The study of the dynamics of thermally isolated many-body systems offers a unique opportunity to address the role of universality in nonequilibrium quantum phenomena. In this talk I will discuss recent results concerning the statistics of the work and of other observables in spin chains and bosonic systems out of equilibrium. I will show that the statistics of the work at low energies for spin chains (or bosonic systems) subject to a generic local or global variation of the transverse field is independent on the detail of the protocol, an example of universal behaviour both in time and space. I will similarly show that the statistics of excitations can be used to discuss universality and detect efficiently dynamical phase transitions.
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