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This research extends random-matrix theory to quantum dots under time-resolved monitoring, deriving a discrete-time quantum master equation for charge transfer. The study numerically validates closed-form predictions based on an equipartition conjecture for monitored particles within the single-particle sector. By bridging algebraic solutions with numerical simulations, the work provides a rigorous framework for analyzing measurement-induced dynamics in chaotic quantum systems.
Monitored chaotic scattering
arXiv:2606.04794v1 Announce Type: cross Abstract: We extend the random-matrix theory of chaotic scattering to quantum dots whose dynamics is monitored by time-resolved measurements. Starting from a scattering matrix drawn from a circular ensemble, we construct the corresponding ensemble of Kraus operators for the monitored evolution of the many-body density matrix. In the single-particle sector the sum over measurement outcomes can be carried out algebraically, giving a discrete-time quantum master equation for the transferred charge. We solve this equation numerically and compare the resulting charge-transfer statistics with closed-form random-matrix predictions. The latter rely on an equipartition rule for monitored particles, which we formulate as a conjecture and test against the master equation.
Abstract:We extend the random-matrix theory of chaotic scattering to quantum dots whose dynamics is monitored by time-resolved measurements. Starting from a scattering matrix drawn from a circular ensemble, we construct the corresponding ensemble of Kraus operators for the monitored evolution of the many-body density matrix. In the single-particle sector the sum over measurement outcomes can be carried out algebraically, giving a discrete-time quantum master equation for the transferred charge. We solve this equation numerically and compare the resulting charge-transfer statistics with closed-form random-matrix predictions. The latter rely on an equipartition rule for monitored particles, which we formulate as a conjecture and test against the master equation.
15 pages, 7 figures; contribution for the special issue of this http URL. on "Random Matrices, Random Graphs, and Quantum Chaos: In Honor of Uzy Smilansky's 85th Birthday"
Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Quantum Physics (quant-ph)
arXiv:2606.04794 [cond-mat.mes-hall]
(or arXiv:2606.04794v1 [cond-mat.mes-hall] for this version)
https://doi.org/10.48550/arXiv.2606.04794 arXiv-issued DOI via DataCite (pending registration)
From: C. W. J. Beenakker [view email] [v1] Wed, 3 Jun 2026 12:20:33 UTC (203 KB)
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