16 research outputs found
Function reconstruction as a classical moment problem: A maximum entropy approach
We present a systematic study of the reconstruction of a non-negative
function via maximum entropy approach utilizing the information contained in a
finite number of moments of the function. For testing the efficacy of the
approach, we reconstruct a set of functions using an iterative entropy
optimization scheme, and study the convergence profile as the number of moments
is increased. We consider a wide variety of functions that include a
distribution with a sharp discontinuity, a rapidly oscillatory function, a
distribution with singularities, and finally a distribution with several spikes
and fine structure. The last example is important in the context of the
determination of the natural density of the logistic map. The convergence of
the method is studied by comparing the moments of the approximated functions
with the exact ones. Furthermore, by varying the number of moments and
iterations, we examine to what extent the features of the functions, such as
the divergence behavior at singular points within the interval, is reproduced.
The proximity of the reconstructed maximum entropy solution to the exact
solution is examined via Kullback-Leibler divergence and variation measures for
different number of moments.Comment: 20 pages, 17 figure
Lyapunov exponent and natural invariant density determination of chaotic maps: An iterative maximum entropy ansatz
We apply the maximum entropy principle to construct the natural invariant
density and Lyapunov exponent of one-dimensional chaotic maps. Using a novel
function reconstruction technique that is based on the solution of Hausdorff
moment problem via maximizing Shannon entropy, we estimate the invariant
density and the Lyapunov exponent of nonlinear maps in one-dimension from a
knowledge of finite number of moments. The accuracy and the stability of the
algorithm are illustrated by comparing our results to a number of nonlinear
maps for which the exact analytical results are available. Furthermore, we also
consider a very complex example for which no exact analytical result for
invariant density is available. A comparison of our results to those available
in the literature is also discussed.Comment: 16 pages including 6 figure
A Unified Treatment of Convexity of Relative Entropy and Related Trace Functions, with Conditions for Equality
We introduce a generalization of relative entropy derived from the
Wigner-Yanase-Dyson entropy and give a simple, self-contained proof that it is
convex. Moreover, special cases yield the joint convexity of relative entropy,
and for the map (A,B) --> Tr K^* A^p K B^{1-p} Lieb's joint concavity for 0 < p
< 1 and Ando's joint convexity for 1 < p < 2. This approach allows us to obtain
conditions for equality in these cases, as well as conditions for equality in a
number of inequalities which follow from them. These include the monotonicity
under partial traces, and some Minkowski type matrix inequalities proved by
Lieb and Carlen for mixed (p,q) norms. In all cases the equality conditions are
independent of p; for extensions to three spaces they are identical to the
conditions for equality in the strong subadditivity of relative entropy.Comment: Final version to appear in Rev. Math. Phys. with many typos and minor
errors correcte
Thermodynamic properties of spontaneous magnetization in Chern-Simons QED_3
The spontaneous magnetization in Chern-Simons QED_3 is discussed in a finite
temperature system. The thermodynamical potential is analyzed within the weak
field approximation and in the fermion massless limit. We find that there is a
linear term with respect to the magnetic field with a negative coefficient at
any finite temperature. This implies that the spontaneous magnetic field does
not vanish even at high temperature. In addition, we examine the photon
spectrum in the system. We find that the bare Chern-Simons coefficient is
cancelled by the radiative effects. The photons then become topologically
massless according to the magnetization, though they are massive by finite
temperature effects. Thus the magnetic field is a long-range force without the
screening even at high temperature.Comment: 32 pages, Latex, 4 eps figure
Catalysis of Dynamical Flavor Symmetry Breaking by a Magnetic Field in Dimensions
It is shown that in dimensions, a constant magnetic field is a strong
catalyst of dynamical flavor symmetry breaking, leading to generating a fermion
dynamical mass even at the weakest attractive interaction between fermions. The
effect is illustrated in the Nambu-Jona-Lasinio model in a magnetic field. The
low-energy effective action in this model is derived and the thermodynamic
properties of the model are established. The relevance of this effect for
planar condensed matter systems is pointed out.Comment: 11 pages, LaTeX. The final version (with minor corrections) which
appeared in Phys.Rev.Lett. 73 (1994) 349
Non linear second order partial differential equations as generalized inverse moment problems
General forms for non linear elliptic, hyperbolic and parabolic partial differential equations are considered. For all these we present a general procedure that transforms they into a Fredholm integral equation of the first kind. The resulting integral equations are then handled as a generalized moment problem. An inversion algorithm as well as conditions for the stability for the solution of this last are given. Some examples show the accuracy of the inversion method.Fil: Pintarelli, MarĂa Beatriz. Universidad Nacional de La Plata. Facultad de IngenierĂa. Departamento de Ciencias BĂĄsicas; ArgentinaFil: Vericat, Fernando. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico Conicet - La Plata. Instituto de FĂsica de LĂquidos y Sistemas BiolĂłgicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de FĂsica de LĂquidos y Sistemas BiolĂłgicos; Argentin
Detailed dynamics of electron beams self-trapped and accelerated in a self-modulated laser wakefield
The electron beam generated in a self-modulated laser-wakefield accelerator is characterized in detail. A transverse normalized emittance of 0.06 Ï mm mrad, the lowest ever for an electron injector, was measured for 2 MeV electrons. The electron beam was observed to have a multicomponent beam profile and energy distribution. The latter also undergoes discrete transitions as the laser power or plasma density is varied. In addition, dark spots that form regular modes were observed in the electron beam profile. These features are explained by analysis and test particle simulations of electron dynamics during acceleration in a three-dimensional plasma wakefield