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We derive general evolution equations describing the ensemble-average quantum dynamics generated by disordered Hamiltonians. The disorder average affects the coherence of the evolution and can be accounted for by suitably tailored effective coupling agents and associated rates which encode the specific statistical properties of the Hamiltonians eigenvectors and eigenvalues, respectively. Spectral disorder and isotropically disordered eigenvector distributions are considered as paradigmatic test cases.
We investigate the time evolution of an open quantum system described by a Lindblad master equation with dissipation acting only on a part of the degrees of freedom ${cal H}_0$ of the system, and targeting a unique dark state in ${cal H}_0$. We show
Most protocols for Quantum Information Processing consist of a series of quantum gates, which are applied sequentially. In contrast, interactions, for example between matter and fields, as well as measurements such as homodyne detection of light, are
We study the out-of-equilibrium dynamics in the quantum Ising model with power-law interactions and positional disorder. For arbitrary dimension $d$ and interaction range $alpha geq d$ we analytically find a stretched exponential decay of the global
The dynamics of interacting quantum systems in the presence of disorder is studied and an exact representation for disorder-averaged quantities via Ito stochastic calculus is obtained. The stochastic integral representation affords many advantages, i
Understanding the dynamics of strongly interacting disordered quantum systems is one of the most challenging problems in modern science, due to features such as the breakdown of thermalization and the emergence of glassy phases of matter. We report o