242,308 research outputs found
Multiscaling in passive scalar advection as stochastic shape dynamics
The Kraichnan rapid advection model is recast as the stochastic dynamics of
tracer trajectories. This framework replaces the random fields with a small set
of stochastic ordinary differential equations. Multiscaling of correlation
functions arises naturally as a consequence of the geometry described by the
evolution of N trajectories. Scaling exponents and scaling structures are
interpreted as excited states of the evolution operator. The trajectories
become nearly deterministic in high dimensions allowing for perturbation theory
in this limit. We calculate perturbatively the anomalous exponent of the third
and fourth order correlation functions. The fourth order result agrees with
previous calculations.Comment: 14 pages, LaTe
Time-like flows of energy-momentum and particle trajectories for the Klein-Gordon equation
The Klein-Gordon equation is interpreted in the de Broglie-Bohm manner as a
single-particle relativistic quantum mechanical equation that defines unique
time-like particle trajectories. The particle trajectories are determined by
the conserved flow of the intrinsic energy density which can be derived from
the specification of the Klein-Gordon energy-momentum tensor in an
Einstein-Riemann space. The approach is illustrated by application to the
simple single-particle phenomena associated with square potentials.Comment: 14 pages, 11 figure
Thermodynamics for Trajectories of a Mass Point
On the basis of information theory, a new formalism of classical
non-relativistic mechanics of a mass point is proposed. The particle
trajectories of a general dynamical system defined on an (1+n)-dimensional
smooth manifold are treated geometrically as dynamical variables. Statistical
mechanics of particle trajectories are constructed in a classical manner.
Thermodynamic variables are introduced through a partition function based on a
canonical ensemble of trajectories. Within this theoretical framework,
classical mechanics can be interpreted as an equilibrium state of statistical
mechanics. The relationships between classical and quantum mechanics are
discussed from this statistical mechanical viewpoint. The maximum entropy
principle is shown to provide a unified view of both classical and quantum
mechanics.Comment: 22 pages, 1 figur
On the Landau Ginzburg theory of MAG projected SU(2) lattice gauge theory
Maximal Abelian gauge fixing and subsequent Abelian projection of SU(2)
lattice gauge theory defines closed trajectories of magnetic monopoles. These
trajectories can be interpreted in terms of an effective scalar field theory of
the MAG monopoles using the worldline representation of the functional
determinants. Employing the monopole worldlines detected in the numerical
simulation, we show that a scalar bound state exists. The screening mass of
this state properly scales towards the continuum limit. We find m ~ 1.3 $GeV
when the string tension sigma = 440 MeV is used as reference scale.Comment: 9 pages, 3 figures, accepted by Phys. Lett.
Pioneer's Anomaly and the Solar Quadrupole Moment
The trajectories of test particles moving in the gravitational field of a
non-spherically symmetric mass distribution become affected by the presence of
multipole moments. In the case of hyperbolic trajectories, the quadrupole
moment of an oblate mass induces a displacement of the trajectory towards the
mass source, an effect that can be interpreted as an additional acceleration
directed towards the source. Although this additional acceleration is not
constant, we perform a general relativistic analysis in order to evaluate the
possibility of explaining Pioneer's anomalous acceleration by means of the
observed Solar quadrupole moment, within the range of accuracy of the observed
anomalous acceleration. We conclude that the Solar quadrupole moment generates
an acceleration which is of the same order of magnitude of Pioneer's constant
acceleration only at distances of a few astronomical units.Comment: Typos corrected, references adde
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