 2018. Dynamical phase transition in drifted Brownian motion. Physical Review E, 98(5):052103, doi:10.1103/PhysRevE.98.052103.
The original publication is available at https://journals.aps.org/pre
The original publication is available at https://journals.aps.org/pre
Keywords
Brownian motion, Dynamical phase transition, Non-Hermitian quantum mechanics, Markov processes
Citation
Nyawo, P. T. & Touchette, H. 2018. Dynamical phase transition in drifted Brownian motion. Physical Review E, 98(5):052103, doi:10.1103/PhysRevE.98.052103