| We'll review some recent results on the spectral structure and the dynamics of Bose-Hubbard systems under static tilt. While it was shown earlier that, generically, the Bose-Hubbard Hamiltonian exhibits "chaotic" level structure in the sense of random matrix theory (RMT), we shall here inspect some practical consequences thereof. On the one hand, we will show that an RMT-inspired analysis allows to define physical conditions for the "efficient" simulability of the complex many-particle dynamics. On the other, we will show that some sort of cooperativity effect within the chaotic level structure leads to the nonlinearity-induced emergence of new, robust many-particle states with solitonic character. |
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