We intend to study many dynamical aspects of quantum spin chains in the presence of quenched disorder. Firstly, we plan to study the dynamical response of quantum spin chains in the low-temperature regime and in thermal equilibrium. This is important in order to correct interpret the NMR and muon-SR experimental data. Secondly, we plan to study the time evolution of these systems in the far-from-equilibrium regime where they are effectively isolated from any thermal bath. In this case, the system may evolve towards a non-ergodic state depending on the disorder strength. This is the dynamical phase transition we intend to investigate.
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