SOLVING THE BETHE--SALPETER EQUATION IN MINKOWSKI SPACE: SCALAR THEORIES

The Bethe-Salpeter (BS) equation for scalar-scalar bound states in scalar theories without derivative coupling is formulated and solved in Minkowski space. This is achieved using the perturbation theory integral representation (PTIR), which allows these amplitudes to be expressed as integrals over weight functions and known singularity structures and hence allows us to convert the BS equation into an integral equation involving weight functions. We obtain numerical solutions using this formalism for a number of scattering kernels to illustrate the generality of the approach. It applies even when the na\"{\i}ve Wick rotation is invalid. As a check we verify, for example, that this method applied to the special case of the massive ladder exchange kernel reproduces the same results as are obtained by Wick rotation.Comment: 8 pages, regular latex, no figures. Entire manuscript available as a ps file at http://www.physics.adelaide.edu.au/theory/home.html Also available via anonymous ftp at ftp://adelphi.adelaide.edu.au/pub/theory/ADP-95-28.T182.p

Bethe-Salpeter equation in Minkowski space with cross-ladder kernel

A new method for solving the Bethe-Salpeter equation is developed. It allows to find the Bethe-Salpeter amplitudes both in Minkowski and in Euclidean spaces and, as a by product, the light-front wave function. The method is valid for any kernel given by irreducible Feynman graphs. Bethe-Salpeter and Light-Front equations for scalar particles with ladder + cross-ladder kernel are solved.Comment: 7 pages, 5 figures, to appear in the proceedings of the Workshop on Light-Cone QCD and Nonperturbative Hadron Physics, Cairns, Australia, July 7-15, 200

On the direct evaluation of the equilibrium distribution of clusters by simulation

An expression is derived that relates the average population of a particular type of cluster in a metastable vapor phase of volume Vtot to the probability, estimated by simulation, of finding this cluster in a system of volume V taken inside Vtot, where V<<Vtot. Correct treatment of the translational free energy of the cluster is crucial for this purpose. We show that the problem reduces to one of devising the proper boundary condition for the simulation. We then verify the result obtained previously for a low vapor density limit [J. Chem. Phys. 108, 3416 (1998)]. The difficulty implicit in our recent calculation [J. Chem. Phys. 110, 5249 (1999)], in which the approach in the former was generalized to higher vapor densities, is shown to be resolved by a method already suggested in that paper

Ion-induced nucleation. II. Polarizable multipolar molecules

Density functional theory is applied to ion-induced nucleation of polarizable multipolar molecules. The asymmetric nature of the ion-molecule interaction is shown to cause the sign preference in ion-induced nucleation. When the ion-molecule interaction is weak, the observed sign preference is consistent with that of the bare ion-molecule interaction potential and decreases with increasing supersaturation. However, as the ion-molecule interaction becomes stronger, the sign preference in the reversible work exhibits some nontrivial behavior. For molecular parameters applicable for CS2 and CH4, the predicted values of the reversible work of nucleation depend on the sign of the ion charge, yielding a difference in the nucleation rate by factors of 10 to 10^(2) and 10 to 10^(5), respectively

Binary nucleation of sulfuric acid-water: Monte Carlo simulation

We have developed a classical mechanical model for the H2SO4/H2O binary system. Monte Carlo simulation was performed in a mixed ensemble, in which the number of sulfuric acid molecules is fixed while that of water molecules is allowed to fluctuate. Simulation in this ensemble is computationally efficient compared to conventional canonical simulation, both in sampling very different configurations of clusters relevant in nucleation and in evaluating the free energy of cluster formation. The simulation yields molecular level information, such as the shape of the clusters and the dissociation behavior of the acid molecule in the cluster. Our results indicate that the clusters are highly nonspherical as a result of the anisotropic intermolecular interactions and that a cluster with a given number of acid molecules has several very different conformations, which are close in free energy and hence equally relevant in nucleation. The dissociation behavior of H2SO4 in a cluster differs markedly from that in bulk solution and depends sensitively on the assumed value of the free energy f(hb) of the dissociation reaction H2SO4+H2O-HSO4-. H3O+. In a small cluster, no dissociation is observed. As the cluster size becomes larger, the probability of having an HSO4-. H3O+ ion pair increases. However, in clusters relevant in nucleation, the resulting ion pairs remain in contact; about 240 water molecules are required to observe behavior that resembles that in bulk solution. If a larger value of f(hb) is assumed to reflect its uncertainty, the probability of dissociation becomes negligible. A reversible work surface obtained for a condition typical of vapor to liquid nucleation suggests that the rate-limiting step of new particle formation is a binary collision of two hydrated sulfuric acid molecules. The ion pairs formed by dissociation play a key role in stabilizing the resulting cluster. The reversible work surface is sensitive to the assumed value of f(hb), thus pointing to the need for an accurate estimate of the quantity either by ab initio calculations or experiments

On the direct evaluation of the equilibrium distribution of clusters by simulation. II

We clarify some of the subtle issues surrounding the observational cluster method, a simulation technique for studying nucleation. The validity of the method is reaffirmed here. The condition of the compact cluster limit is quantified and its implications are elucidated in terms of the correct enumeration of configuration space

Balmer-Like Series for Baryon Resonances

The pole positions of various baryon resonances have been found to reveal a well pronounced clustering, the so-called H"ohler cluster. In a previous work, the H"ohler clusters have been shown to be identical to Lorentz multiplets of the type (1/2+l', 1/2+l')*[(1/2,0)+(0,1/2)] with l' integer. Here we show that the cluster positions are well described by means of a Balmer-series like recursive mass formula.Comment: 5 pages LaTex, World Scientific style, two tables. A missing additive factor of +1 on the rhs of Eq. (2) has been inserted and thereby a misprint, not an error, correcte

Ion-induced nucleation: A density functional approach

Density functional theory is applied to ion-induced nucleation of dipolar molecules. The predicted reversible work shows a sign preference, resulting in a difference in the nucleation rate by a factor of 10–10^2, for realistic values of model parameters. The sign effect is found to decrease systematically as the supersaturation is increased. The asymmetry of a molecule is shown to be directly responsible for the sign preference in ion-induced nucleation

Angular and Polarization Response of Multimode Sensors with Resistive-Grid Absorbers

High sensitivity receiver systems with near ideal polarization sensitivity are highly desirable for development of millimeter and sub-millimeter radio astronomy. Multimoded bolometers provide a unique solution to achieve such sensitivity, for which hundreds of single-mode sensors would otherwise be required. The primary concern in employing such multimoded sensors for polarimetery is the control of the polarization systematics. In this paper, we examine the angular- and polarization- dependent absorption pattern of a thin resistive grid or membrane, which models an absorber used for a multimoded bolometer. The result shows that a freestanding thin resistive absorber with a surface resistivity of \eta/2, where \eta\ is the impedance of free space, attains a beam pattern with equal E- and H-plane responses, leading to zero cross polarization. For a resistive-grid absorber, the condition is met when a pair of grids is positioned orthogonal to each other and both have a resistivity of \eta/2. When a reflective backshort termination is employed to improve absorption efficiency, the cross-polar level can be suppressed below -30 dB if acceptance angle of the sensor is limited to <60degrees. The small cross-polar systematics have even-parity patterns and do not contaminate the measurements of odd-parity polarization patterns, for which many of recent instruments for cosmic microwave background are designed. Underlying symmetry that suppresses these cross-polar systematics is discussed in detail. The estimates and formalism provided in this paper offer key tools in the design consideration of the instruments using the multimoded polarimeters.Comment: 22 pages, 15 figure