Unusual shock wave in two-species driven systems with an umbilic point

Abstract

Using dynamical Monte-Carlo simulations we observe the occurrence of an unexpected shock wave in driven diffusive systems with two conserved species of particles. This U-shock is microscopically sharp, but does not satisfy the usual criteria for the stability of shocks. Exact analysis of the large-scale hydrodynamic equations of motion reveals the presence of an umbilical point which we show to be responsible for this phenomenon. We prove that such an umbilical point is a general feature of multi-species driven diffusive systems with reflection symmetry of the bulk dynamics. We argue that an U-shock will occur whenever there are strong repulsive interactions such that the current-density relation develops a double-well and the umbilical point becomes isolated.

14 pages, 6 figures; typo in Eq (5) corrected

References in corpus (5)

• Phase transitions in systems with two species of molecular motors
• Spurious phase in a model for traffic on a bridge
• Rigorous results on spontaneous symmetry breaking in a one-dimensional driven particle system
• Robustness of spontaneous symmetry breaking in a bridge model
• Hierarchy of boundary driven phase transitions in multi-species particle systems

Cited by in corpus (5)

• Coupled Kardar-Parisi-Zhang Equations in One Dimension
• Universality classes in two-component driven diffusive systems
• Non-KPZ modes in two-species driven diffusive systems
• Self-duality and shock dynamics in the $n$-component priority ASEP
• Universality in many-body driven systems with an umbilic point