Deterministic and randomized motions in single-well potentials. (26th September 2019)

• Record Type: Journal Article
• Authors: Mandrysz, Michał; Dybiec, Bartłomiej
• Is Part Of: Journal of physics. Volume 52:Number 42(2019)
• Publication Date: 2019-09-26
• Subjects: velocity reversals -- randomized motion -- Lévy walks -- probability densities -- single-well potential; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ab4350
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: Newtonian, undamped motion in single-well potentials belong to a class of well-studied conservative systems. Here, we investigate and compare long-time properties of fully deterministic motions in single-well potentials with analogous randomized systems. We consider a special type of energy-conserving randomization process: the deterministic motion is interrupted by hard velocity reversals at random time instants t i . In the 1D case, for fixed initial conditions, the differences in probability distributions disappear in the long-time limit making asymptotic densities insensitive to the selection of random time instants when velocity is reversed. Substantially different probability distributions can be obtained, for instance, through the additional randomization of initial conditions. Analogously, in 2D setups, the probability distributions asymptotically are insensitive to a protocol of velocity reversals.