A transfer matrix method for the analysis of fractal quantum potentials

The scattering properties of quantum particles on fractal potentials at different stages of fractal growth are obtained by means of the transfer matrix method. This approach can be easily adopted for project assignments in introductory quantum mechanics for undergraduates. The reflection coefficients for both the fractal potential and the finite periodic potential are calculated and compared. It is shown that the reflection coefficient for the fractal has a self-similar structure associated with the fractal distribution of the potential

Longitudinal spin transport in diluted magnetic semiconductor superlattices: the effect of the giant Zeeman splitting

Longitudinal spin transport in diluted magnetic semiconductor superlattices is investigated theoretically. The longitudinal magnetoconductivity (MC) in such systems exhibits an oscillating behavior as function of an external magnetic field. In the weak magnetic field region the giant Zeeman splitting plays a dominant role which leads to a large negative magnetoconductivity. In the strong magnetic field region the MC exhibits deep dips with increasing magnetic field. The oscillating behavior is attributed to the interplay between the discrete Landau levels and the Fermi surface. The decrease of the MC at low magnetic field is caused by the $s-d$ exchange interaction between the electron in the conduction band and the magnetic ions.Comment: 6 pages, 9 figures, submitted to Phys. Rev.

An Algebraic Analysis of Conchoids to Algebraic Curves

We study the conchoid to an algebraic affine plane curve C from the perspective of algebraic geometry, analyzing their main algebraic properties. Beside C, the notion of conchoid involves a point A in the affine plane (the focus) and a nonzero field element d (the distance).We introduce the formal definition of conchoid by means of incidence diagrams.We prove that the conchoid is a 1-dimensional algebraic set having atmost two irreducible components. Moreover, with the exception of circles centered at the focus A and taking d as its radius, all components of the corresponding conchoid have dimension 1. In addition, we introduce the notions of special and simple components of a conchoid. Furthermore we state that, with the exception of lines passing through A, the conchoid always has at least one simple component and that, for almost every distance, all the components of the conchoid are simple. We state that, in the reducible case, simple conchoid components are birationally equivalent to C, and we show how special components can be used to decide whether a given algebraic curve is the conchoid of another curve

The HubBLe Trial: haemorrhoidal artery ligation (HAL) versus rubber band ligation (RBL) for symptomatic second- and third-degree haemorrhoids: a multicentre randomised controlled trial and health-economic evaluation.

BACKGROUND: Optimal surgical intervention for low-grade haemorrhoids is unknown. Rubber band ligation (RBL) is probably the most common intervention. Haemorrhoidal artery ligation (HAL) is a novel alternative that may be more efficacious. OBJECTIVE: The comparison of HAL with RBL for the treatment of grade II/III haemorrhoids. DESIGN: A multicentre, parallel-group randomised controlled trial. PERSPECTIVE: UK NHS and Personal Social Services. SETTING: 17 NHS Trusts. PARTICIPANTS: Patients aged ≥ 18 years presenting with grade II/III (second- and third-degree) haemorrhoids, including those who have undergone previous RBL. INTERVENTIONS: HAL with Doppler probe compared with RBL. OUTCOMES: Primary outcome - recurrence at 1 year post procedure; secondary outcomes - recurrence at 6 weeks; haemorrhoid severity score; European Quality of Life-5 Dimensions, 5-level version (EQ-5D-5L); Vaizey incontinence score; pain assessment; complications; and cost-effectiveness. RESULTS: A total of 370 participants entered the trial. At 1 year post procedure, 30% of the HAL group had evidence of recurrence compared with 49% after RBL [adjusted odds ratio (OR) = 2.23, 95% confidence interval (CI) 1.42 to 3.51; p = 0.0005]. The main reason for the difference was the number of extra procedures required to achieve improvement/cure. If a single HAL is compared with multiple RBLs then only 37.5% recurred in the RBL arm (adjusted OR 1.35, 95% CI 0.85 to 2.15; p = 0.20). Persistence of significant symptoms at 6 weeks was lower in both arms than at 1 year (9% HAL and 29% RBL), suggesting significant deterioration in both groups over the year. Symptom score, EQ-5D-5L and Vaizey score improved in both groups compared with baseline, but there was no difference between interventions. Pain was less severe and of shorter duration in the RBL group; most of the HAL group who had pain had mild to moderate pain, resolving by 3 weeks. Complications were low frequency and not significantly different between groups. It appeared that HAL was not cost-effective compared with RBL. In the base-case analysis, the difference in mean total costs was £1027 higher for HAL. Quality-adjusted life-years (QALYs) were higher for HAL; however, the difference was very small (0.01) resulting in an incremental cost-effectiveness ratio of £104,427 per additional QALY. CONCLUSIONS: At 1 year, although HAL resulted in fewer recurrences, recurrence was similar to repeat RBL. Symptom scores, complications, EQ-5D-5L and continence score were no different, and patients had more pain in the early postoperative period after HAL. HAL is more expensive and unlikely to be cost-effective in terms of incremental cost per QALY. LIMITATIONS: Blinding of participants and site staff was not possible. FUTURE WORK: The incidence of recurrence may continue to increase with time. Further follow-up would add to the evidence regarding long-term clinical effectiveness and cost-effectiveness. The polysymptomatic nature of haemorrhoidal disease requires a validated scoring system, and the data from this trial will allow further assessment of validity of such a system. These data add to the literature regarding treatment of grade II/III haemorrhoids. The results dovetail with results from the eTHoS study [Watson AJM, Hudson J, Wood J, Kilonzo M, Brown SR, McDonald A, et al. Comparison of stapled haemorrhoidopexy with traditional excisional surgery for haemorrhoidal disease (eTHoS): a pragmatic, multicentre, randomised controlled trial. Lancet 2016, in press.] comparing stapled haemorrhoidectomy with excisional haemorrhoidectomy. Combined results will allow expansion of analysis, allowing surgeons to tailor their treatment options to individual patients. TRIAL REGISTRATION: Current Controlled Trials ISRCTN41394716. FUNDING: This project was funded by the NIHR Health Technology Assessment programme and will be published in full in Health Technology Assessment; Vol. 20, No. 88. See the NIHR Journals Library website for further project information

Envelope-function theory without spurious real solutions

Spurious real solutions $k_S\ge 1$\un{{\AA}^{-1}} of the bulk $\bm{k}\bullet\bm{p}$ Hamiltonian for semiconductors can lead to spurious bands and nonnormalizable wave functions in the envelope function approximation (EFA). Since physical observables cannot depend on layer width variations on the scale of 1\un{\AA} —less than a typical interface width or the precision of defining an interface— we form coherent superpositions of spurious real solutions that satisfy boundary conditions with interface boundaries varying on the scale of $k_S^{-1}$. The superposition leads to a total destructive interference, which demonstrates that real spurious solutions do not contribute to the envelope function away from interfaces. In the interfacial region, we show that real spurious solutions should be replaced with evanescent solutions that decay within $k_S^{-1}$. The present technique is demonstrated in a model case and in a superlattice calculation using the $8\times 8$ EFA