Saddle Points and Stark Ladders: Exact Calculations of Exciton Spectra in Superlattices

A new, exact method for calculating excitonic absorption in superlattices is described. It is used to obtain high resolution spectra showing the saddle point exciton feature near the top of the miniband. The evolution of this feature is followed through a series of structures with increasing miniband width. The Stark ladder of peaks produced by an axial electric field is investigated, and it is shown that for weak fields the line shapes are strongly modified by coupling to continuum states, taking the form of Fano resonances. The calculated spectra, when suitably broadened, are found to be in good agreement with experimental results.Comment: 9 pages Revtex v3.0, followed by 4 uuencoded postscript figures, SISSA-CM-94-00

Partition function of the eight-vertex model with domain wall boundary condition

We derive the recursive relations of the partition function for the eight-vertex model on an $N\times N$ square lattice with domain wall boundary condition. Solving the recursive relations, we obtain the explicit expression of the domain wall partition function of the model. In the trigonometric/rational limit, our results recover the corresponding ones for the six-vertex model.Comment: Latex file, 20 pages; V2, references adde

The eVALuate study: two parallel randomised trials, one comparing laparoscopic with abdominal hysterectomy, the other comparing laparoscopic with vaginal hysterectomy

OBJECTIVE: To compare the effects of laparoscopic hysterectomy and abdominal hysterectomy in the abdominal trial, and laparoscopic hysterectomy and vaginal hysterectomy in the vaginal trial. DESIGN: Two parallel, multicentre, randomised trials. Setting 28 UK centres and two South African centres. Participants 1380 women were recruited; 1346 had surgery; 937 were followed up at one year. PRIMARY OUTCOME: outcome Rate of major complications. RESULTS: In the abdominal trial laparoscopic hysterectomy was associated with a higher rate of major complications than abdominal hysterectomy (11.1% v 6.2%, P = 0.02; difference 4.9%, 95% confidence interval 0.9% to 9.1%) and the number needed to treat to harm was 20. Laparoscopic hysterectomy also took longer to perform (84 minutes v 50 minutes) but was less painful (visual analogue scale 3.51 v 3.88, P = 0.01) and resulted in a shorter stay in hospital after the operation (3 days v 4 days). Six weeks after the operation, laparoscopic hysterectomy was associated with less pain and better quality of life than abdominal hysterectomy (SF-12, body image scale, and sexual activity questionnaires). In the vaginal trial we found no evidence of a difference in major complication rates between laparoscopic hysterectomy and vaginal hysterectomy (9.8% v 9.5%, P = 0.92; difference 0.3%, − 5.2% to 5.8%), and the number needed to treat to harm was 333.We found no evidence of other differences between laparoscopic hysterectomy and vaginal hysterectomy except that laparoscopic hysterectomy took longer to perform (72 minutes v 39 minutes) and was associated with a higher rate of detecting unexpected pathology (16.4% v 4.8%, P = < 0.01). However, this trial was underpowered. CONCLUSIONS: Laparoscopic hysterectomy was associated with a significantly higher rate of major complications than abdominal hysterectomy. It also took longer to perform but was associated with less pain, quicker recovery, and better short term quality of life. The trial comparing vaginal hysterectomy with laparoscopic hysterectomy was underpowered and is inconclusive on the rate of major complications; however, vaginal hysterectomy took less time

Anomalous relaxation kinetics of biological lattice-ligand binding models

We discuss theoretical models for the cooperative binding dynamics of ligands to substrates, such as dimeric motor proteins to microtubules or more extended macromolecules like tropomyosin to actin filaments. We study the effects of steric constraints, size of ligands, binding rates and interaction between neighboring proteins on the binding dynamics and binding stoichiometry. Starting from an empty lattice the binding dynamics goes, quite generally, through several stages. The first stage represents fast initial binding closely resembling the physics of random sequential adsorption processes. Typically this initial process leaves the system in a metastable locked state with many small gaps between blocks of bound molecules. In a second stage the gaps annihilate slowly as the ligands detach and reattach. This results in an algebraic decay of the gap concentration and interesting scaling behavior. Upon identifying the gaps with particles we show that the dynamics in this regime can be explained by mapping it onto various reaction-diffusion models. The final approach to equilibrium shows some interesting dynamic scaling properties. We also discuss the effect of cooperativity on the equilibrium stoichiometry, and their consequences for the interpretation of biochemical and image reconstruction results.Comment: REVTeX, 20 pages, 17 figures; review, to appear in Chemical Physics; v2: minor correction

Semiclassical Analysis of the Wigner 12j12j Symbol with One Small Angular Momentum

We derive an asymptotic formula for the Wigner $12j$ symbol, in the limit of one small and 11 large angular momenta. There are two kinds of asymptotic formulas for the $12j$ symbol with one small angular momentum. We present the first kind of formula in this paper. Our derivation relies on the techniques developed in the semiclassical analysis of the Wigner $9j$ symbol [L. Yu and R. G. Littlejohn, Phys. Rev. A 83, 052114 (2011)], where we used a gauge-invariant form of the multicomponent WKB wave-functions to derive asymptotic formulas for the $9j$ symbol with small and large angular momenta. When applying the same technique to the $12j$ symbol in this paper, we find that the spinor is diagonalized in the direction of an intermediate angular momentum. In addition, we find that the geometry of the derived asymptotic formula for the $12j$ symbol is expressed in terms of the vector diagram for a $9j$ symbol. This illustrates a general geometric connection between asymptotic limits of the various $3nj$ symbols. This work contributes the first known asymptotic formula for the $12j$ symbol to the quantum theory of angular momentum, and serves as a basis for finding asymptotic formulas for the Wigner $15j$ symbol with two small angular momenta.Comment: 15 pages, 14 figure

Statistical mechanics of an ideal Bose gas in a confined geometry

We study the behaviour of an ideal non-relativistic Bose gas in a three-dimensional space where one of the dimensions is compactified to form a circle. In this case there is no phase transition like that for the case of an infinite volume, nevertheless Bose-Einstein condensation signified by a sudden buildup of particles in the ground state can occur. We use the grand canonical ensemble to study this problem. In particular, the specific heat is evaluated numerically, as well as analytically in certain limits. We show analytically how the familiar result for the specific heat is recovered as we let the size of the circle become large so that the infinite volume limit is approached. We also examine in detail the behaviour of the chemical potential and establish the precise manner in which it approaches zero as the volume becomes large.Comment: 13 pages, 2 eps figures, revtex

Towards a CPT Invariant Quantum Field Theory on Elliptic de Sitter Space

Consequences of Schr\"{o}dinger's antipodal identification on quantum field theory in de Sitter space are investigated. The elliptic $\mathbb{Z}_2$ identification provides observers with complete information. We show that a suitable confinement on dimension of the elliptic de Sitter space guarantees the existence of globally defined spinors and orientable $dS/\mathbb{Z}_2$ manifold. In Beltrami coordinates, we give exact solutions of scalar and spinor fields. The CPT invariance of quantum field theory on the elliptic de Sitter space is presented explicitly.Comment: 16 pages, some references have been added, the structure of paper have been revised, accepted for publication in Int. J. Mod. Phys.

Free Energy of the Eight Vertex Model with an Odd Number of Lattice Sites

We calculate the bulk contribution for the doubly degenerated largest eigenvalue of the transfer matrix of the eight vertex model with an odd number of lattice sites N in the disordered regime using the generic equation for roots proposed by Fabricius and McCoy. We show as expected that in the thermodynamic limit the result coincides with the one in the N even case.Comment: 11 pages LaTeX New introduction, Method change

From non-degenerate conducting polymers to dense matter in the massive Gross-Neveu model

Using results from the theory of non-degenerate conducting polymers like cis-polyacetylene, we generalize our previous work on dense baryonic matter and the soliton crystal in the massless Gross-Neveu model to finite bare fermion mass. In the large N limit, the exact crystal ground state can be constructed analytically, in close analogy to the bipolaron lattice in polymers. These findings are contrasted to the standard scenario with homogeneous phases only and a first order phase transition at a critical chemical potential.Comment: 12 pages, 7 figures, revtex; v2: improved readability, following advice of PRD referee; accepted for publicatio

Spacetime Encodings II - Pictures of Integrability

I visually explore the features of geodesic orbits in arbitrary stationary axisymmetric vacuum (SAV) spacetimes that are constructed from a complex Ernst potential. Some of the geometric features of integrable and chaotic orbits are highlighted. The geodesic problem for these SAV spacetimes is rewritten as a two degree of freedom problem and the connection between current ideas in dynamical systems and the study of two manifolds sought. The relationship between the Hamilton-Jacobi equations, canonical transformations, constants of motion and Killing tensors are commented on. Wherever possible I illustrate the concepts by means of examples from general relativity. This investigation is designed to build the readers' intuition about how integrability arises, and to summarize some of the known facts about two degree of freedom systems. Evidence is given, in the form of orbit-crossing structure, that geodesics in SAV spacetimes might admit, a fourth constant of motion that is quartic in momentum (by contrast with Kerr spacetime, where Carter's fourth constant is quadratic).Comment: 11 pages, 10 figure