Suppression of modes in the random phase approximation

A general but simple method is proposed to eliminate the quantum fluctuations generated by selected one-body operators in the excitation spectrum of a discrete random phase approximation (RPA) Hamiltonian. This method provides an outstanding tool for the removal of the contaminating spurious effects originated from symmetry violations. It can be also applied as a mode filter for analyzing RPA response functions.     

Symmetry-conserving random phase approximation

The projected random phase approximation (PRPA) is derived from a generator coordinate ansatz. It allows the calculation of excited states in the region of phase transitions, where conventional RPA breaks down. The theory is applied for an approximate solution of the R(8) model which shows a pairing collapse at large angular momenta.     

Laguerre approximation of random foams

Stochastic models for the microstructure of foams are valuable tools to study the relations between microstructure characteristics and macroscopic properties. Owing to the physical laws behind the formation of foams, Laguerre tessellations have turned out to be suitable models for foams. Laguerre tessellations are weighted generalizations of Voronoi tessellations, where polyhedral cells are formed through the interaction of weighted generator points. While both share the same topology, the cell curvature of foams allows only an approximation by Laguerre tessellations. This makes the model fitting a challenging task, especially when the preservation of the local topology is required. In this work, we propose an inversion-based approach to fit a Laguerre tessellation model to a foam. The idea is to find a set of generator points whose tessellation best fits the foam’s cell system. For this purpose, we transform the model fitting into a minimization problem that can be solved by gradient descent-based optimization. The proposed algorithm restores the generators of a tessellation if it is known to be Laguerre. If, as in the case of foams, no exact solution is possible, an approximative solution is obtained that maintains the local topology.     

Current conserving random phase approximation

The consequences of the continuity equation for the RPA are exploited, if charge and current densities are given. Simple, yet stringent conditions for the RPA amplitudes and the residual interaction are obtained. Under these conditions the RPA equations are simplified and exactly reduced to a hermitean eigenvalue problem of half the original dimensionality. Transition current matrix elements are then similar to those of an effective current recently proposed for TDA calculations.     

Bimaximal mixing in seesaw models

Neutrino masses and mixing are discussed in seesaw models assuming hierarchical structure of Dirac masses and predicting bimaximal mixing for three light neutrinos.     

Extension of the renormalized quasiparticle random phase approximation

The quasiparticle random phase approximation is extended in order to restore of the Pauli principle beyond the renormalized approach by treating the so-called scattering terms in the QRPA phonon operators. It has been shown that this new framework can be described in a case of a single nuclear shell occupied by both protons and neutrons in terms of the QRPA(14,3) algebra. An application of the formalism to the double beta decay of calcium⁴⁸Ca is discussed to some extent. Presented by W.A. Kamiński at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997. This work has been supported in part by the State Committee for Scientific Research (Poland), Contract No. 2 P03B 189 09.     

Nuclear matter properties in the relativistic random phase approximation

Nuclear matter properties at zero temperature are studied in terms of the relativistic σ-ω model, including the random phase approximation (RPA) contribution. At normal density, the medium polarization adds about −35 MeV of binding energy to the mean field result. The scalar and vector effective interaction strengths are fitted to the nuclear matter saturation conditions under various approximations for the energy functional including the RPA term. The effective mass and bulk modulus are calculated with these parameters. The relative importance of different contributions to the binding energy is analyzed.     

Numerical solution of the optimized random phase approximation

An accurate, efficient and robust numerical method for the solution of the optimized random phase approximation (ORPA) of classical liquids is presented. The uniqueness of the solution of the ORPA is proved rigorously. The method, hinging on the characterization of the generating functional, improves significantly on previous algorithms. Higher accuracy is obtained by using the values of the unknown functions on the grid points as independent variables instead of the usual coefficients of an expansion in orthogonal polynomials. It is shown that minimizing a suitably modified functional with a conjugate-gradient algorithm results in a very efficient and robust algorithm.     

A solvable version of the collisional random phase approximation

We derive the markovian limit of the collisional Random Phase Approximation (CRPA) by resort to the linearization of the Collisional Time-Dependent-Hartree-Fock (CTDHF) equation of motion for the one-body density matrix. The CRPA spectral problem is numerically solved in the frame of a model consisting of a finite fermion system with axial symmetry interacting by means of a separable force. Calculations are performed within a range of interaction strengths, temperature and size parameters and it is shown that both the centroids and the widths of the high energy collective modes exhibit the trend of experimental data.     

Bs-Bs mixing in grand unified models

We study Bs-Bs mixing in supersymmetry grand unified SO(10), SU(5) models where the mixings among the second and third generation squarks arise due to the existence of flavor violating sources in the Dirac and Majorana couplings which are responsible for neutrino mixings. We find that when the branching ratio of tau-->mugamma decay is enhanced to be around the current experimental bound, Bs-Bs mixing may also contain large contribution from supersymmetry in the SO(10) boundary condition. Consequently, the phase of Bs-Bs mixing is large (especially for small tanbeta and large scalar mass m0) and can be tested by measuring CP asymmetries of Bs decay modes.     

Isovector M6 excitations in the open-shell random phase approximation

OSRPA predictions are made for the excitation energies and transition amplitudes of J^π = 6^?, T = 1 excited states in the even N = Z sd shell nuclei. The results are employed in the calculation of electron scattering form factors. New expressions are given for the double commutators appearing in the OSRPA equations, which greatly facilitate their evaluation.     

Plasma oscillations in fullerene molecules within the random phase approximation

A method is presented for calculating the density of plasma excitation modes in fullerene molecules, which makes it possible to describe more accurately the specific features of the spectra as compared to the models proposed previously. The method is based on the inclusion of the total contribution of π and σ electrons to the spectra of collective oscillations in the molecules. This allows one to consider fullerene molecules with an arbitrary symmetry and arbitrary substituents. A comparative analysis of the experimental curves obtained for resonance electron capture and the results of numerical simulations for C₆₀, C₇₀, and C₇₆ molecules has demonstrated that not only the main maxima but also the ranges of the formation of negative ions coincide.     

Imaging of random surfaces and inverse scattering in the Kirchoff approximation

Abstract

Imaging of random surfaces can be modelled by integration over angular spectra of scattered plane waves. This approach suggests the representation of surface scattering in the Kirchhoff approximation using the concept of three-dimensional spatial frequencies. Optical methods of surface profiling can thus be modelled, leading to an insight into reconstruction of surface profiles from scattering data. The methods can also be extended to cover thin-film multilayer structures.     

Core polarization effects and the random phase approximation solution

A metricg _ik=η _ik+Hξ _iξ_k+2Jξ _(iPk) is investigated. WhenJ=0 this reduces to the well-known Kerr metric. Conditions on the vectorp _i are obtained under which a geodetic, shear-free null congruenceξ _i in the Minkowskian space-time (with metricη _ik) will continue to remain geodetic and shear-free in the Riemannian space-time ofg _ik. A general solution of Einstein’s equationR _ik=σξ _iξ_k is obtained whenp _iξⁱ=0 andξ _i is twist-free.     

Supersymmetry and quenched random fields beyond the tree approximation

We show how to generalize the Parisi-Sourlas treatment of quenched random fields to include corrections to the tree approximation.     

Pseudoscalar mesons and mixing models

We take the charmonium state at 2.98 GeV to be the η _c and show that it can be included in quadratic and linear mass matrix mixing models, and also in those having radial excited states, in a way consistent with perturbative QCD. The effect on the models of the Crystal Ball measurement of BR (ι→γη′)/BR(ι→γη) is studied and the ratio is found to depend strongly on the mass of the strange quark: the consequences of this are considered. Pseudoscalar mesons in the upsilon spectrum are discussed.     

Neutrino mixing discriminates geo-reactor models

Geo-reactor models suggest the existence of natural nuclear reactors at different deep-earth locations with loosely defined output power. Reactor fission products undergo beta decay with the emission of electron antineutrinos, which routinely escape the earth. Neutrino mixing distorts the energy spectrum of the electron antineutrinos. Characteristics of the distorted spectrum observed at the earth's surface could specify the location of a geo-reactor, discriminating the models and facilitating more precise power measurement.     

Generalized random phase approximation and gauge theories

Mean-field treatments of Yang-Mills theory face the problem of how to treat the Gauss law constraint. In this paper we try to face this problem by studying the excited states instead of the ground state. For this purpose we extend the operator approach to the Random Phase Approximation (RPA) well-known from nuclear physics and recently also employed in pion physics to general bosonic theories with a standard kinetic term. We focus especially on conservation laws, and how they are translated from the full to the approximated theories, demonstrate that the operator approach has the same spectrum as the RPA derived from the time-dependent variational principle, and give—for Yang-Mills theory—a discussion of the moment of inertia connected to the energy contribution of the zero modes to the RPA ground state energy. We also indicate a line of thought that might be useful to improve the results of the Random Phase Approximation.     

On the bethe approximation for the random bond Ising model

A random bond Ising model is considered in terms of the pair approximation, which is equivalent to the Bethe approximation, of the cluster variation method. On taking the configurational average over the random distribution of bonds ±J, we take into account the nearest neighbor correlations between effective fields and bonds. We investigate their effects to the phase transition temperature from the paramagnetic phase to the ferro- (or antiferro-) magnetic phase and to the spin glass phase for the Ising model on the square lattice. It turns out that the correlation effects act favorably to the spin glass phase and bend upward the line of transition temperature from the paramagnetic phase to the spin glass phase as the concentration being apart from 0.5. In the appendix, we derive the expression of free energy in the weak interaction limit.