Rare-History Transitions in Temporally Random Integrable Quantum Circuits

Abstract:We study current fluctuations in a temporally random integrable quantum circuit. Commutativity reduces every drive history exactly to its layer composition, turning annealed fluctuations into a competition between current gain and the large-deviation cost of rare compositions. For each fixed composition, homogeneous thermodynamic Bethe ansatz dressing supplemented by ballistic fluctuation theory yields the conditional current statistics. Their annealed large-deviation contraction predicts a first-order switch between two dominant history classes, terminating on a line of regular cusp endpoints. Finite-time analysis shows how the switch is rounded. Thus temporal randomness can act as an emergent order-parameter-like coordinate in trajectory space.

5 pages, 2 figures. Supplemental Material will be submitted separately. This is an initial draft, and comments are welcome

Statistical Mechanics (cond-mat.stat-mech); Exactly Solvable and Integrable Systems (nlin.SI); Quantum Physics (quant-ph)

arXiv:2609.11415 [cond-mat.stat-mech]

(or arXiv:2609.11415v1 [cond-mat.stat-mech] for this version)

https://doi.org/10.48550/arXiv.2609.11415 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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