Abstract

Large deviation functions of non-equilibrium accumulative/integrated quantities have been intensively studied in the last decade in thermally fluctuated particles (e.g., Brownian particles, biological motors, Granular particles) as well as in exactly solvable lattice gas models (e.g., ASEP , KPZ, KCMs). Although large deviations show many interesting physics, studying them is difficult, as rare fluctuations showing these large deviations are hardly observed. In this seminar, I will explain an algorithm to accelerate the observation of these rare events in numerical simulations. The algorithm uses an idea of population dynamics/diffusion quantum Monte-Carlo method [1]: an ensemble of the copies of the system is simulated, where the dynamics of the ensemble include a selection-mutation process, namely, rare copies are multiplied (have descendants) but typical ones are killed (become extinct). I will also review our recent works that focus on the fundamental aspects of the algorithm (convergence property [2] and an improvement to the algorithm by introducing a control force [3]) as well as on the application of the algorithm to active matter [4].

[1] Cristian Giardinà, Jorge Kurchan and Luca Peliti, Phys. Rev. Lett. 96, 120603 (2006). [2] T.N., Esteban Guevara and Vivien Lecomte, PRE 95 ,012102(2017) and E.G., T.N. and V.L. PRE 95 ,062134 (2017). [3] T.N., Freddy Bouchet, Robert L. Jack and V.L.,PRE 93,062123(2016) and T.N., R.L.J. and V.L., PRL 118 ,115702(2017). [4] T.N., Michael E. Cates, Étienne Fodor, R.L.J. and Julien Tailleur in preparation.