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This research extends random-matrix theory to describe chaotic scattering in quantum dots under continuous monitoring via time-resolved measurements. By deriving a discrete-time quantum master equation, the study numerically validates charge-transfer statistics against closed-form predictions based on an equipartition rule for monitored particles. The work advances fundamental understanding of open quantum systems and measurement-induced dynamics within mesoscopic physics.
Monitored chaotic scattering
arXiv:2606.04794v2 Announce Type: replace-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:2606.04794v2 [cond-mat.mes-hall] for this version)
From: C. W. J. Beenakker [view email] [v1] Wed, 3 Jun 2026 12:20:33 UTC (203 KB) [v2] Tue, 18 Aug 2026 20:24:47 UTC (204 KB)
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