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DY: Fachverband Dynamik und Statistische Physik
DY 9: Statistical Physics far from Thermal Equilibrium
DY 9.5: Hauptvortrag
Montag, 17. März 2025, 16:00–16:30, H47
Large-deviation simulations of non-equilibrium stochastic processes — •Alexander K. Hartmann — University of Oldenburg, Germany
Stochastic processes are investigated by obtaining the probability distributions P(S) of relevant quantities S of interest. A full description is obtained, if P(S) is known over its full range of support. Also the structure of the entities contributing to the different parts of P(S) are of interest. Usually analytical calculations are not feasible, so most of the time one has to use numerical simulations. Unfortunately, most of the support, in particular in the tails, is not accessible by standard algorithms.
By applying special large-deviation algorithms, also the tails can be accessed, down to probabilities such as 10−200, or even much smaller. Here, a very general black-box algorithm [1] is explained, which allows one to study rather arbitrary stochastic processes. Some application examples are shown, such as force-induced RNA unfolding [2], S being the physical work W; interface growth [3], S being the height H; fractional Brownian motion [4], S being the area A under the curve; or the spread of diseases [5], S being the number of infected.
[1] A.K. Hartmann, Phys. Rev. E 89, 052103 (2014)
[2] P. Werner and A.K. Hartmann, Phys. Rev. E 104, 034407 (2021)
[3] A.K. Hartmann, P. Le Doussal, S.N. Majumdar, A. Rosso and G. Schehr, Europhys. Lett. 121, 67004 (2018)
[4] A.K. Hartmann and B. Meerson, Phys. Rev. E 109, 014146 (2024)
[5] Y. Feld and A.K. Hartmann, Phys. Rev. E 105, 034313 (2022)
Keywords: large-deviation properties; Monte Carlo simulations; stochastic motion; non-equilibrium processes; rare events