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Multispecies totally asymmetric simple exclusion process with long-range swap
by Eunghyun Lee
Submission summary
| Authors (as registered SciPost users): | Eunghyun Lee |
| Submission information | |
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| Preprint Link: | scipost_202509_00002v2 (pdf) |
| Date submitted: | Dec. 17, 2025, 1:42 a.m. |
| Submitted by: | Eunghyun Lee |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| 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 comments upon resubmission
List of changes
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.
Response to Referee 2:
We thank the referee for this suggestion. 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.