Coagulation kinetics beyond mean field theory using an optimised Poisson representation

Binary particle coagulation can be modelled as the repeated random process of the combination of two particles to form a third. The kinetics can be represented by population rate equations based on a mean field assumption, according to which the rate of aggregation is taken to be proportional to the product of the mean populations of the two participants. This can be a poor approximation when the mean populations are small. However, using the Poisson representation it is possible to derive a set of rate equations that go beyond mean field theory, describing pseudo-populations that are continuous, noisy and complex, but where averaging over the noise and initial conditions gives the mean of the physical population. Such an approach is explored for the simple case of a size-independent rate of coagulation between particles. Analytical results are compared with numerical computations and with results derived by other means. In the numerical work we encounter instabilities that can be eliminated using a suitable 'gauge' transformation of the problem [P. D. Drummond, Eur. Phys. J. B38, 617 (2004)] which we show to be equivalent to the application of the Cameron-Martin-Girsanov formula describing a shift in a probability measure. The cost of such a procedure is to introduce additional statistical noise into the numerical results, but we identify an optimised gauge transformation where this difficulty is minimal for the main properties of interest. For more complicated systems, such an approach is likely to be computationally cheaper than Monte Carlo simulation

Heisenberg XXZ Model and Quantum Galilei Group

The 1D Heisenberg spin chain with anisotropy of the XXZ type is analyzed in terms of the symmetry given by the quantum Galilei group Gamma_q(1). We show that the magnon excitations and the s=1/2, n-magnon bound states are determined by the algebra. Thus the Gamma_q(1) symmetry provides a description that naturally induces the Bethe Ansatz. The recurrence relations determined by Gamma_q(1) permit to express the energy of the n-magnon bound states in a closed form in terms of Tchebischeff polynomials.Comment: (pag. 10

Can slow roll inflation induce relevant helical magnetic fields?

We study the generation of helical magnetic fields during single field inflation induced by an axial coupling of the electromagnetic field to the inflaton. During slow roll inflation, we find that such a coupling always leads to a blue spectrum with $B^2(k) \propto k$, as long as the theory is treated perturbatively. The magnetic energy density at the end of inflation is found to be typically too small to backreact on the background dynamics of the inflaton. We also show that a short deviation from slow roll does not result in strong modifications to the shape of the spectrum. We calculate the evolution of the correlation length and the field amplitude during the inverse cascade and viscous damping of the helical magnetic field in the radiation era after inflation. We conclude that except for low scale inflation with very strong coupling, the magnetic fields generated by such an axial coupling in single field slow roll inflation with perturbative coupling to the inflaton are too weak to provide the seeds for the observed fields in galaxies and clusters.Comment: 33 pages 6 figures; v4 to match the accepted version to appear in JCA

A large sample study of spin relaxation and magnetometric sensitivity of paraffin-coated Cs vapor cells

We have manufactured more than 250 nominally identical paraffin-coated Cs vapor cells (30 mm diameter bulbs) for multi-channel atomic magnetometer applications. We describe our dedicated cell characterization apparatus. For each cell we have determined the intrinsic longitudinal, \sGamma{01}, and transverse, \sGamma{02}, relaxation rates. Our best cell shows \sGamma{01}/2\pi\approx 0.5 Hz, and \sGamma{02}/2\pi\approx 2 Hz. We find a strong correlation of both relaxation rates which we explain in terms of reservoir and spin exchange relaxation. For each cell we have determined the optimal combination of rf and laser powers which yield the highest sensitivity to magnetic field changes. Out of all produced cells, 90% are found to have magnetometric sensitivities in the range of 9 to 30 fTHz. Noise analysis shows that the magnetometers operated with such cells have a sensitivity close to the fundamental photon shot noise limit

The gravitational-wave memory from eccentric binaries

The nonlinear gravitational-wave memory causes a time-varying but nonoscillatory correction to the gravitational-wave polarizations. It arises from gravitational waves that are sourced by gravitational waves. Previous considerations of the nonlinear memory effect have focused on quasicircular binaries. Here, I consider the nonlinear memory from Newtonian orbits with arbitrary eccentricity. Expressions for the waveform polarizations and spin-weighted spherical-harmonic modes are derived for elliptic, hyperbolic, parabolic, and radial orbits. In the hyperbolic, parabolic, and radial cases the nonlinear memory provides a 2.5 post-Newtonian (PN) correction to the leading-order waveforms. This is in contrast to the elliptical and quasicircular cases, where the nonlinear memory corrects the waveform at leading (0PN) order. This difference in PN order arises from the fact that the memory builds up over a short "scattering" time scale in the hyperbolic case, as opposed to a much longer radiation-reaction time scale in the elliptical case. The nonlinear memory corrections presented here complete our knowledge of the leading-order (Peters-Mathews) waveforms for elliptical orbits. These calculations are also relevant for binaries with quasicircular orbits in the present epoch which had, in the past, large eccentricities. Because the nonlinear memory depends sensitively on the past evolution of a binary, I discuss the effect of this early-time eccentricity on the value of the late-time memory in nearly circularized binaries. I also discuss the observability of large "memory jumps" in a binary's past that could arise from its formation in a capture process. Lastly, I provide estimates of the signal-to-noise ratio of the linear and nonlinear memories from hyperbolic and parabolic binaries.Comment: 25 pages, 8 figures. v2: minor changes to match published versio

Wind-induced ground motion: dynamic model and non-uniform structure for ground

Wind-induced ground vibrations are a source of noise in seismic surveys. In a previous study, a wind-ground coupling theory was developed to predict the power spectral density (PSD) of ground motions caused by wind perturbations on the ground surface. The prediction was developed using a superposition of the point source response of an elastic isotropic homogeneous medium deforming quasi-statically with the statistical description of the wind-induced pressure fluctuations on the ground. Model predictions and field measurements were in agreement for the normal component of the displacement but under predicted the horizontal component. In this paper, two generalizations are investigated to see if they lead to increased horizontal displacement predictions: 1. First, the dynamic point source response is calculated and incorporated in the ground displacement calculation. Measured ground responses are used to incorporate losses into the dynamic calculation. 2. The quasi-static response function for three different types of non-uniform grounds are calculated and used in the seismic wind noise superposition. The dynamic point source response and the three more realistic ground models result in larger horizontal displacements for the point source at distances on the order of 1 m or greater from the source. However, the superposition to predict the seismic wind noise is dominated by the displacements very close to the point source where the prediction is unchanged. This research indicates that the modeling of the wind-induced pressure source distribution must be improved to predict the observed equivalency of the vertical and horizontal displacements

A field-theoretic approach to the Wiener Sausage

The Wiener Sausage, the volume traced out by a sphere attached to a Brownian particle, is a classical problem in statistics and mathematical physics. Initially motivated by a range of field-theoretic, technical questions, we present a single loop renormalised perturbation theory of a stochastic process closely related to the Wiener Sausage, which, however, proves to be exact for the exponents and some amplitudes. The field-theoretic approach is particularly elegant and very enjoyable to see at work on such a classic problem. While we recover a number of known, classical results, the field-theoretic techniques deployed provide a particularly versatile framework, which allows easy calculation with different boundary conditions even of higher momenta and more complicated correlation functions. At the same time, we provide a highly instructive, non-trivial example for some of the technical particularities of the field-theoretic description of stochastic processes, such as excluded volume, lack of translational invariance and immobile particles. The aim of the present work is not to improve upon the well-established results for the Wiener Sausage, but to provide a field-theoretic approach to it, in order to gain a better understanding of the field-theoretic obstacles to overcome.Comment: 45 pages, 3 Figures, Springer styl

Single particle multipole expansions from Micromagnetic Tomography

Micromagnetic tomography aims at reconstructing large numbers of individual magnetizations of magnetic particles from combining high-resolution magnetic scanning techniques with micro X-ray computed tomography (microCT). Previous work demonstrated that dipole moments can be robustly inferred, and mathematical analysis showed that the potential field of each particle is uniquely determined. Here, we describe a mathematical procedure to recover higher orders of the magnetic potential of the individual magnetic particles in terms of their spherical harmonic expansions (SHE). We test this approach on data from scanning superconducting quantum interference device microscopy and microCT of a reference sample. For particles with high signal-to-noise ratio of the magnetic scan we demonstrate that SHE up to order $n=3$ can be robustly recovered. This additional level of detail restricts the possible internal magnetization structures of the particles and provides valuable rock magnetic information with respect to their stability and reliability as paleomagnetic remanence carriers. Micromagnetic tomography therefore enables a new approach for detailed rock magnetic studies on large ensembles of individual particles.Comment: 21 pages, 4 Figures, 3 Tables. For Supplemental Material see "Ancillary files" in this arxiv websit

H^+_2$ in a strong magnetic field described via a solvable model

We consider the hydrogen molecular ion $H^+_2$ in the presence of a strong homogeneous magnetic field. In this regime, the effective Hamiltonian is almost one dimensional with a potential energy which looks like a sum of two Dirac delta functions. This model is solvable, but not close enough to our exact Hamiltonian for relevant strenght of the magnnetic field. However we show that the correct values of the equilibrium distance as well as the binding energy of the ground state of the ion, can be obtained when incorporating perturbative corrections up to second order. Finally, we show that $He_2^{3+}$ exists for sufficiently large magnetic fields

Self-Consistent Electron-Nucleus Cusp Correction for Molecular Orbitals

We describe a method for imposing the correct electron-nucleus (e-n) cusp in molecular orbitals expanded as a linear combination of (cuspless) Gaussian basis functions. Enforcing the e-n cusp in trial wave functions is an important asset in quantum Monte Carlo calculations as it significantly reduces the variance of the local energy during the Monte Carlo sampling. In the method presented here, the Gaussian basis set is augmented with a small number of Slater basis functions. Note that, unlike other e-n cusp correction schemes, the presence of the Slater function is not limited to the vicinity of the nuclei. Both the coefficients of these cuspless Gaussian and cusp-correcting Slater basis functions may be self-consistently optimized by diagonalization of an orbital-dependent effective Fock operator. Illustrative examples are reported for atoms (\ce{H}, \ce{He} and \ce{Ne}) as well as for a small molecular system (\ce{BeH2}). For the simple case of the \ce{He} atom, we observe that, with respect to the cuspless version, the variance is reduced by one order of magnitude by applying our cusp-corrected scheme.Comment: 23 pages, 5 figure