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 $T$'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 $\cal PT$-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 $\cal PT$-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