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[en] Superflow of a Bose-Einstein condensate in an optical lattice is represented by a Bloch wave, a plane wave with periodic modulation of the amplitude. We review the theoretical results of the interaction effects in the energy dispersion of the Bloch waves and in the linear stability of such waves. For sufficiently strong repulsion between the atoms, the lowest Bloch band develops a loop at the edge of the Brillouin zone, with the dramatic consequence of a finite probability of Landau-Zener tunnelling even in the limit of a vanishing external force. Superfluidity can exist in the central region of the Brillouin zone in the presence of a repulsive interaction, beyond which Landau instability takes place where the system can lower its energy by making a transition into states with smaller Bloch wavenumbers. In the outer part of the region of Landau instability, the Bloch waves are also dynamically unstable in the sense that a small initial deviation grows exponentially in time. In the inner region of Landau instability, a Bloch wave is dynamically stable in the absence of persistent external perturbations. Experimental implications of our findings will be discussed
[en] The deviations from linearity in the concentration dependence of lattice spacings in AgcPd1-c have been recently related to the topology changes shown by the Fermi Surface, or Electronic Topological Transitions (ETTs), of this alloy. Using an extension of the ETTs theory to finite-temperature and impurity scattering case, and in terms of a simple Rigid Band Model, the paper studies such deviations and interpret them as the results of the filling of the hole pocket centered at the X point of the Brillouin Zone, remarking the role of the finiteness of the quasi-particle lifetime of the relevant states. It also shows how ab initio calculations based on the Coherent Potential Approximation underestimate these lifetimes
[en] We report a theoretical work on the properties of modulational instability and bright type nonlinear localized modes in one-dimensional easy-axis weak ferromagnetic spin lattices involving next-nearest-neighbor couplings. With a linear stability analysis, we calculate the growth rates of the modulational instability, and plot the instability regions. When the strength of the next-nearest-neighbor coupling is large enough, two new asymmetric modulational instability regions appear near the boundary of the first Brillouin zone. Furthermore, analytical forms of the bright nonlinear localized modes are constructed by means of a quasi-discreteness approach. The influence of the next-nearest-neighbor coupling on the Brillouin zone center mode and boundary mode are discussed. In particular, we discover a reversal phenomenon of the propagation direction of the Brillouin zone boundary mode. (paper)
[en] The mechanism of opening a band gap in the free phononic crystal (PC) thin plate with or without a mirror plane is investigated. It is found that, in a PC plate with a mirror plane, the permitted modes can be separated into symmetric and antisymmetric modes, and the band gap in such a system can be opened by the interaction between the modes of the same kind and/or the breaking of the degeneracy of the mode at the edge of the Brillouin zone. However, for a PC plate without a mirror plane, mode separation can no longer be performed, and interaction can occur between any two permitted modes. As a result, a new kind of band gap can be opened.
[en] We first recall some theorems on the extrema of functions defined on a compact manifold M invariant under the action of a finite group acting on M and blend them with Morse theory. We apply this study to functions on two- or three-dimensional Brillouin zones invariant under crystal symmetry and time reversal. After recalling some facts on invariant theory, we give explicitly the general form of these functions for the 13 arithmetic classes in two dimensions
[en] We describe a method that allows transient suppression of spontaneous emission-induced diffusion in the atom-optics realization of the kicked rotor. The system is prepared in an initial state with a momentum distribution concentrated in an interval much sharper than the Brillouin zone; the measure of the momentum distribution is restricted to this interval of quasimomenta. Because most of the atoms undergoing decoherence processes fall outside this detection range and thus are not detected, the measured signal is effectively free of decoherence-induced diffusion effects.
[en] We investigate the Landau-Zener tunnelling of two-component Bose-Einstein condensates (BECs) in optical lattices. In the neighborhood of the Brillouin zone edge, the system can be reduced to two coupled nonlinear two-level models. From the models, we calculate the change of the tunnelling probability for each component with the linear sweeping rate. It is found that the probability for each component exhibits regular oscillating behavior for the larger sweeping rate, but for smaller rate the oscillation is irregular. Moreover, the asymmetry of the tunnelling between the two components can be induced by the unbalanced initial populations or the inequality of the two self-interactions when the cross-interaction between the components exists. The result can not be found in the single component BECs. (general)
[en] The transversal nature of the Boson peak in crystals and glasses is investigated by using a model inspired from rigidity theory of glasses. By tuning the rigidity of the network using second-neighbor interactions, we show that the transversal van Hove singularity – associated with the Boson peak – arises when the transverse dispersion branch touches for the first time the boundary of the first Brillouin zone, leading to an anomaly in the low frequency region. The frequency of the singularity is determined by the rigidity of the network. For the disordered version of the model, the singularity arises when the transversal dispersion branch touches the limit of a pseudo-Brillouin zone, suggesting that the Boson peak in glasses has a similar origin. Increasing rigidity shifts the position of the Boson peak towards high frequencies while its intensity decreases. This provides an important clue to understand pressure effects on the Boson peak in glasses and crystals