Optical absorption of non-interacting tight-binding electrons in a Peierls-distorted chain at half band-filling

In this first of three articles on the optical absorption of electrons in half-filled Peierls-distorted chains we present analytical results for non-interacting tight-binding electrons. We carefully derive explicit expressions for the current operator, the dipole transition matrix elements, and the optical absorption for electrons with a cosine dispersion relation of band width $W$ and dimerization parameter $\delta$. New correction (``$\eta$''-)terms to the current operator are identified. A broad band-to-band transition is found in the frequency range $W\delta < \omega < W$ whose shape is determined by the joint density of states for the upper and lower Peierls subbands and the strong momentum dependence of the transition matrix elements.Comment: 17 pages REVTEX 3.0, 2 postscript figures; hardcopy versions before May 96 are obsolete; accepted for publication in The Philosophical Magazine

A hazard and probabilistic safety analysis of a high-level waste transfer process

This paper describes a safety analysis of a transfer process for high-level radioactive and toxic waste. The analysis began with a hazard assessment that used elements of What If, Checklist, Failure Modes and Effects Analysis, and Hazards and Operability Study (HAZOP) techniques to identify and rough-in accident sequences. Based on this preliminary analysis, the most significant accident sequences were developed further using event trees. Quantitative frequency estimates for the accident sequences were based on operational data taken from the historical record of the site where the process is performed. Several modeling challenges were encountered in the course of the study. These included linked initiating and accident progression events, fire propagation modeling, accounting for administrative control violations, and handling mission-phase effects

Modular Invariance and Characteristic Numbers

We show that a general miraculous cancellation formula, the divisibility of certain characteristic numbers and some other topologiclal results are con- sequences of the modular invariance of elliptic operators on loop spaces. Previously we have shown that modular invariance also implies the rigidity of many elliptic operators on loop spaces.Comment: 14 page

Effective Hamiltonian for Excitons with Spin Degrees of Freedom

Starting from the conventional electron-hole Hamiltonian ${\cal H}_{eh}$, we derive an effective Hamiltonian $\tilde{\cal H}_{1s}$ for $1s$ excitons with spin degrees of freedom. The Hamiltonian describes optical processes close to the exciton resonance for the case of weak excitation. We show that straightforward bosonization of ${\cal H}_{eh}$ does not give the correct form of $\tilde{\cal H}_{1s}$, which we obtain by a projection onto the subspace spanned by the $1s$ excitons. The resulting relaxation and renormalization terms generate an interaction between excitons with opposite spin. Moreover, exciton-exciton repulsive interaction is greatly reduced by the renormalization. The agreement of the present theory with the experiment supports the validity of the description of a fermionic system by bosonic fields in two dimensions.Comment: 12 pages, no figures, RevTe

Non-abelian Harmonic Oscillators and Chiral Theories

We show that a large class of physical theories which has been under intensive investigation recently, share the same geometric features in their Hamiltonian formulation. These dynamical systems range from harmonic oscillations to WZW-like models and to the KdV dynamics on $Diff_oS^1$. To the same class belong also the Hamiltonian systems on groups of maps. The common feature of these models are the 'chiral' equations of motion allowing for so-called chiral decomposition of the phase space.Comment: 1

A survey of the Mycoplasma genitalium genome by using random sequencing.

A total of 508 random clones from five Mycoplasma genitalium genomic libraries were partially sequenced and analyzed. This resulted in the identification of 291 unique contigs. Sequence information from these clones (100,993 nucleotides), representing approximately 17% of this pathogen's genome, was analyzed by comparison to the DNA and protein sequence data bases. The frequency with which clones could be identified, by virtue of possessing homology to another data base entry, was 46%. Sequence analysis indicated the following. (i) The M. genitalium genome contains many genes involved in various metabolic processes. (ii) Repetitive DNA may comprise as much as 4% of this genome. (iii) The MgPa adhesin gene may be the result of horizontal transfer from an unknown origin. (iv) Not all dinucleotide pairs are present in this genome at the expected frequency. (v) This genome potentially encodes approximately 390 proteins and makes very efficient use of its limited amount of DNA. In addition, this study allowed us to estimate the number of genes involved with various cellular functions

Mixed biexcitons in single quantum wells

Biexcitonic complexes in a ZnSe single quantum well are investigated by spectrally resolved four-wave mixing (FWM). The formation of heavy-heavy-hole XXh and of mixed heavy-light-hole XXm biexcitons showing binding energies of Δh=4.8meV and Δm=2.8meV is identified by polarization selection rules. The coherent dynamics of the FWM response and the observed FWM intensity ratio between the XXh and XXm biexciton-induced nonlinear signals are in agreement with the solution of an extended optical Bloch equation

Static solitons with non-zero Hopf number

We investigate a generalized non-linear O(3) $\sigma$-model in three space dimensions where the fields are maps $S^3 \mapsto S^2$. Such maps are classified by a homotopy invariant called the Hopf number which takes integer values. The model exhibits soliton solutions of closed vortex type which have a lower topological bound on their energies. We explicitly compute the fields for topological charge 1 and 2 and discuss their shapes and binding energies. The effect of an additional potential term is considered and an approximation is given for the spectrum of slowly rotating solitons.Comment: 13 pages, RevTeX, 7 Postscript figures, minor changes have been made, a reference has been corrected and a figure replace

Possible Origin of Fermion Chirality and Gut Structure From Extra Dimensions

The fundamental chiral nature of the observed quarks and leptons and the emergence of the gauge group itself are most puzzling aspects of the standard model. Starting from general considerations of topological properties of gauge field configurations in higher space-time dimensions, it is shown that the existence of non-trivial structures in ten dimensions would determine a class of models corresponding to a grand unified GUT structure with complex fermion representations with respect to $SU(3)_C \otimes SU(2)_L \otimes U(1)_Y$. The discussion is carried out within the framework of string theories with characteristic energy scales below the Planck mass. Avoidance of topological obstructions upon continuous deformation of field configurations leads to global chiral symmetry breaking of the underlying fundamental theory, imposes rigorous restrictions on the structure of the vacuum and space-time itself and determines uniquely the gauge structure and matter content.Comment: final version to appear in Phys. Rev.

Early Cenozoic denudation of central west Britain in response to transient and permanent uplift above a mantle plume

Upwelling mantle plumes beneath continental crust are predicted to produce difficult to quantify, modest uplift and denudation. The contribution of permanent and transient components to the uplift is also difficult to distinguish. A pulse of denudation in Britain in the Early Paleogene has been linked, although with some controversy, with the arrival of the proto-Iceland mantle plume. In this contribution we show that combining apatite and zircon (U-Th-Sm)/He and apatite fission track analyses from central west Britain with numerical modeling clearly identifies a pulse of early Cenozoic denudation. The data indicate that rock uplift and denudation were centered on the northern East Irish Sea Basin and 1.0–2.4 km of rocks were removed during the latest Cretaceous-early Paleogene. Uplift and erosion appears to have started a few million years before the earliest magmatism in the region. The regional denudation pattern mirrors the distribution of low-density magmatic rocks that has been imaged in the deep crust. However, the injection of the underplating melt is not enough to account for the total denudation. An additional regional uplift of at least 300 m is required, which is consistent with a transient thermal effect from the hot mantle plume. The rapid exhumation event ceased by ~40 Ma and the data do not require significant Neogene exhumation