# Traffic models and traffic-jam transition in quantum (N+1)-level systems

### Submission summary

 As Contributors: Andrea Nava · Marco Rossi Preprint link: scipost_202203_00017v1 Date accepted: 2022-03-24 Date submitted: 2022-03-14 13:20 Submitted by: Nava, Andrea Submitted to: SciPost Physics Core Academic field: Physics Specialties: Quantum Physics Approaches: Theoretical, Computational

### Abstract

We propose a model to implement and simulate different traffic-flow conditions in terms of quantum graphs hosting an (N+1)-level dot at each site, which allows us to keep track of the type and of the destination of each vehicle. By implementing proper Lindbladian local dissipators, we derive the master equations that describe the traffic flow in our system. To show the versatility and the reliability of our technique, we employ it to model different types of traffic flow (the symmetric three-way roundabout and the three-road intersection). Eventually, we successfully compare our predictions with results from classical models.

Published as SciPost Phys. Core 5, 022 (2022)

### Submission & Refereeing History

#### Published as SciPost Phys. Core 5, 022 (2022)

Submission scipost_202203_00017v1 on 14 March 2022

## Reports on this Submission

### Anonymous Report 1 on 2022-3-18 (Invited Report)

• Cite as: Anonymous, Report on arXiv:scipost_202203_00017v1, delivered 2022-03-18, doi: 10.21468/SciPost.Report.4723

### Report

I have looked through the changes and confirm that the authors have addressed the minor issues concerning their presentation. I thus recommend publication in SciPost Physics Core.

There are just some small details (see "Requested changes") that the authors might still wish to implement in order to ensure a smooth production process.

### Requested changes

To be considered, preferably for the version going into production:

1- The statement "Despite its potentially wide applicability, the formalism based on the effective Hamiltonian $\hat{H}$ is not easy to implement, since it is not easy to compute the operator expectation values" on page 2 might be disputable since this has actually been done in previous works. The authors might thus wish to reconsider this statement.
2- Page 5, 3 lines above Eq. (5): I think there is an article "the" missing before "next Section".
3- Page 7, last but one line: remove space between "(" and "including".
4- Fig. 12: Maybe the authors have increased the size of the numbers in the blue dots, but they still look (too) small to me. Maybe the authors could try again to make both the blue dots and the numbers inside them bigger.

• validity: good
• significance: good
• originality: good
• clarity: top
• formatting: excellent
• grammar: excellent