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arXiv:2606.04794 · Journal of Mathematical Physics

Monitored chaotic scattering

C. W. J. Beenakker, J. Sánchez Fernán, J. Tworzydło

cond-mat.mes-hallquant-phSubmitted Jun 3, 2026• Announced Jun 4, 2026• 0 citations
v1 · Jun 3, 2026v2 · Aug 18, 2026
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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.

Journal reference
J. Math. Phys. 67, 091901 (2026)
DOI
10.1063/5.0346430
Comments
15 pages, 7 figures; contribution for the special issue of J.Math.Phys. on "Random Matrices, Random Graphs, and Quantum Chaos: In Honor of Uzy Smilansky's 85th Birthday"

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