The general properties of two-dimensional generalized Bessel functions are discussed. Various asymptotic approximations are derived and applied to analyze the basic structure of the two-dimensional Bessel functions as well as their nodal lines.A further direct result is a symmetry relation for even values of one of the p, q-indices, say q. Using J n (−z) = (−1) n J n (z) we get
We consider the dynamics of a quantum particle in a one-dimensional periodic potential (lattice) under the action of a static and time-periodic field. The analysis is based on a nearest-neighbor tightbinding model which allows a convenient closed form description of the transport properties in terms of generalized Bessel functions. The case of bichromatic driving is analyzed in detail and the intricate transport and localization phenomena depending on the communicability of the two excitation frequencies and the Bloch frequency are discussed. The case of polychromatic driving is also discussed, in particular for flipped static fields, i.e. rectangular pulses, which can support an almost dispersionless transport with a velocity independent of the field amplitude.
We explore the non-equilibrium dynamics of two coupled zig-zag chains of trapped ions in a double well potential. Following a quench of the potential barrier between both wells, the induced coupling between both chains due to the long-range interaction of the ions leads to their complete melting. The resulting dynamics is however not exclusively irregular but leads to phases of motion during which various ordered structures appear with ions arranged in arcs, lines and crosses. We quantify the emerging order by introducing a suitable measure and complement our analysis of the ion dynamics using a normal mode analysis showing a decisive population transfer between only a few distinguished modes.
We investigate the nonequilibrium dynamics of coupled Coulomb crystals of different sizes trapped in a double well potential. The dynamics is induced by an instantaneous quench of the potential barrier separating the two crystals. Due to the intra- and intercrystal Coulomb interactions and the asymmetric population of the potential wells, we observe a complex reordering of ions within the two crystals as well as ion transfer processes from one well to the other. The study and analysis of the latter processes constitutes the main focus of this work. In particular, we examine the dependence of the observed ion transfers on the quench amplitude performing an analysis for different crystalline configurations ranging from one-dimensional ion chains via two-dimensional zigzag chains and ring structures to three-dimensional spherical structures. Such an analysis provides us with the means to extract the general principles governing the ion transfer dynamics and we gain some insight on the structural disorder caused by the quench of the barrier height.
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