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Monitored chaotic scattering

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

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Cite

BibTeXRIS
BibTeX
@misc{beenakker2026monitored,
  title = {{Monitored chaotic scattering}},
  author = {C. W. J. Beenakker and J. Sánchez Fernán and J. Tworzydło},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2606.04794},
  eprint = {2606.04794},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.04794},
}
RIS
TY  - UNPB
TI  - Monitored chaotic scattering
AU  - C. W. J. Beenakker
AU  - J. Sánchez Fernán
AU  - J. Tworzydło
PY  - 2026
DA  - 2026/08/18
PB  - arXiv
DO  - 10.48550/arxiv.2606.04794
UR  - https://arxiv.org/abs/2606.04794
AB  - 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.
ER  -