4,268 research outputs found
Dynamical stabilization of classical multi electron targets against autoionization
We demonstrate that a recently published quasiclassical M\oller type approach
[Geyer and Rost 2002, J. Phys. B 35 1479] can be used to overcome the problem
of autoionization, which arises in classical trajectory calculations for many
electron targets. In this method the target is stabilized dynamically by a
backward--forward propagation scheme. We illustrate this refocusing and present
total cross sections for single and double ionization of helium by electron
impact.Comment: LaTeX, 6 pages, 2 figures; submitted to J. Phys.
Detecting multivariate interactions in spatial point patterns with Gibbs models and variable selection
We propose a method for detecting significant interactions in very large
multivariate spatial point patterns. This methodology develops high dimensional
data understanding in the point process setting. The method is based on
modelling the patterns using a flexible Gibbs point process model to directly
characterise point-to-point interactions at different spatial scales. By using
the Gibbs framework significant interactions can also be captured at small
scales. Subsequently, the Gibbs point process is fitted using a
pseudo-likelihood approximation, and we select significant interactions
automatically using the group lasso penalty with this likelihood approximation.
Thus we estimate the multivariate interactions stably even in this setting. We
demonstrate the feasibility of the method with a simulation study and show its
power by applying it to a large and complex rainforest plant population data
set of 83 species
Entropic effects in large-scale Monte Carlo simulations
The efficiency of Monte Carlo samplers is dictated not only by energetic
effects, such as large barriers, but also by entropic effects that are due to
the sheer volume that is sampled. The latter effects appear in the form of an
entropic mismatch or divergence between the direct and reverse trial moves. We
provide lower and upper bounds for the average acceptance probability in terms
of the Renyi divergence of order 1/2. We show that the asymptotic finitude of
the entropic divergence is the necessary and sufficient condition for
non-vanishing acceptance probabilities in the limit of large dimensions.
Furthermore, we demonstrate that the upper bound is reasonably tight by showing
that the exponent is asymptotically exact for systems made up of a large number
of independent and identically distributed subsystems. For the last statement,
we provide an alternative proof that relies on the reformulation of the
acceptance probability as a large deviation problem. The reformulation also
leads to a class of low-variance estimators for strongly asymmetric
distributions. We show that the entropy divergence causes a decay in the
average displacements with the number of dimensions n that are simultaneously
updated. For systems that have a well-defined thermodynamic limit, the decay is
demonstrated to be n^{-1/2} for random-walk Monte Carlo and n^{-1/6} for Smart
Monte Carlo (SMC). Numerical simulations of the LJ_38 cluster show that SMC is
virtually as efficient as the Markov chain implementation of the Gibbs sampler,
which is normally utilized for Lennard-Jones clusters. An application of the
entropic inequalities to the parallel tempering method demonstrates that the
number of replicas increases as the square root of the heat capacity of the
system.Comment: minor corrections; the best compromise for the value of the epsilon
parameter in Eq. A9 is now shown to be log(2); 13 pages, 4 figures, to appear
in PR
General approach for studying first-order phase transitions at low temperatures
By combining different ideas, a general and efficient protocol to deal with
discontinuous phase transitions at low temperatures is proposed. For small
's, it is possible to derive a generic analytic expression for appropriate
order parameters, whose coefficients are obtained from simple simulations. Once
in such regimes simulations by standard algorithms are not reliable, an
enhanced tempering method, the parallel tempering -- accurate for small and
intermediate system sizes with rather low computational cost -- is used.
Finally, from finite size analysis, one can obtain the thermodynamic limit. The
procedure is illustrated for four distinct models, demonstrating its power,
e.g., to locate coexistence lines and the phases density at the coexistence.Comment: 5 page
Effects of phase transitions in devices actuated by the electromagnetic vacuum force
We study the influence of the electromagnetic vacuum force on the behaviour
of a model device based on materials, like germanium tellurides, that undergo
fast and reversible metal-insulator transitions on passing from the crystalline
to the amorphous phase. The calculations are performed at finite temperature
and fully accounting for the behaviour of the material dielectric functions.
The results show that the transition can be exploited to extend the distance
and energy ranges under which the device can be operated without undergoing
stiction phenomena. We discuss the approximation involved in adopting the
Casimir expression in simulating nano- and micro- devices at finite
temperature
Reconstruction of thermally-symmetrized quantum autocorrelation functions from imaginary-time data
In this paper, I propose a technique for recovering quantum dynamical
information from imaginary-time data via the resolution of a one-dimensional
Hamburger moment problem. It is shown that the quantum autocorrelation
functions are uniquely determined by and can be reconstructed from their
sequence of derivatives at origin. A general class of reconstruction algorithms
is then identified, according to Theorem 3. The technique is advocated as
especially effective for a certain class of quantum problems in continuum
space, for which only a few moments are necessary. For such problems, it is
argued that the derivatives at origin can be evaluated by Monte Carlo
simulations via estimators of finite variances in the limit of an infinite
number of path variables. Finally, a maximum entropy inversion algorithm for
the Hamburger moment problem is utilized to compute the quantum rate of
reaction for a one-dimensional symmetric Eckart barrier.Comment: 15 pages, no figures, to appear in Phys. Rev.
Coordinate Singularities in Harmonically-sliced Cosmologies
Harmonic slicing has in recent years become a standard way of prescribing the
lapse function in numerical simulations of general relativity. However, as was
first noticed by Alcubierre (1997), numerical solutions generated using this
slicing condition can show pathological behaviour. In this paper, analytic and
numerical methods are used to examine harmonic slicings of Kasner and Gowdy
cosmological spacetimes. It is shown that in general the slicings are prevented
from covering the whole of the spacetimes by the appearance of coordinate
singularities. As well as limiting the maximum running times of numerical
simulations, the coordinate singularities can lead to features being produced
in numerically evolved solutions which must be distinguished from genuine
physical effects.Comment: 21 pages, REVTeX, 5 figure
On the efficient Monte Carlo implementation of path integrals
We demonstrate that the Levy-Ciesielski implementation of Lie-Trotter
products enjoys several properties that make it extremely suitable for
path-integral Monte Carlo simulations: fast computation of paths, fast Monte
Carlo sampling, and the ability to use different numbers of time slices for the
different degrees of freedom, commensurate with the quantum effects. It is
demonstrated that a Monte Carlo simulation for which particles or small groups
of variables are updated in a sequential fashion has a statistical efficiency
that is always comparable to or better than that of an all-particle or
all-variable update sampler. The sequential sampler results in significant
computational savings if updating a variable costs only a fraction of the cost
for updating all variables simultaneously or if the variables are independent.
In the Levy-Ciesielski representation, the path variables are grouped in a
small number of layers, with the variables from the same layer being
statistically independent. The superior performance of the fast sampling
algorithm is shown to be a consequence of these observations. Both mathematical
arguments and numerical simulations are employed in order to quantify the
computational advantages of the sequential sampler, the Levy-Ciesielski
implementation of path integrals, and the fast sampling algorithm.Comment: 14 pages, 3 figures; submitted to Phys. Rev.
Electron impact double ionization of helium from classical trajectory calculations
With a recently proposed quasiclassical ansatz [Geyer and Rost, J. Phys. B 35
(2002) 1479] it is possible to perform classical trajectory ionization
calculations on many electron targets. The autoionization of the target is
prevented by a M\o{}ller type backward--forward propagation scheme and allows
to consider all interactions between all particles without additional
stabilization. The application of the quasiclassical ansatz for helium targets
is explained and total and partially differential cross sections for electron
impact double ionization are calculated. In the high energy regime the
classical description fails to describe the dominant TS1 process, which leads
to big deviations, whereas for low energies the total cross section is
reproduced well. Differential cross sections calculated at 250 eV await their
experimental confirmation.Comment: LaTeX, 22 pages, 10 figures, submitted to J. Phys.
Non-Hermitian oscillator Hamiltonian and su(1,1): a way towards generalizations
The family of metric operators, constructed by Musumbu {\sl et al} (2007 {\sl
J. Phys. A: Math. Theor.} {\bf 40} F75), for a harmonic oscillator Hamiltonian
augmented by a non-Hermitian -symmetric part, is re-examined in the
light of an su(1,1) approach. An alternative derivation, only relying on
properties of su(1,1) generators, is proposed. Being independent of the
realization considered for the latter, it opens the way towards the
construction of generalized non-Hermitian (not necessarily -symmetric)
oscillator Hamiltonians related by similarity to Hermitian ones. Some examples
of them are reviewed.Comment: 11 pages, no figure; changes in title and in paragraphs 3 and 5;
final published versio
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