Monitored chaotic scattering

Journal of Mathematical Physics, vol. 67

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.

Authors 3

1. C. W. J. Beenakker Aachen Instituut-Lorentz

   Leiden University

   Affiliation as printed

   Instituut-Lorentz, Universiteit Leiden 1 , P.O. Box 9506, 2300 RA Leiden,

2. Jose Sánchez Fernán Aachen Instituut-Lorentz

   Leiden University

   Affiliation as printed

   Instituut-Lorentz, Universiteit Leiden 1 , P.O. Box 9506, 2300 RA Leiden,

3. J. Tworzydło

   University of Warsaw

   Affiliation as printed

   Faculty of Physics, University of Warsaw 2 , ul. Pasteura 5, 02–093 Warszawa,