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Quenched Large Deviations of Birkhoff Sums Along Random Quantum Measurements

https://doi.org/10.1007/s00023-025-01553-3

Raquépas, R; Schenker, J (March 2025, Annales Henri Poincaré)

Free, publicly-accessible full text available March 12, 2026
Dynamical Localization for Random Band Matrices Up to $$W\ll N^{1/4}$$

https://doi.org/10.1007/s00220-024-04948-1

Cipolloni, Giorgio; Peled, Ron; Schenker, Jeffrey; Shapiro, Jacob (March 2024, Communications in Mathematical Physics)

We prove that a large class of N × N Gaussian random band matrices with band width W exhibits dynamical Anderson localization at all energies when $$W <
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Law of large numbers and central limit theorem for ergodic quantum processes

https://doi.org/10.1063/5.0153483

Pathirana, Lubashan; Schenker, Jeffrey (August 2023, Journal of Mathematical Physics)

A discrete quantum process is represented by a sequence of quantum operations, which are completely positive maps that are not necessarily trace preserving. We consider quantum processes that are obtained by repeated iterations of a quantum operation with noise. Such ergodic quantum processes generalize independent quantum processes. An ergodic theorem describing convergence to equilibrium for a general class of such processes has been recently obtained by Movassagh and Schenker. Under irreducibility and mixing conditions, we obtain a central limit type theorem describing fluctuations around the ergodic limit.
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