Monitored chaotic scattering
arXiv:2606.04794
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 JMathPhys. on "Random Matrices, Random Graphs, and Quantum Chaos: In Honor of Uzy Smilansky's 85th Birthday"