2,321 research outputs found
Symmetry Decomposition of Chaotic Dynamics
Discrete symmetries of dynamical flows give rise to relations between
periodic orbits, reduce the dynamics to a fundamental domain, and lead to
factorizations of zeta functions. These factorizations in turn reduce the labor
and improve the convergence of cycle expansions for classical and quantum
spectra associated with the flow. In this paper the general formalism is
developed, with the -disk pinball model used as a concrete example and a
series of physically interesting cases worked out in detail.Comment: CYCLER Paper 93mar01
Echoes in classical dynamical systems
Echoes arise when external manipulations to a system induce a reversal of its
time evolution that leads to a more or less perfect recovery of the initial
state. We discuss the accuracy with which a cloud of trajectories returns to
the initial state in classical dynamical systems that are exposed to additive
noise and small differences in the equations of motion for forward and backward
evolution. The cases of integrable and chaotic motion and small or large noise
are studied in some detail and many different dynamical laws are identified.
Experimental tests in 2-d flows that show chaotic advection are proposed.Comment: to be published in J. Phys.
High-temperature liquid-mercury cathodes for ion thrusters Quarterly progress report, 1 Dec. 1966 - 28 Feb. 1967
High temperature liquid mercury cathodes for ion thrusters - thermal design analysi
Semiclassical Quantization by Pade Approximant to Periodic Orbit Sums
Periodic orbit quantization requires an analytic continuation of
non-convergent semiclassical trace formulae. We propose a method for
semiclassical quantization based upon the Pade approximant to the periodic
orbit sums. The Pade approximant allows the re-summation of the typically
exponentially divergent periodic orbit terms. The technique does not depend on
the existence of a symbolic dynamics and can be applied to both bound and open
systems. Numerical results are presented for two different systems with chaotic
and regular classical dynamics, viz. the three-disk scattering system and the
circle billiard.Comment: 7 pages, 3 figures, submitted to Europhys. Let
Semiclassical cross section correlations
We calculate within a semiclassical approximation the autocorrelation
function of cross sections. The starting point is the semiclassical expression
for the diagonal matrix elements of an operator. For general operators with a
smooth classical limit the autocorrelation function of such matrix elements has
two contributions with relative weights determined by classical dynamics. We
show how the random matrix result can be obtained if the operator approaches a
projector onto a single initial state. The expressions are verified in
calculations for the kicked rotor.Comment: 6 pages, 2 figure
Truncated-Unity Parquet Equations: Application to the Repulsive Hubbard Model
The parquet equations are a self-consistent set of equations for the
effective two-particle vertex of an interacting many-fermion system. The
application of these equations to bulk models is, however, demanding due to the
complex emergent momentum and frequency structure of the vertex. Here, we show
how a channel-decomposition by means of truncated unities, which was developed
in the context of the functional renormalization group to efficiently treat the
momentum dependence, can be transferred to the parquet equations. This leads to
a significantly reduced numerical effort scaling only linearly with the number
of discrete momenta. We apply this technique to the half-filled repulsive
Hubbard model on the square lattice and present approximate solutions for the
channel-projected vertices and the full reducible vertex.Comment: Consistent with published version in Phys. Rev.
Casimir interaction between normal or superfluid grains in the Fermi sea
We report on a new force that acts on cavities (literally empty regions of
space) when they are immersed in a background of non-interacting fermionic
matter fields. The interaction follows from the obstructions to the (quantum
mechanical) motions of the fermions caused by the presence of bubbles or other
(heavy) particles in the Fermi sea, as, for example, nuclei in the neutron sea
in the inner crust of a neutron star or superfluid grains in a normal Fermi
liquid. The effect resembles the traditional Casimir interaction between
metallic mirrors in the vacuum. However, the fluctuating electromagnetic fields
are replaced by fermionic matter fields. We show that the fermionic Casimir
problem for a system of spherical cavities can be solved exactly, since the
calculation can be mapped onto a quantum mechanical billiard problem of a
point-particle scattered off a finite number of non-overlapping spheres or
disks. Finally we generalize the map method to other Casimir systems,
especially to the case of a fluctuating scalar field between two spheres or a
sphere and a plate under Dirichlet boundary conditions.Comment: 8 pages, 2 figures, submitted to the Proceedings of QFEXT'05,
Barcelona, Sept. 5-9, 200
Clustering dynamics of Lagrangian tracers in free-surface flows
We study the formation of clusters of passive Lagrangian tracers in a
non-smooth turbulent flow in a flat free-slip surface as a model for particle
dynamics on free surfaces. Single particle and pair dispersion show different
behavior for short and large times: on short times particles cluster
exponentially rapidly until patches of the size of the divergence correlation
length are depleted; on larger times the pair dispersion is dominated by almost
ballistic hopping between clusters. We also find that the distribution of
particle density is close to algebraic and can trace this back to the
exponential distribution of the divergence field of the surface flow.Comment: 5 pages, 5 Postscript figure
Liquid mercury cathode electron bombardment ion thrusters Summary report, 1 Aug. 1964 - 31 Oct. 1966
Life tests of liquid mercury cathodes for electron bombardment ion thruster
How does flow in a pipe become turbulent?
The transition to turbulence in pipe flow does not follow the scenario
familiar from Rayleigh-Benard or Taylor-Couette flow since the laminar profile
is stable against infinitesimal perturbations for all Reynolds numbers.
Moreover, even when the flow speed is high enough and the perturbation
sufficiently strong such that turbulent flow is established, it can return to
the laminar state without any indication of the imminent decay. In this
parameter range, the lifetimes of perturbations show a sensitive dependence on
initial conditions and an exponential distribution. The turbulence seems to be
supported by three-dimensional travelling waves which appear transiently in the
flow field. The boundary between laminar and turbulent dynamics is formed by
the stable manifold of an invariant chaotic state. We will also discuss the
relation between observations in short, periodically continued domains, and the
dynamics in fully extended puffs.Comment: for the proceedings of statphys 2
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