436 research outputs found
Average Case Tractability of Non-homogeneous Tensor Product Problems
We study d-variate approximation problems in the average case setting with
respect to a zero-mean Gaussian measure. Our interest is focused on measures
having a structure of non-homogeneous linear tensor product, where covariance
kernel is a product of univariate kernels. We consider the normalized average
error of algorithms that use finitely many evaluations of arbitrary linear
functionals. The information complexity is defined as the minimal number n(h,d)
of such evaluations for error in the d-variate case to be at most h. The growth
of n(h,d) as a function of h^{-1} and d depends on the eigenvalues of the
covariance operator and determines whether a problem is tractable or not. Four
types of tractability are studied and for each of them we find the necessary
and sufficient conditions in terms of the eigenvalues of univariate kernels. We
illustrate our results by considering approximation problems related to the
product of Korobov kernels characterized by a weights g_k and smoothnesses r_k.
We assume that weights are non-increasing and smoothness parameters are
non-decreasing. Furthermore they may be related, for instance g_k=g(r_k) for
some non-increasing function g. In particular, we show that approximation
problem is strongly polynomially tractable, i.e., n(h,d)\le C h^{-p} for all d
and 0<h<1, where C and p are independent of h and d, iff liminf |ln g_k|/ln k
>1. For other types of tractability we also show necessary and sufficient
conditions in terms of the sequences g_k and r_k
The effect of electronic entropy on temperature peculiarities of the frequency characteristics of two interacting anharmonic vibrational modes in Zr
A 2D temperature-dependent effective potential is calculated for the
interacting longitudinal and transverse phonons of zirconium in the
frozen-phonon model. The effective potentials obtained for different
temperatures are used for the numerical solution of a set of stochastic
differential equations with a thermostat of the white-noise type. Analysis of
the spectral density of transverse vibrations allows one to determine the
temperature at which -Zr becomes unstable with respect to the
longitudinal vibrations. The obtained temperature value practically
coincides with the experimental temperature of the
structural transition in zirconium. The role of electronic entropy in the
Zr stability is discussed.Comment: 9 pages, 10 figures (submitted in Phys.Rev.
Recent developments in the determination of the amplitude and phase of quantum oscillations for the linear chain of coupled orbits
De Haas-van Alphen oscillations are studied for Fermi surfaces (FS)
illustrating the model proposed by Pippard in the early sixties, namely the
linear chain of orbits coupled by magnetic breakdown. This FS topology is
relevant for many multiband quasi-two dimensional (q-2D) organic metals such as
-(BEDT-TTF)Cu(NCS) and
-(BEDT-TTF)CoBr(CHCl) which are considered in
detail. Whereas the Lifshits-Kosevich model only involves a first order
development of field- and temperature-dependent damping factors, second order
terms may have significant contribution on the Fourier components amplitude for
such q-2D systems at high magnetic field and low temperature. The strength of
these second order terms depends on the relative value of the involved damping
factors, which are in turns strongly dependent on parameters such as the
magnetic breakdown field, effective masses and, most of all, effective
Land\'{e} factors. In addition, the influence of field-dependent Onsager phase
factors on the oscillation spectra is considered.Comment: arXiv admin note: text overlap with arXiv:1304.665
Runaway Quarks
When heavy nuclei collide, a quark-gluon plasma is formed. The plasma is
subject to strong electric field due to the charge of the colliding nuclei. The
electric field can influence the behavior of the quark-gluon plasma. In
particular, we might observe an increased number of quarks moving in the
direction of that field, as we do in the standard electron-ion plasma. In this
paper we show that this phenomenon, called the runaway quarks, does not exist.Comment: 13 pages, uses harvmac.tex, epsf.te
Probing quantum-mechanical level repulsion in disordered systems by means of time-resolved selectively-excited resonance fluorescence
We argue that the time-resolved spectrum of selectively-excited resonance
fluorescence at low temperature provides a tool for probing the
quantum-mechanical level repulsion in the Lifshits tail of the electronic
density of states in a wide variety of disordered materials. The technique,
based on detecting the fast growth of a fluorescence peak that is red-shifted
relative to the excitation frequency, is demonstrated explicitly by simulations
on linear Frenkel exciton chains.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Let
The Localization Length of Stationary States in the Nonlinear Schreodinger Equation
For the nonlinear Schreodinger equation (NLSE), in presence of disorder,
exponentially localized stationary states are found. In the present Letter it
is demonstrated analytically that the localization length is typically
independent of the strength of the nonlinearity and is identical to the one
found for the corresponding linear equation. The analysis makes use of the
correspondence between the stationary NLSE and the Langevin equation as well as
of the resulting Fokker-Planck equation. The calculations are performed for the
``white noise'' random potential and an exact expression for the exponential
growth of the eigenstates is obtained analytically. It is argued that the main
conclusions are robust
Instability of Magnons in Two-dimensional Antiferromagnet at High Magnetic Fields
Spin dynamics of the square lattice Heisenberg antiferromagnet, \BaMnGeO, is
studied by a combination of bulk measurements, neutron diffraction, and
inelastic neutron scattering techniques. Easy plane type antiferromagnetic
order is identified at K. The exchange interactions are estimated
as = 27.8(3)eV and = 1.0(1) eV, and the saturation
field is 9.75 T. Magnetic excitation measurements with high
experimental resolution setup by triple axis neutron spectrometer reveals the
instability of one magnon excitation in the field range of .Comment: 5 pgase, 5 figuers, to be published in PRB R
Linear Amplifier Breakdown and Concentration Properties of a Gaussian Field Given that its -Norm is Large
In the context of linear amplification for systems driven by the square of a
Gaussian noise, we investigate the realizations of a Gaussian field in the
limit where its -norm is large. Concentration onto the eigenspace
associated with the largest eigenvalue of the covariance of the field is
proved. When the covariance is trace class, the concentration is in probability
for the -norm. A stronger concentration, in mean for the sup-norm, is
proved for a smaller class of Gaussian fields, and an example of a field
belonging to that class is given. A possible connection with Bose-Einstein
condensation is briefly discussed.Comment: REVTeX file, 11 pages, 1 added paragraph in the introduction, 2 added
references, minor modifications in the text and abstract, submitted to J.
Stat. Phy
Small Deviations of Smooth Stationary Gaussian Processes
We investigate the small deviation probabilities of a class of very smooth
stationary Gaussian processes playing an important role in Bayesian statistical
inference. Our calculations are based on the appropriate modification of the
entropy method due to Kuelbs, Li, and Linde as well as on classical results
about the entropy of classes of analytic functions. They also involve
Tsirelson's upper bound for small deviations and shed some light on the limits
of sharpness for that estimate
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