# Kardar-Parisi-Zhang universality of the Nagel-Schreckenberg model.

@article{deGier2019KardarParisiZhangUO, title={Kardar-Parisi-Zhang universality of the Nagel-Schreckenberg model.}, author={Jan de Gier and Andreas Schadschneider and Johannes Schmidt and Gunter M. Sch{\"u}tz}, journal={Physical review. E}, year={2019}, volume={100 5-1}, pages={ 052111 } }

Dynamical universality classes are distinguished by their dynamical exponent z and unique scaling functions encoding space-time asymmetry for, e.g., slow-relaxation modes or the distribution of time-integrated currents. So far the universality class of the Nagel-Schreckenberg (NaSch) model, which is a paradigmatic model for traffic flow on highways, was not known. Only the special case v_{max}=1, where the model corresponds to the totally asymmetric simple exclusion process, is known to belong…

## 6 Citations

### Detection of Kardar–Parisi–Zhang hydrodynamics in a quantum Heisenberg spin-1/2 chain

- PhysicsNature Physics
- 2020

Classical hydrodynamics is a remarkably versatile description of the coarse-grained behavior of many-particle systems once local equilibrium has been established. The form of the hydrodynamical…

### Power laws and phase transitions in heterogenous car following with reaction times.

- PhysicsPhysical review. E
- 2021

It is concluded that the nonzero reaction times of drivers in heterogeneous traffic significantly change the behavior of the free flow to congestion transition while it doesn't alter the kinetics of relaxation to stationary state.

### Pinned or moving: States of a single shock in a ring.

- PhysicsPhysical review. E
- 2020

These studies provide an explicit route to control the quantitative extent of domain-wall fluctuations in driven periodic inhomogeneous systems, and should be relevant in any quasi-one-dimensional transport processes where the availability of carriers is the rate-limiting constraint.

### Self-Organized Criticality of Traffic Flow: There is Nothing Sweet about the Sweet Spot

- Computer Science
- 2021

This paper shows that the kinematic wave model exhibits self-organized criticality when initialized with random initial conditions around the critical density. A direct consequence is that…

### Riemann surfaces for KPZ with periodic boundaries

- MathematicsSciPost Physics
- 2020

The Riemann surface for polylogarithms of half-integer index, which has the topology of an infinite dimensional hypercube, is studied in relation to one-dimensional KPZ universality in finite volume.…

### A lattice Gas Model for Generic One-Dimensional Hamiltonian Systems

- PhysicsJournal of Statistical Physics
- 2021

We present a three-lane exclusion process that exhibits the same universal fluctuation pattern as generic one-dimensional Hamiltonian dynamics with short-range interactions, viz., with two sound…

## References

SHOWING 1-10 OF 99 REFERENCES

### The Kardar-Parisi-Zhang equation and universality class

- Mathematics
- 2011

Brownian motion is a continuum scaling limit for a wide class of random processes, and there has been great success in developing a theory for its properties (such as distribution functions or…

### Height distribution tails in the Kardar–Parisi–Zhang equation with Brownian initial conditions

- Mathematics
- 2017

For stationary interface growth, governed by the Kardar–Parisi–Zhang (KPZ) equation in 1+1 dimensions, typical fluctuations of the interface height at long times are described by the Baik–Rains…

### One-dimensional Kardar-Parisi-Zhang equation: an exact solution and its universality.

- Mathematics, PhysicsPhysical review letters
- 2010

The solution confirms that the KPZ equation describes the interface motion in the regime of weak driving force, and provides a determinantal formula for the probability distribution function of the height h(x,t) for all t>0.

### Fibonacci family of dynamical universality classes

- PhysicsProceedings of the National Academy of Sciences
- 2015

It is shown that the two best-known examples of nonequilibrium universality classes, the diffusive and Kardar−Parisi−Zhang classes, are only part of an infinite discrete family, which strongly indicates the existence of a simpler underlying mechanism that determines the different classes.

### Scaling Limit for the Space-Time Covariance of the Stationary Totally Asymmetric Simple Exclusion Process

- Mathematics
- 2005

The totally asymmetric simple exclusion process (TASEP) on the one-dimensional lattice with the Bernoulli ρ measure as initial conditions, 0<ρ<1, is stationary in space and time. Let Nt(j) be the…

### Bethe ansatz solution for crossover scaling functions of the asymmetric XXZ chain and the Kardar-Parisi-Zhang-type growth model.

- PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1995

A perturbative method is developed to calculate the finite size corrections of the low lying energies of the asymmetric XXZ hamiltonian near the stochastic line. The crossover from isotropic to…

### Exact spectral gaps of the asymmetric exclusion process with open boundaries

- Physics
- 2006

We derive the Bethe ansatz equations describing the complete spectrum of the transition matrix of the partially asymmetric exclusion process with the most general open boundary conditions. By…

### Growth models, random matrices and Painlevé transcendents

- Mathematics
- 2003

The Hammersley process relates to the statistical properties of the maximum length of all up/right paths connecting random points of a given density in the unit square from (0, 0) to (1, 1). This…

### Finite-Time Fluctuations for the Totally Asymmetric Exclusion Process.

- Mathematics, PhysicsPhysical review letters
- 2016

The one-dimensional totally asymmetric simple exclusion process, a Markov process describing classical hard-core particles hopping in the same direction, is considered on a periodic lattice of L sites, and exact expressions depending explicitly on the rescaled time are obtained.

### Exact scaling solution of the mode coupling equations for non-linear fluctuating hydrodynamics in one dimension

- Physics, Mathematics
- 2016

We obtain the exact solution of the one-loop mode-coupling equations for the dynamical structure function in the framework of non-linear fluctuating hydrodynamics in one space dimension for the…