534 research outputs found
The Strong Levinson Theorem for the Dirac Equation
We consider the Dirac equation in one space dimension in the presence of a
symmetric potential well. We connect the scattering phase shifts at E=+m and
E=-m to the number of states that have left the positive energy continuum or
joined the negative energy continuum respectively as the potential is turned on
from zero.Comment: Submitted to Physical Review Letter
Spin-polarized tunneling spectroscopy in tunnel junctions with half-metallic electrodes
We have studied the magnetoresistance (TMR) of tunnel junctions with
electrodes of La2/3Sr1/3MnO3 and we show how the variation of the conductance
and TMR with the bias voltage can be exploited to obtain a precise information
on the spin and energy dependence of the density of states. Our analysis leads
to a quantitative description of the band structure of La2/3Sr1/3MnO3 and
allows the determination of the gap delta between the Fermi level and the
bottom of the t2g minority spin band, in good agreement with data from
spin-polarized inverse photoemission experiments. This shows the potential of
magnetic tunnel junctions with half-metallic electrodes for spin-resolved
spectroscopic studies.Comment: To appear in Physical Review Letter
Spatiotemporal Characterization of Supercontinuum Extending from the Visible to the Mid-Infrared in Multimode Graded-Index Optical Fiber
We experimentally demonstrate that pumping a graded-index multimode fiber
with sub-ns pulses from a microchip Nd:YAG laser leads to spectrally flat
supercontinuum generation with a uniform bell-shaped spatial beam profile
extending from the visible to the mid-infrared at 2500\,nm. We study the
development of the supercontinuum along the multimode fiber by the cut-back
method, which permits us to analyze the competition between the Kerr-induced
geometric parametric instability and stimulated Raman scattering. We also
performed a spectrally resolved temporal analysis of the supercontinuum
emission.Comment: 5 pages 7 figure
Evolution of reference networks with aging
We study the growth of a reference network with aging of sites defined in the
following way. Each new site of the network is connected to some old site with
probability proportional (i) to the connectivity of the old site as in the
Barab\'{a}si-Albert's model and (ii) to , where is the
age of the old site. We consider of any sign although reasonable
values are . We find both from simulation and
analytically that the network shows scaling behavior only in the region . When increases from to 0, the exponent of the
distribution of connectivities ( for large ) grows
from 2 to the value for the network without aging, i.e. to 3 for the
Barab\'{a}si-Albert's model. The following increase of to 1 makes
to grow to . For the distribution is
exponentional, and the network has a chain structure.Comment: 4 pages revtex (twocolumn, psfig), 5 figure
Convergence of finite volume scheme for degenerate parabolic problem with zero flux boundary condition
This note is devoted to the study of the finite volume methods used in the discretization of degenerate parabolic-hyperbolic equation with zero-flux boundary condition. The notion of an entropy-process solution, successfully used for the Dirichlet problem, is insufficient to obtain a uniqueness and convergence result because of a lack of regularity of solutions on the boundary. We infer the uniqueness of an entropy-process solution using the tool of the nonlinear semigroup theory by passing to the new abstract notion of integral-process solution. Then, we prove that numerical solution converges to the unique entropy solution as the mesh size tends to 0
Random spread on the family of small-world networks
We present the analytical and numerical results of a random walk on the
family of small-world graphs. The average access time shows a crossover from
the regular to random behavior with increasing distance from the starting point
of the random walk. We introduce an {\em independent step approximation}, which
enables us to obtain analytic results for the average access time. We observe a
scaling relation for the average access time in the degree of the nodes. The
behavior of average access time as a function of , shows striking similarity
with that of the {\em characteristic length} of the graph. This observation may
have important applications in routing and switching in networks with large
number of nodes.Comment: RevTeX4 file with 6 figure
Structure of Growing Networks: Exact Solution of the Barabasi--Albert's Model
We generalize the Barab\'{a}si--Albert's model of growing networks accounting
for initial properties of sites and find exactly the distribution of
connectivities of the network and the averaged connectivity
of a site in the instant (one site is added per unit of
time). At long times at and
at , where the exponent
varies from 2 to depending on the initial attractiveness of sites. We
show that the relation between the exponents is universal.Comment: 4 pages revtex (twocolumn, psfig), 1 figur
Ising model in small-world networks
The Ising model in small-world networks generated from two- and
three-dimensional regular lattices has been studied. Monte Carlo simulations
were carried out to characterize the ferromagnetic transition appearing in
these systems. In the thermodynamic limit, the phase transition has a
mean-field character for any finite value of the rewiring probability p, which
measures the disorder strength of a given network. For small values of p, both
the transition temperature and critical energy change with p as a power law. In
the limit p -> 0, the heat capacity at the transition temperature diverges
logarithmically in two-dimensional (2D) networks and as a power law in 3D.Comment: 6 pages, 7 figure
Small world effects in evolution
For asexual organisms point mutations correspond to local displacements in
the genotypic space, while other genotypic rearrangements represent long-range
jumps. We investigate the spreading properties of an initially homogeneous
population in a flat fitness landscape, and the equilibrium properties on a
smooth fitness landscape. We show that a small-world effect is present: even a
small fraction of quenched long-range jumps makes the results indistinguishable
from those obtained by assuming all mutations equiprobable. Moreover, we find
that the equilibrium distribution is a Boltzmann one, in which the fitness
plays the role of an energy, and mutations that of a temperature.Comment: 13 pages and 5 figures. New revised versio
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