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 [1] or many-particle  [2] wavefunction localization. However, alike classical models for glassy behavior, ergodicity breakdown may not necessarily require disorder.  [3] 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.  [4] 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.  [5] 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.  [4] 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
[1] P. W. Anderson, Phys. Rev. 109, 1492 (1958).
[2] D. Basko, I. Aleiner and B. Altshuler, Annals of Physics 321,1126 (2006)
[3] G. Biroli and M. Mezard Phys. Rev. Lett. 88, 025501 (2001).
[4] G. Carleo, F. Becca, M. Schiro and M. Fabrizio, arXiv:1109.2516 (2011).
[5] C. Kollath, A. M. Lauchli and E. Altman, Phys. Rev. Lett. 98, 180601 (2007).