SciPost Submission Page
Multispecies totally asymmetric simple exclusion process with long-range swap
by Eunghyun Lee
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Eunghyun Lee |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202509_00002v1 (pdf) |
| Date submitted: | Sept. 1, 2025, 11:34 a.m. |
| Submitted by: | Eunghyun Lee |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
The author(s) disclose that the following generative AI tools have been used in the preparation of this submission:
I, as a non-native English speaker, made use of ChatGPT only for English editing and polishing purposes. All mathematical content, proofs, derivations, and scientific arguments were conceived, written, and verified entirely by the authors.
Abstract
We introduce the multispecies totally asymmetric simple exclusion process (mTASEP) with long-range swap, a new interacting particle system combining the backward-push rule with the forward-jump rule. Although governed by local dynamics, the model induces effective long-range particle exchanges. We establish its integrability by proving two-particle reducibility and showing that the associated scattering matrix satisfies the Yang-Baxter equation. In addition, we derive explicit contour integral formulas for transition probabilities. These results position the long-range swap model as a novel exactly solvable multispecies process, characterized by distinctive algebraic features and opening new directions for further study in integrable probability and statistical mechanics.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Strengths
2 Explicit contour integral formulas for transition probabilities
Weaknesses
2 No physics motivation for introducing this model
Report
including a dynamical phase transition discussed in generic terms in A. Lazarescu, Generic dynamical phase transition in one-dimensional bulk-driven lattice gases with exclusion, J. Phys. A 50, 254004 (2017).
With such a revision I would recommend publication, even though I feel that the paper might be more appropriate for SciPost core.
Requested changes
1 Provide a physical motivation for introducing this model, e.g. by discussing the two papers mentioned in the report.
Recommendation
Ask for minor revision
Strengths
1- Clean final result, eq. (65), (61), from which asymptotic analysis appears plausible.
Weaknesses
1- Yet another integrable variant of the exclusion process, without a clear physical motivation, such as whether a new large scale behaviour is expected compared to earlier models.
Report
The paper is reasonably well written, with an introduction explaining the dynamics of the model in a clear way.
The paper is however quite technical. Additionally, the paper ultimately deals only with some variant of a model solved before, with a final result quite similar in structure to earlier results for other kinds of multispecies exclusion processes. As such, I think that the paper would be a better fit for SciPost Physics Core.
Requested changes
1- It would be useful to write explicitly how the coefficients A_sigma in your case differ from those of the earlier multispecies TASEP.
2-Multispecies exclusion processes are related to q-deformed SU(N) quantum groups, and a nested Bethe ansatz procedure is generally used to diagonalize the generator of the evolution. On the other hand, your formula (65) for the propagator involves a single set of Bethe rapidities. Can you comment on this ?
Recommendation
Accept in alternative Journal (see Report)
Response to Comment 1:
We thank the referee for this suggestion.
We have clarified this point in Section~3.2 of the revised manuscript. In particular,
in Section~3.2.1, we now explicitly display the two-particle scattering matrix for the present model and compare it with the corresponding matrix for the usual multispecies TASEP; after the full construction of the multi-particle coefficients
$\mathbf{A}_\sigma$, we added a remark (Remark 3.3) emphasizing that, unlike the triangular scattering matrices of the usual multispecies TASEP reflecting priority-based interactions, the scattering matrices in our model involve both
$\mathbf{B}$ and $\mathbf{B}'$ and encode nontrivial long-range swap processes. As a consequence, the resulting coefficients $\mathbf{A}_\sigma$ differ qualitatively from those appearing in earlier multispecies exclusion processes.
Response to Comment 2:
We appreciate this insightful comment. We added a remark (Remark 3.2) immediately after the Bethe ansatz formula for the propagator (Eq.~(65) in the revised manuscript) clarifying this point. In our approach, the Bethe ansatz is applied to the
spatial evolution in order to construct the transition probabilities, rather than to a spectral diagonalization of the generator. The dependence on particle species is encoded in the matrix-valued amplitudes $\mathbf{A}_\sigma$, which
are constructed from the two-particle scattering matrices $\mathbf{R}_{\beta\alpha}$ and $\mathbf{T}_{i,\beta\alpha}$. The consistency of this construction follows from two-particle reducibility and the Yang--Baxter relations established in Section~3.2. This explains why a single set of spectral parameters is sufficient in our formulation.
Author: Eunghyun Lee on 2025-12-17 [id 6153]
(in reply to Report 2 on 2025-11-26)We thank the referee for the careful reading of the manuscript and for the constructive suggestion regarding the physical motivation of the model.
We have added a new motivation paragraph near the end of the Introduction. There we explain that one of the motivations for introducing the present model is to investigate whether effective long-range interactions, even when generated by purely local update rules, can lead to new large-scale dynamical behavior. As suggested by the referee, we now explicitly cite and briefly discuss related works by Karevski and Sch\"{u}tz (Phys.\ Rev.\ Lett.\ \textbf{118}, 030601 (2017)) and Lazarescu (J.\ Phys.\ A:\ Math.\ Theor.\ \textbf{50}, 254004 (2017)), and we clarify that the present work focuses on integrability and exact transition probabilities, while leaving large-time asymptotic analysis for future investigation.