The q-PushASEP: A New Integrable Model for Traffic in 1+1 Dimension

Understand

We introduce a new interacting (stochastic) particle system q-PushASEP which interpolates between the q-TASEP introduced by Borodin and Corwin (see arXiv:1111.4408, and also arXiv:1207.5035; arXiv:1305.2972; arXiv:1212.6716) and the q-PushTASEP introduced recently by Borodin and Petrov (arXiv:1305.5501).

• In the q-PushASEP, particles can jump to the left or to the right, and there is a certain partially asymmetric pushing mechanism present.
• This particle system has a nice interpretation as a model of traffic on a one-lane highway in which cars are able to accelerate or slow down.
• Using the quantum many body system approach, we explicitly compute the expectations of a large family of observables for this system in terms of nested contour integrals.