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arXiv · 1805.02871

Self--averaging of random quantum dynamics

Marcin Łobejko·Jerzy Dajka·Jerzy Łuczka
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Abstract

Stochastic dynamics of a quantum system driven by $N$ statistically independent random sudden quenches in a fixed time interval is studied. We reveal that with growing $N$ the system approaches a deterministic limit indicating self-averaging with respect to its temporal unitary evolution. This phenomenon is quantified by the variance of the unitary matrix governing the time evolution of a finite dimensional quantum system which according to an asymptotic analysis decreases at least as $1/N$. For a special class of protocols (when the averaged Hamiltonian commutes at different times), we prove that for finite $N$ the distance (according to the Frobenius norm) between the averaged unitary evolution operator generated by the Hamiltonian $H$ and the unitary evolution operator generated by the averaged Hamiltonian $\langle H \rangle$ scales as $1/N$. Numerical simulations enlarge this result to a broader class of the non-commuting protocols.

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Marcin Łobejko, Jerzy Dajka, Jerzy Łuczka. 2018-05-08. Self--averaging of random quantum dynamics. https://doi.org/10.1103/physreva.98.022111

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