Self--averaging of random quantum dynamics

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 $⟨H⟩$ scales as $1/N$. Numerical simulations enlarge this result to a broader class of the non-commuting protocols.

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Cited by in corpus (5)

• Self-averaging in many-body quantum systems out of equilibrium: Chaotic systems
• Multifractality and self-averaging at the many-body localization transition
• Self-averaging in many-body quantum systems out of equilibrium. II. Approach to the localized phase
• Floquet topological transition by unpolarized light
• Reducing dynamical fluctuations and enforcing self-averaging by opening many-body quantum systems