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arXiv · 2607.26262

The boundary-driven multispecies harmonic process

Francesco Casini·Rouven Frassek·Cristian Giardinà
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Abstract

We introduce the multispecies version of the harmonic process on a one-dimensional chain in contact with boundary reservoirs. This process is a continuous-time Markov chain where each site can host an unbounded number of colored particles. The symmetric bulk dynamics is put in contact with reservoirs, which inject and remove particles driving the system out-of-equilibrium. The Markov generator of the process is identified with the integrable Hamiltonian of an open rational Heisenberg spin chain of higher rank. We derive the underlying R- and K-matrices in operator form and construct the double-row transfer matrix following Sklyanin. Similar to the monospecies case the R-matrix factorises into two R-operators, each factor corresponding to left and right moving particles. We further define three dual models: an absorbing particle model, a hidden parameter model and a heat conduction model.

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Francesco Casini, Rouven Frassek, Cristian Giardinà. 2026-07-28. The boundary-driven multispecies harmonic process. https://arxiv.org/abs/2607.26262

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