554 research outputs found
Convergent sequences of perturbative approximations for the anharmonic oscillator II. Compact time approach
We present an alternative pathway in the application of the variation
improvement of ordinary perturbation theory exposed in [1] which can preserve
the internal symmetries of a model by means of a time compactification.Comment: 21 pages, 4 Postscript figures available through anonymous ftp at
ftp://algol.lpm.univ-montp2.fr ; replaces version which could not be
postscripted presumably for lack of figures.uu fil
Convergent sequences of perturbative approximations for the anharmonic oscillator I. Harmonic approach
We present numerical evidence that a simple variational improvement of the
ordinary perturbation theory of the quantum anharmonic oscillator can give a
convergent sequence of approximations even in the extreme strong coupling
limit, the purely anharmonic case. Some of the new techniques of this paper can
be extended to renormalizable field theories.Comment: 29 pages, 12 Postscript figures available through anonymous ftp at
ftp://algol.lpm.univ-montp2.fr ; replaces earlier version which could not be
postscripted presumably due to lack of figures.uu fil
Variational solution of the Gross-Neveu model at finite temperature in the large N limit
We use a nonperturbative variational method to investigate the phase
transition of the Gross-Neveu model. It is shown that the variational procedure
can be generalized to the finite temperature case. The large N result for the
phase transition is correctly reproduced.Comment: 12 p., 1 fig, this is the version which will appear in the Phys Lett
B, it differs from the previous one in what concerns the introduction and
conclusions (re written), several references have been adde
Convergence of the Linear Delta Expansion in the Critical O(N) Field Theory
The linear delta expansion is applied to the 3-dimensional O(N) scalar field
theory at its critical point in a way that is compatible with the large-N
limit. For a range of the arbitrary mass parameter, the linear delta expansion
for converges, with errors decreasing like a power of the order n in
delta. If the principal of minimal sensitivity is used to optimize the
convergence rate, the errors seem to decrease exponentially with n.Comment: 26 pages, latex, 8 figure
Convergent sequences of perturbative approximations for the anharmonic oscillator; 1, harmonic approach
We present numerical evidence that a simple variational improvement of the ordinary perturbation theory of the quantum anharmonic oscillator can give a convergent sequence of approximations even in the extreme strong coupling limit, the purely anharmonic case. Some of the new techniques of this paper can be extended to renormalizable field theories
A new improved optimization of perturbation theory: applications to the oscillator energy levels and Bose-Einstein critical temperature
Improving perturbation theory via a variational optimization has generally
produced in higher orders an embarrassingly large set of solutions, most of
them unphysical (complex). We introduce an extension of the optimized
perturbation method which leads to a drastic reduction of the number of
acceptable solutions. The properties of this new method are studied and it is
then applied to the calculation of relevant quantities in different
models, such as the anharmonic oscillator energy levels and the critical
Bose-Einstein Condensation temperature shift recently investigated
by various authors. Our present estimates of , incorporating the
most recently available six and seven loop perturbative information, are in
excellent agreement with all the available lattice numerical simulations. This
represents a very substantial improvement over previous treatments.Comment: 9 pages, no figures. v2: minor wording changes in title/abstract, to
appear in Phys.Rev.
Intersubband transitions in nonpolar GaN/Al(Ga)N heterostructures in the short and mid-wavelength infrared regions
This paper assesses nonpolar m- and a-plane GaN/Al(Ga)N multi-quantum-wells
grown on bulk GaN for intersubband optoelectronics in the short- and
mid-wavelength infrared ranges. The characterization results are compared to
those for reference samples grown on the polar c-plane, and are verified by
self-consistent Schr\"odinger-Poisson calculations. The best results in terms
of mosaicity, surface roughness, photoluminescence linewidth and intensity, as
well as intersubband absorption are obtained from m-plane structures, which
display room-temperature intersubband absorption in the range from 1.5 to 2.9
um. Based on these results, a series of m-plane GaN/AlGaN multi-quantum-wells
were designed to determine the accessible spectral range in the mid-infrared.
These samples exhibit tunable room-temperature intersubband absorption from 4.0
to 5.8 um, the long-wavelength limit being set by the absorption associated
with the second order of the Reststrahlen band in the GaN substrates
Yes, Topology Matters in Decentralized Optimization: Refined Convergence and Topology Learning under Heterogeneous Data
One of the key challenges in federated and decentralized learning is to
design algorithms that efficiently deal with highly heterogeneous data
distributions across agents. In this paper, we revisit the analysis of
Decentralized Stochastic Gradient Descent algorithm (D-SGD), a popular
decentralized learning algorithm, under data heterogeneity. We exhibit the key
role played by a new quantity, that we call neighborhood heterogeneity, on the
convergence rate of D-SGD. Unlike prior work, neighborhood heterogeneity is
measured at the level of the neighborhood of an agent in the graph topology. By
coupling the topology and the heterogeneity of the agents' distributions, our
analysis sheds light on the poorly understood interplay between these two
concepts in decentralized learning. We then argue that neighborhood
heterogeneity provides a natural criterion to learn sparse data-dependent
topologies that reduce (and can even eliminate) the otherwise detrimental
effect of data heterogeneity on the convergence time of D-SGD. For the
important case of classification with label skew, we formulate the problem of
learning such a good topology as a tractable optimization problem that we solve
with a Frank-Wolfe algorithm. Our approach provides a principled way to design
a sparse topology that balances the number of iterations and the per-iteration
communication costs of D-SGD under data heterogeneity
Ferromagnetic (Ga,Mn)N epilayers versus antiferromagnetic GaMnN clusters
Mn-doped wurtzite GaN epilayers have been grown by nitrogen plasma-assisted
molecular beam epitaxy. Correlated SIMS, structural and magnetic measurements
show that the incorporation of Mn strongly depends on the conditions of the
growth. Hysteresis loops which persist at high temperature do not appear to be
correlated to the presence of Mn. Samples with up to 2% Mn are purely
substitutional GaMnN epilayers, and exhibit paramagnetic
properties. At higher Mn contents, precipitates are formed which are identified
as GaMnN clusters by x-ray diffraction and absorption: this induces a
decrease of the paramagnetic magnetisation. Samples co-doped with enough Mg
exhibit a new feature: a ferromagnetic component is observed up to
K, which cannot be related to superparamagnetism of unresolved magnetic
precipitates.Comment: Revised versio
Structure and magnetism of self-organized Ge(1-x)Mn(x) nano-columns
We report on the structural and magnetic properties of thin Ge(1-x)Mn(x)films
grown by molecular beam epitaxy (MBE) on Ge(001) substrates at temperatures
(Tg) ranging from 80deg C to 200deg C, with average Mn contents between 1 % and
11 %. Their crystalline structure, morphology and composition have been
investigated by transmission electron microscopy (TEM), electron energy loss
spectroscopy and x-ray diffraction. In the whole range of growth temperatures
and Mn concentrations, we observed the formation of manganese rich
nanostructures embedded in a nearly pure germanium matrix. Growth temperature
mostly determines the structural properties of Mn-rich nanostructures. For low
growth temperatures (below 120deg C), we evidenced a two-dimensional spinodal
decomposition resulting in the formation of vertical one-dimensional
nanostructures (nanocolumns). Moreover we show in this paper the influence of
growth parameters (Tg and Mn content) on this decomposition i.e. on nanocolumns
size and density. For temperatures higher than 180deg C, we observed the
formation of Ge3Mn5 clusters. For intermediate growth temperatures nanocolumns
and nanoclusters coexist. Combining high resolution TEM and superconducting
quantum interference device magnetometry, we could evidence at least four
different magnetic phases in Ge(1-x)Mn(x) films: (i) paramagnetic diluted Mn
atoms in the germanium matrix, (ii) superparamagnetic and ferromagnetic low-Tc
nanocolumns (120 K 400 K) and
(iv) Ge3Mn5 clusters.Comment: 10 pages 2 colonnes revTex formatte
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