Quantum theory of large amplitude collective motion and the Born-Oppenheimer method

We study the quantum foundations of a theory of large amplitude collective motion for a Hamiltonian expressed in terms of canonical variables. In previous work the separation into slow and fast (collective and non-collective) variables was carried out without the explicit intervention of the Born Oppenheimer approach. The addition of the Born Oppenheimer assumption not only provides support for the results found previously in leading approximation, but also facilitates an extension of the theory to include an approximate description of the fast variables and their interaction with the slow ones. Among other corrections, one encounters the Berry vector and scalar potential. The formalism is illustrated with the aid of some simple examples, where the potentials in question are actually evaluated and where the accuracy of the Born Oppenheimer approximation is tested. Variational formulations of both Hamiltonian and Lagrangian type are described for the equations of motion for the slow variables.Comment: 29 pages, 1 postscript figure, preprint no UPR-0085NT. Latex + epsf styl

Classical mappings of the symplectic model and their application to the theory of large-amplitude collective motion

We study the algebra Sp(n,R) of the symplectic model, in particular for the cases n=1,2,3, in a new way. Starting from the Poisson-bracket realization we derive a set of partial differential equations for the generators as functions of classical canonical variables. We obtain a solution to these equations that represents the classical limit of a boson mapping of the algebra. The relationship to the collective dynamics is formulated as a theorem that associates the mapping with an exact solution of the time-dependent Hartree approximation. This solution determines a decoupled classical symplectic manifold, thus satisfying the criteria that define an exactly solvable model in the theory of large amplitude collective motion. The models thus obtained also provide a test of methods for constructing an approximately decoupled manifold in fully realistic cases. We show that an algorithm developed in one of our earlier works reproduces the main results of the theorem.Comment: 23 pages, LaTeX using REVTeX 3.

Implications of \u3cem\u3eCaritas in Veritate\u3c/em\u3e for Marketing and Business Ethics

In an effort to assess the latest thinking in the Roman Catholic Church on economic matters, we examine the newest encyclical by Pope Benedict XVI, Caritas in Veritate (Charity in Truth) for guidance concerning marketing and business strategy. Core ethical values, consistent with historical Catholic Social Teachings (CST), are retained. However, some important nuances are added to previous treatments, and, reflecting the mind of the current Pontiff, certain points of emphasis are shifted to account for recent global developments. Key areas of consistency and differences (as we perceive them) are spelled out along with some brief commentary on the evolution of the CST position on matters of importance to business decision makers. We close our analysis with a brief discussion of how the lessons of the encyclical can be applied to selected marketing problems embedded with ethical issues, including some criteria for evaluating marketing programs. Finally, we note some editorial commentary published in the wake of the letter’s release along with our own summation

'Aurora'-a time domain based meta-algorithm for the rapid simulation and design of complex optical circuits

A new simulation tool called ‘Aurora’, specifically developed to efficiently simulate highly complex optical devices such as OADMs and Routers based on (higher order)microring resonators, is presented. The meta-simulation algorithm used by Aurora creates a framework in which many different simulation algorithms can be properly combined rather than providing a simulation algorithm itself. The calculations of this program use a simple scheme based in the time domain from which the frequency response can easily be derived. Simulation results of a 4-port OADM and waveguide gratings show excellent agreement when compared to experimentally obtained measurement data and conventional simulation methods

Caritas in Veritate: Updating Catholic Social Teachings for Macromarketing and Business

In an effort to assess the latest thinking in the Roman Catholic Church on economic matters, this communications note briefly highlights the recent publication of a new encyclical by Pope Benedict XVI, Caritas in Veritate (Charity in Truth). Core ethical values, consistent with previous examples of Catholic Social Teaching (CST), are retained. However, some important nuances are added to previous treatments and certain points of emphasis are shifted to account for recent global developments. Key areas that relate to abiding marketing issues are spelled out and some brief commentary on matters of importance to macromarketing is offered

Applying Catholic Social Teachings to Ethical Issues in Marketing

This article updates earlier work by the authors and proposes the social teachings of the Roman Catholic Church to be an encompassing and coherent normative theory, a source of principles that address contemporary issues in marketing, especially when a manager faces ethically charged questions. The authors propose that this application of a tradition in moral theology offers a novel approach for helping resolve contemporary ethical problems in marketing. Their approach to this task pursues two paths. First, the main tenets of Catholic social teaching are presented, along with some discussion of sources. Then, some of the ethical issues associated with contemporary marketing are introduced. These two paths are joined together by connecting Catholic social teaching principles to these questions. Finally, they argue for the value of this approach outside the framework of any denominational or sectarian context

Stability of the proton-to-electron mass ratio

We report a limit on the fractional temporal variation of the proton-to-electron mass ratio as, obtained by comparing the frequency of a rovibrational transition in SF6 with the fundamental hyperfine transition in Cs. The SF6 transition was accessed using a CO2 laser to interrogate spatial 2-photon Ramsey fringes. The atomic transition was accessed using a primary standard controlled with a Cs fountain. This result is direct and model-free

Further application of a semi-microscopic core-particle coupling method to the properties of Gd155,157, and Dy159

In a previous paper a semi-microscopic core-particle coupling method that includes the conventional strong coupling core-particle model as a limiting case, was applied to spectra and electromagnetic properties of several well-deformed odd nuclei. This work, coupled a large single-particle space to the ground state bands of the neighboring even cores. In this paper, we generalize the theory to include excited bands of the cores, such as beta and gamma bands, and thereby show that the resulting theory can account for the location and structure of all bands up to about 1.5 MeV.Comment: 15 pages including 9 figure(postscript), submitted to Phys.Rev.

Self-consistent theory of large amplitude collective motion: Applications to approximate quantization of non-separable systems and to nuclear physics

The goal of the present account is to review our efforts to obtain and apply a ``collective'' Hamiltonian for a few, approximately decoupled, adiabatic degrees of freedom, starting from a Hamiltonian system with more or many more degrees of freedom. The approach is based on an analysis of the classical limit of quantum-mechanical problems. Initially, we study the classical problem within the framework of Hamiltonian dynamics and derive a fully self-consistent theory of large amplitude collective motion with small velocities. We derive a measure for the quality of decoupling of the collective degree of freedom. We show for several simple examples, where the classical limit is obvious, that when decoupling is good, a quantization of the collective Hamiltonian leads to accurate descriptions of the low energy properties of the systems studied. In nuclear physics problems we construct the classical Hamiltonian by means of time-dependent mean-field theory, and we transcribe our formalism to this case. We report studies of a model for monopole vibrations, of $^{28}$Si with a realistic interaction, several qualitative models of heavier nuclei, and preliminary results for a more realistic approach to heavy nuclei. Other topics included are a nuclear Born-Oppenheimer approximation for an {\em ab initio} quantum theory and a theory of the transfer of energy between collective and non-collective degrees of freedom when the decoupling is not exact. The explicit account is based on the work of the authors, but a thorough survey of other work is included.Comment: 203 pages, many figure