Browsing by Author "Nyawo, Pelerine Tsobgni"
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- ItemDriven nonequilibrium systems modeled with Markov processes(Stellenbosch : Stellenbosch University, 2017-12) Nyawo, Pelerine Tsobgni; Touchette, Hugo; Kastner, Michael; Stellenbosch University. Faculty of Science. Dept. of Physics.ENGLISH ABSTRACT : We study in this thesis the fluctuations of time-integrated functionals of Markov processes, which represent physical observables that can be measured in time for noisy systems driven in nonequilibrium steady states. The goal of the thesis is to illustrate how techniques from the theory of large deviations can be used to obtain the probability distribution of these observables in the long-time limit through the knowledge of an important function, called the rate function. We also illustrate in this thesis a recent theory of driven processes that aims to describe how fluctuations of observables are created in time by means of an effective process with modified forces or potentials. This is done by studying two simple models of nonequilibrium processes based on the Langevin equation. The first is a periodic diffusion that has current fluctuations, whereas the second is the simple drifted Brownian motion for which we study the occupation fluctuations. For these two models, we calculate analytically and numerically the rate function, as well as the associated driven process. The results for the periodic diffusion show, on the one hand, that there is a Gaussian to non-Gaussian crossover in the current fluctuations, which can easily be interpreted from the form of the driven process. On the other hand, the Brownian model provides one of the simplest examples of a dynamical phase transition, that is, a phase transition in the fluctuations of observables. Other connections with fluctuation relations, Josephson junctions, and the geometric Brownian motion are discussed.
- ItemDynamical phase transition in drifted Brownian motion(American Physical Society, 2018) Nyawo, Pelerine Tsobgni; Touchette, HugoWe 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.