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arXiv · 2602.16544

The Quantum Symmetric Simple Exclusion Process in the Continuum and Free Processes

Denis Bernard
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Abstract

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.

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Denis Bernard. 2026-02-18. The Quantum Symmetric Simple Exclusion Process in the Continuum and Free Processes. https://arxiv.org/abs/2602.16544

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