The dynamics of a passive particle in a hydrodynamical flow behind a cylinder is investigated. The velocity field has been determined both by a numerical simulation of the Navier-Stokes flow and by an analytically defined model flow. To analyze the Lagrangian dynamics, we apply methods coming from chaotic scattering: periodic orbits, time delay function, decay statistics. The asymptotic delay time statistics are dominated by the influence of the boundary conditions on the wall and exhibit algebraic decay. The short time behavior is exponential and represents hyperbolic effects.

We present an approach for the analysis of Bose-Einstein condensates in a few mode approximation. This method has already been used to successfully analyze the vibrational modes in various molecular systems and offers a perspective on the dynamics in many particle bosonic systems. We discuss a system consisting of a Bose-Einstein condensate in a triple well potential. Such systems correspond to classical Hamiltonian systems with three degrees of freedom. The semiclassical approach allows a simple visualization of the eigenstates of the quantum system referring to the underlying classical dynamics. From this classification we can read off the dynamical properties of the eigenstates such as particle exchange between the wells and entanglement without further calculations. In addition, this approach offers insights into the validity of the mean-field description of the many particle system by the Gross-Pitaevskii equation, since we make use of exactly this correspondence in our semiclassical analysis. We choose a three mode system in order to visualize it easily and, moreover, to have a sufficiently interesting structure, although the method can also be extended to higher dimensional systems.⌽ ͑r ជ͒ = ͚ n,m n,m ͑r ជ͒â n,m , ͑2͒where we assume that the basis functions ͕ n,m ͖ of the oneparticle Hilbert space are exponentially localized in space and real, as is the case for the Wannier functions ͓22͔. The index n describes basis functions in different wells and we *Electronic address: mossmann@fis.unam.mx PHYSICAL REVIEW A 74, 033601 ͑2006͒

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Techniques of quantum, semiclassical, and nonlinear classical mechanics are employed to investigate the bending dynamics of acetylene, as represented by a recently reported effective Hamiltonian ͓J. Chem. Phys. 109, 121 ͑1998͔͒, with particular emphasis on the dynamics near 15 000 cm Ϫ1 of internal energy. At this energy, the classical mechanics associated with the bending system is profoundly different from that at low energy, where normal mode motions ͑trans and cis bend͒ dominate. Specifically, at 15 000 cm Ϫ1 , classical chaos coexists with stable classical motions that are unrelated to the normal mode motions; these high-energy stable bending motions include those that we call ''local bend'' ͑one hydrogen bending͒ and ''counter-rotation'' ͑the two hydrogens undergoing circular motion at opposite ends of the molecule͒, as well as more complicated motions which can be considered hybrids of the local bend and counter-rotation motions. The vast majority of the bending quantum eigenstates near 15 000 cm Ϫ1 have nodal coordinates which coincide with the stable periodic orbits, and thus can be assigned semiclassical quantum numbers representing the number of nodes along the stable classical motions.