The Quantum Symmetric Simple Exclusion Process in the Continuum and Free Processes
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866912911900803072 |
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| author | Bernard, Denis |
| author_facet | Bernard, Denis |
| contents | The quantum symmetric simple exclusion process (QSSEP) is a recent extension of the symmetric simple exclusion process, designed to model quantum coherent fluctuating effects in noisy diffusive systems. It models stochastic nearest-neighbor fermionic hopping on a lattice, possibly driven out-of-equilibrium by boundary processes. We present a direct formulation in the continuum, and establish how this formulation captures the scaling limit of the discrete version. In the continuum, QSSEP emerges as a non-commutative process, driven by free increments, conditioned on the algebra of functions on the ambiant space to encode spatial correlations. We actually develop a more general framework dealing with conditioned orbits with free increments which may find applications beyond the present context. We view this construction as a preliminary step toward formulating a quantum extension of the macroscopic fluctuation theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16544 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Quantum Symmetric Simple Exclusion Process in the Continuum and Free Processes Bernard, Denis Mathematical Physics Statistical Mechanics Probability The quantum symmetric simple exclusion process (QSSEP) is a recent extension of the symmetric simple exclusion process, designed to model quantum coherent fluctuating effects in noisy diffusive systems. It models stochastic nearest-neighbor fermionic hopping on a lattice, possibly driven out-of-equilibrium by boundary processes. We present a direct formulation in the continuum, and establish how this formulation captures the scaling limit of the discrete version. In the continuum, QSSEP emerges as a non-commutative process, driven by free increments, conditioned on the algebra of functions on the ambiant space to encode spatial correlations. We actually develop a more general framework dealing with conditioned orbits with free increments which may find applications beyond the present context. We view this construction as a preliminary step toward formulating a quantum extension of the macroscopic fluctuation theory. |
| title | The Quantum Symmetric Simple Exclusion Process in the Continuum and Free Processes |
| topic | Mathematical Physics Statistical Mechanics Probability |
| url | https://arxiv.org/abs/2602.16544 |