Randinduzierte Phasenübergänge in Systemen selbstangetriebener Teilchen
Zusammenfassung der Projektergebnisse
We have studied universal properties of driven diffusive systems far from equilibrium mainly in one spatial dimension. In the first period of the project we have shown that the well-known diffusive and Kardar-Parisi-Zhang (KPZ) universality classes are members of a whole new infinite family of universality classes which we call the Fibonacci family since the dynamical exponents z of the members of this class are ratios of consecutive Fibonacci numbers. The main goal was to obtain a better understanding of this new family of universality classes. A simple explanation for the surprising form of the dynamical exponents, e.g. through underlying symmetries, remains elusive. However, we have been able to substantially improve our understanding of fluctuations in these systems, both in one and higher dimensions. Several new results, especially for the KPZ class, could be derived through the development of dedicated numerical and statistical methods which allowed to analyse the results of large-scale Monte Carlo simulations with improved statistical significance and obtain a detailed description of finite-time and non-stationary effects. For future research this opens up the possibility of studying more complex systems, e.g. other members of the Fibonacci class, multi-component and more realistic traffic models, with reliable interpretations of the numerical results. The systems investigated here have natural applications to biophysical problems, in particular molecular motors, and traffic systems. One important result is providing clear evidence that the popular Nagel-Schreckenberg model for highway traffic belongs to the KPZ universality class, resolving a problem that has been pending for more than 20 years. Going further, we investigated driven diffusive systems beyond one dimension. For networks of one-dimensional models we could surprisingly show that the (in)famous Braess paradox, which states that building a new street can lead to higher travel times for everybody, is indeed a rather generic phenomenon that can not even be avoided by traffic information systems. For a 2-dimensional driven lattice gas we provided for the first time strong numerical evidence for marginal superdiffusivity. Furthermore we found surprising new connections between classical and quantum driven systems that go beyond the previously known formal similarities. This opens new approaches especially for investigations of driven quantum systems. The project has shown that systems far from equilibrium still provide many open problems for fundamental research as well as being highly relevant for many applications which are often interdisciplinary in nature in the biophysical study of the cell and to transport in vehicular traffic flow.
Projektbezogene Publikationen (Auswahl)
- Braess paradox in a network of totally asymmetric exclusion processes, Phys. Rev. E 94, 062312 (2016)
S. Bittihn, A. Schadschneider
(Siehe online unter https://doi.org/10.1103/PhysRevE.94.062312) - Exact scaling solution of the mode coupling equations for non-linear fluctuating hydrodynamics in one dimension, JSTAT (2016) 093211
V. Popkov, A. Schadschneider, J. Schmidt, G.M. Schütz
(Siehe online unter https://doi.org/10.1088/1742-5468/2016/09/093211) - Height distribution tails in the Kardar-Parisi-Zhang equation with Brownian initial conditions, JSTAT (2017) 103207
B. Meerson, J. Schmidt
(Siehe online unter https://doi.org/10.1088/1742-5468/aa8c12) - Kardar-Parisi-Zhang modes in d-dimensional directed polymers, Phys. Rev. E 96, 032119 (2017)
G.M. Schütz, B. Wehefritz-Kaufmann
(Siehe online unter https://doi.org/10.1103/PhysRevE.96.032119) - Logarithmic superdiffusion in two dimensional driven lattice gases, J. Stat. Phys. 172, 493 (2018)
J. Krug, R.A. Neiss, A. Schadschneider, J. Schmidt
(Siehe online unter https://doi.org/10.1007/s10955-018-1995-z) - Self-duality and shock dynamics in the nspecies priority ASEP, Stoch. Process. Their Appl. 128, 1165 (2018)
V. Belitsky, G.M. Schütz
(Siehe online unter https://doi.org/10.1016/j.spa.2017.07.003)
