2,157 research outputs found

    Poincar\'e Husimi representation of eigenstates in quantum billiards

    Full text link
    For the representation of eigenstates on a Poincar\'e section at the boundary of a billiard different variants have been proposed. We compare these Poincar\'e Husimi functions, discuss their properties and based on this select one particularly suited definition. For the mean behaviour of these Poincar\'e Husimi functions an asymptotic expression is derived, including a uniform approximation. We establish the relation between the Poincar\'e Husimi functions and the Husimi function in phase space from which a direct physical interpretation follows. Using this, a quantum ergodicity theorem for the Poincar\'e Husimi functions in the case of ergodic systems is shown.Comment: 17 pages, 5 figures. Figs. 1,2,5 are included in low resolution only. For a version with better resolution see http://www.physik.tu-dresden.de/~baecker

    Probability density adjoint for sensitivity analysis of the Mean of Chaos

    Full text link
    Sensitivity analysis, especially adjoint based sensitivity analysis, is a powerful tool for engineering design which allows for the efficient computation of sensitivities with respect to many parameters. However, these methods break down when used to compute sensitivities of long-time averaged quantities in chaotic dynamical systems. The following paper presents a new method for sensitivity analysis of {\em ergodic} chaotic dynamical systems, the density adjoint method. The method involves solving the governing equations for the system's invariant measure and its adjoint on the system's attractor manifold rather than in phase-space. This new approach is derived for and demonstrated on one-dimensional chaotic maps and the three-dimensional Lorenz system. It is found that the density adjoint computes very finely detailed adjoint distributions and accurate sensitivities, but suffers from large computational costs.Comment: 29 pages, 27 figure

    Anomalous shell effect in the transition from a circular to a triangular billiard

    Get PDF
    We apply periodic orbit theory to a two-dimensional non-integrable billiard system whose boundary is varied smoothly from a circular to an equilateral triangular shape. Although the classical dynamics becomes chaotic with increasing triangular deformation, it exhibits an astonishingly pronounced shell effect on its way through the shape transition. A semiclassical analysis reveals that this shell effect emerges from a codimension-two bifurcation of the triangular periodic orbit. Gutzwiller's semiclassical trace formula, using a global uniform approximation for the bifurcation of the triangular orbit and including the contributions of the other isolated orbits, describes very well the coarse-grained quantum-mechanical level density of this system. We also discuss the role of discrete symmetry for the large shell effect obtained here.Comment: 14 pages REVTeX4, 16 figures, version to appear in Phys. Rev. E. Qualities of some figures are lowered to reduce their sizes. Original figures are available at http://www.phys.nitech.ac.jp/~arita/papers/tricirc

    Directed Chaotic Transport in Hamiltonian Ratchets

    Full text link
    We present a comprehensive account of directed transport in one-dimensional Hamiltonian systems with spatial and temporal periodicity. They can be considered as Hamiltonian ratchets in the sense that ensembles of particles can show directed ballistic transport in the absence of an average force. We discuss general conditions for such directed transport, like a mixed classical phase space, and elucidate a sum rule that relates the contributions of different phase-space components to transport with each other. We show that regular ratchet transport can be directed against an external potential gradient while chaotic ballistic transport is restricted to unbiased systems. For quantized Hamiltonian ratchets we study transport in terms of the evolution of wave packets and derive a semiclassical expression for the distribution of level velocities which encode the quantum transport in the Floquet band spectra. We discuss the role of dynamical tunneling between transporting islands and the chaotic sea and the breakdown of transport in quantum ratchets with broken spatial periodicity.Comment: 22 page
    • 

    corecore