When classical systems fail to explore their entire configurationalspace, intriguing macroscopicphenomena like aging and glass formation may emerge. Also closed quanto-mechanical systems may stop wandering freely around the whole Hilbert space, even if they are initially prepared into a macroscopically large combination of eigenstates. This phenomenon is actually known to occur in presence of disorder and manifests itself either by single-particle  or many-particle  wavefunction localization. However, alike classical models for glassy behavior, ergodicity breakdown may not necessarily require disorder.  In this talk I will report numerical evidences that the dynamics of strongly interacting lattice bosons driven sufficiently far from equilibrium can be trapped into extremely long-lived inhomogeneous metastable states.  The slowing down of incoherent density excitations above a threshold energy, much reminiscent of a dynamical arrest on the verge of a glass transition, is identified as the key feature of this phenomenon. We argue that the resulting long-lived inhomogeneities are responsible for the lack of thermalization observed in large systems.  Such a rich phenomenology could be experimentally uncovered upon probing the out-of-equilibrium dynamics of conveniently prepared quantum states of trapped cold atoms which I will discuss. The approach used to extensively investigate this phenomenon is based both on the exact solution of the quantum dynamics and on a novel real- time variational Quantum Monte Carlo method we have introduced.  The latter approach offers a reliable accuracy and stability in the study of 1-dimensional systems while also o_ering a seamless exploration of higher dimensional geometries. REFERENCES  P. W. Anderson, Phys. Rev. 109, 1492 (1958).  D. Basko, I. Aleiner and B. Altshuler, Annals of Physics 321,1126 (2006)  G. Biroli and M. Mezard Phys. Rev. Lett. 88, 025501 (2001).  G. Carleo, F. Becca, M. Schiro and M. Fabrizio, arXiv:1109.2516 (2011).  C. Kollath, A. M. Lauchli and E. Altman, Phys. Rev. Lett. 98, 180601 (2007).
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