19,312 research outputs found
IFSM representation of Brownian motion with applications to simulation
Several methods are currently available to simulate paths of the Brownian
motion. In particular, paths of the BM can be simulated using the properties of
the increments of the process like in the Euler scheme, or as the limit of a
random walk or via L2 decomposition like the Kac-Siegert/Karnounen-Loeve
series.
In this paper we first propose a IFSM (Iterated Function Systems with Maps)
operator whose fixed point is the trajectory of the BM. We then use this
representation of the process to simulate its trajectories. The resulting
simulated trajectories are self-affine, continuous and fractal by construction.
This fact produces more realistic trajectories than other schemes in the sense
that their geometry is closer to the one of the true BM's trajectories. The
IFSM trajectory of the BM can then be used to generate more realistic solutions
of stochastic differential equations
Symmetries of the Einstein Equations
Generalized symmetries of the Einstein equations are infinitesimal
transformations of the spacetime metric that formally map solutions of the
Einstein equations to other solutions. The infinitesimal generators of these
symmetries are assumed to be local, \ie at a given spacetime point they are
functions of the metric and an arbitrary but finite number of derivatives of
the metric at the point. We classify all generalized symmetries of the vacuum
Einstein equations in four spacetime dimensions and find that the only
generalized symmetry transformations consist of: (i) constant scalings of the
metric (ii) the infinitesimal action of generalized spacetime diffeomorphisms.
Our results rule out a large class of possible ``observables'' for the
gravitational field, and suggest that the vacuum Einstein equations are not
integrable.Comment: 15 pages, FTG-114-USU, Plain Te
Transverse-momentum resummation for heavy-quark hadroproduction
We consider the production of a pair of heavy quarks () in
hadronic collisions. When the transverse momentum of the heavy-quark pair
is much smaller than its invariant mass, the QCD perturbative expansion is
affected by large logarithmic terms that must be resummed to all-orders. This
behavior is well known from the simpler case of hadroproduction of colourless
high-mass systems, such as vector or Higgs boson(s). In the case of
production, the final-state heavy quarks carry colour charge and are
responsible for additional soft radiation (through direct emission and
interferences with initial-state radiation) that complicates the evaluation of
the logarithmically-enhanced terms in the small- region. We present the
all-order resummation structure of the logarithmic contributions, which
includes colour flow evolution factors due to soft wide-angle radiation.
Resummation is performed at the completely differential level with respect to
the kinematical variables of the produced heavy quarks. Soft-parton radiation
produces azimuthal correlations that are fully taken into account by the
resummation formalism. These azimuthal correlations are entangled with those
that are produced by initial-state collinear radiation. We present explicit
analytical results up to next-to-leading order and next-to-next-to-leading
logarithmic accuracy.Comment: Some comments expanded and references added. Version published on NP
Translation-Rotation Coupling in Transient Grating Experiments : Theoretical and Experimental Evidences
The results of a Transient Grating experiment in a supercooled molecular
liquid of anisotropic molecules and its theoretical interpretation are
presented. These results show the existence of two distinct dynamical
contributions in the response function of this experiment, density and
orientation dynamics. These dynamics can be experimentally disentangled by
varying the polarisation of the probe and diffracted beams and they have been
identified and measured in a Heterodyne Detected experiment performed on
m-toluidine. The results of the theory show a good qualitative agreement with
the measurements at all temperatures.Comment: PDF format, 14 pages including 4 figures, accepted for publication in
EPL. minor modification
Non-local transport and the Hall viscosity of 2D hydrodynamic electron liquids
In a fluid subject to a magnetic field the viscous stress tensor has a
dissipationless antisymmetric component controlled by the so-called Hall
viscosity. We here propose an all-electrical scheme that allows a determination
of the Hall viscosity of a two-dimensional electron liquid in a solid-state
device.Comment: 12 pages, 4 figure
Solitary Waves in Massive Nonlinear S^N-Sigma Models
The solitary waves of massive (1+1)-dimensional nonlinear S^N-sigma models
are unveiled. It is shown that the solitary waves in these systems are in
one-to-one correspondence with the separatrix trajectories in the repulsive
N-dimensional Neumann mechanical problem. There are topological (heteroclinic
trajectories) and non-topological (homoclinic trajectories) kinks. The
stability of some embedded sine-Gordon kinks is discussed by means of the
direct estimation of the spectra of the second-order fluctuation operators
around them, whereas the instability of other topological and non-topological
kinks is established applying the Morse index theorem
Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force
The problem of building supersymmetry in the quantum mechanics of two
Coulombian centers of force is analyzed. It is shown that there are essentially
two ways of proceeding. The spectral problems of the SUSY (scalar) Hamiltonians
are quite similar and become tantamount to solving entangled families of Razavy
and Whittaker-Hill equations in the first approach. When the two centers have
the same strength, the Whittaker-Hill equations reduce to Mathieu equations. In
the second approach, the spectral problems are much more difficult to solve but
one can still find the zero-energy ground states.Comment: This is a contribution to the Proc. of the Seventh International
Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007,
Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
State determination: an iterative algorithm
An iterative algorithm for state determination is presented that uses as
physical input the probability distributions for the eigenvalues of two or more
observables in an unknown state . Starting form an arbitrary state
, a succession of states is obtained that converges to
or to a Pauli partner. This algorithm for state reconstruction is
efficient and robust as is seen in the numerical tests presented and is a
useful tool not only for state determination but also for the study of Pauli
partners. Its main ingredient is the Physical Imposition Operator that changes
any state to have the same physical properties, with respect to an observable,
of another state.Comment: 11 pages 3 figure
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