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We study the spectral and dynamical properties of cold bosonic
atoms in the optical lattices using the Bose-Hubbard formalism,
i.e. beyond the mean field approximation. In the case of relatively shallow 3D lattices (optical potential depth 2-10
recoil energies), where the atomic kinetic energy is of the same order as the interaction energy, and filling factor (mean number of the atoms per lattice site) about unity, the energy spectrum of the system is found to obey Wigner-Dyson statistics (for the Gaussian orthogonal ensemble) and, hence, it can be considered as a quantum chaotic system [1]. This property of `chaoticity' is shown to have a number of important physical consequences. In particular, we consider the response of the system to a static force [2-4]. Neglecting the atom-atom
interaction, this response would be periodic Bloch oscillations of the mean atomic momentum. The atom-atom interaction profoundly modifies these oscillations, which are now quasiperiodic in the case of strong forcing [2], and decay irreversably, for a weak static force [3]. These two different dynamical regimes are shown to be a manifestation of an `order-to-chaos' transition in the system, with the magnitude of the static force as the control parameter.
[1] A. R. Kolovsky and A. Buchleitner, e-print cond-mat/0403213 (2004). [2] A. R. Kolovsky, Phys. Rev. Lett. 90, 213002 (2003). [3] A. Buchleitner and A. R. Kolovsky, Phys. Rev. Lett. 91, 253002 (2003). [4] A. R. Kolovsky and A. Buchleitner, Phys. Rev. E 68, 056213 (2003). |