ASEP — Asymmetric Exclusion Process

Particles hop right with rate p and left with rate q=1-p, subject to hard-core exclusion. The ASEP is exactly solvable via Bethe ansatz and exhibits KPZ universality for fluctuations.

Lattice (gray=empty, colored=particle)

Current J vs density ρ

Space-time diagram

Parameters

Hop rate p (rightward): 0.75 Density ρ: 0.50 System size L: 108

J = 0

Exact current:
J = (p−q)ρ(1−ρ)

Phase diagram (TASEP, open BC):
• Low density phase
• High density phase
• Maximal current phase

KPZ fluctuations: σ ~ t^(1/3)

ASEP — Asymmetric Simple Exclusion Process

Parameters