On the Time-Dependent Analysis of Gamow Decay

Gamow's explanation of the exponential decay law uses complex "eigenvalues" and exponentially growing "eigenfunctions". This raises the question, how Gamow's description fits into the quantum mechanical description of nature, which is based on real eigenvalues and square integrable wave functions. Observing that the time evolution of any wave function is given by its expansion in generalized eigenfunctions, we shall answer this question in the most straightforward manner, which at the same time is accessible to graduate students and specialists. Moreover the presentation can well be used in physics lectures to students.Comment: 10 pages, 4 figures; heuristic argument simplified, different example discussed, calculation of decay rate adde

A Study of Degenerate Four-quark states in SU(2) Lattice Monte Carlo

The energies of four-quark states are calculated for geometries in which the quarks are situated on the corners of a series of tetrahedra and also for geometries that correspond to gradually distorting these tetrahedra into a plane. The interest in tetrahedra arises because they are composed of {\bf three } degenerate partitions of the four quarks into two two-quark colour singlets. This is an extension of earlier work showing that geometries with {\bf two} degenerate partitions (e.g.\ squares) experience a large binding energy. It is now found that even larger binding energies do not result, but that for the tetrahedra the ground and first excited states become degenerate in energy. The calculation is carried out using SU(2) for static quarks in the quenched approximation with $\beta=2.4$ on a $16^3\times 32$ lattice. The results are analysed using the correlation matrix between different euclidean times and the implications of these results are discussed for a model based on two-quark potentials.Comment: Original Raw PS file replace by a tarred, compressed and uuencoded PS fil

Gelatine matrix with human thrombin decreases blood loss in adolescents undergoing posterior spinal fusion for idiopathic scoliosis A MULTICENTRE, RANDOMISED CLINICAL TRIAL

Aims In a multicentre, randomised study of adolescents undergoing posterior spinal fusion for idiopathic scoliosis, we investigated the effect of adding gelatine matrix with human thrombin to the standard surgical methods of controlling blood loss. Patients and Methods Patients in the intervention group (n = 30) were randomised to receive a minimum of two and a maximum of four units of gelatine matrix with thrombin in addition to conventional surgical methods of achieving haemostasis. Only conventional surgical methods were used in the control group (n = 30). We measured the intra-operative and total blood loss (intra-operative blood loss plus post-operative drain output). Results Each additional hour of operating time increased the intra-operative blood loss by 356.9 ml (p <0.001) and the total blood loss by 430.5 ml (p <0.001). Multiple linear regression analysis showed that the intervention significantly decreased the intra-operative (-171 ml, p = 0.025) and total blood loss (-177 ml, p = 0.027). The decrease in haemoglobin concentration from the day before the operation to the second post-operative day was significantly smaller in the intervention group (-6 g/I, p = 0.013) than in the control group. Conclusion The addition of gelatine matrix with human thrombin to conventional methods of achieving haemostasis reduces both the intra-operative blood loss and the decrease in haemoglobin concentration post-operatively in adolescents undergoing posterior spinal fusion for idiopathic scoliosis. Take home message: A randomised clinical trial showed that gelatine matrix with human thrombin decreases intra-operative blood loss by 30% when added to traditional surgical haemostatic methods in adolescents undergoing posterior spinal fusion for idiopathic scoliosis.Peer reviewe

Cut-off values to evaluate exercise-induced asthma in eucapnic voluntary hyperventilation test for children

Background and Aim The eucapnic voluntary hyperventilation (EVH) testing is a diagnostic tool for diagnostics of exercise-induced bronchoconstriction; while the testing has become more common among children, data on the test's feasibility among children remain limited. Our aim was to investigate EVH testing feasibility among children, diagnostic testing cut-off values, and which factors affect testing outcomes. Methods We recruited 134 patients aged 10-16 years with a history of exercise-induced dyspnoea and 100 healthy control children to undergo 6-min EVH testing. Testing feasibility was assessed by the children's ability to achieve >= 70% of the target minute ventilation of 30 times forced expiratory volume in 1 s (FEV1). Bronchoconstriction was assessed as a minimum of 8%, 10%, 12%, 15% or 20% fall in FEV1. Patient characteristics were correlated with EVH outcomes. Results Overall, 98% of the children reached >= 70%, 88% reached >= 80%, 79% reached >= 90% and 62% reached >= 100% of target ventilation in EVH testing; of children with a history of exercise-induced dyspnoea, the decline percentages were as follows: 24% (>= 8% fall), 17% (>= 10% fall), 10% (>= 12% fall), 6% (>= 15% fall) and 5% (>= 20% fall) in FEV1, compared to 11%, 4%, 3%, 1% and 0% among the healthy controls, respectively. Healthy controls and boys performed testing at higher ventilation rates (p < .05). Conclusion Eucapnic voluntary hyperventilation testing is feasible among children aged 10-16 years and has diagnostic value in evaluating exercise-induced dyspnoea among children. A minimum 10% fall in FEV1 is a good diagnostic cut-off value. Disease status appears to be important covariates

Thermal conductivity in harmonic lattices with random collisions

We review recent rigorous mathematical results about the macroscopic behaviour of harmonic chains with the dynamics perturbed by a random exchange of velocities between nearest neighbor particles. The random exchange models the effects of nonlinearities of anharmonic chains and the resulting dynamics have similar macroscopic behaviour. In particular there is a superdiffusion of energy for unpinned acoustic chains. The corresponding evolution of the temperature profile is governed by a fractional heat equation. In non-acoustic chains we have normal diffusivity, even if momentum is conserved.Comment: Review paper, to appear in the Springer Lecture Notes in Physics volume "Thermal transport in low dimensions: from statistical physics to nanoscale heat transfer" (S. Lepri ed.

Not to normal order - Notes on the kinetic limit for weakly interacting quantum fluids

The derivation of the Nordheim-Boltzmann transport equation for weakly interacting quantum fluids is a longstanding problem in mathematical physics. Inspired by the method developed to handle classical dilute gases, a conventional approach is the use of the BBGKY hierarchy for the time-dependent reduced density matrices. In contrast, our contribution is motivated by the kinetic theory of the weakly nonlinear Schrodinger equation. The main observation is that the results obtained in the latter context carry over directly to weakly interacting quantum fluids provided one does not insist on normal order in the Duhamel expansion. We discuss the term by term convergence of the expansion and the equilibrium time correlation .Comment: 43 pages, corrected typos, updated assumptions in sec.

Simulation of heat transport in low-dimensional oscillator lattices

The study of heat transport in low-dimensional oscillator lattices presents a formidable challenge. Theoretical efforts have been made trying to reveal the underlying mechanism of diversified heat transport behaviors. In lack of a unified rigorous treatment, approximate theories often may embody controversial predictions. It is therefore of ultimate importance that one can rely on numerical simulations in the investigation of heat transfer processes in low-dimensional lattices. The simulation of heat transport using the non-equilibrium heat bath method and the Green-Kubo method will be introduced. It is found that one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) momentum-conserving nonlinear lattices display power-law divergent, logarithmic divergent and constant thermal conductivities, respectively. Next, a novel diffusion method is also introduced. The heat diffusion theory connects the energy diffusion and heat conduction in a straightforward manner. This enables one to use the diffusion method to investigate the objective of heat transport. In addition, it contains fundamental information about the heat transport process which cannot readily be gathered otherwise.Comment: Article published in: Thermal transport in low dimensions: From statistical physics to nanoscale heat transfer, S. Lepri, ed. Lecture Notes in Physics, vol. 921, pp. 239 - 274, Springer-Verlag, Berlin, Heidelberg, New York (2016

Anomalous Heat Conduction and Anomalous Diffusion in Low Dimensional Nanoscale Systems

Thermal transport is an important energy transfer process in nature. Phonon is the major energy carrier for heat in semiconductor and dielectric materials. In analogy to Ohm's law for electrical conductivity, Fourier's law is a fundamental rule of heat transfer in solids. It states that the thermal conductivity is independent of sample scale and geometry. Although Fourier's law has received great success in describing macroscopic thermal transport in the past two hundreds years, its validity in low dimensional systems is still an open question. Here we give a brief review of the recent developments in experimental, theoretical and numerical studies of heat transport in low dimensional systems, include lattice models, nanowires, nanotubes and graphenes. We will demonstrate that the phonon transports in low dimensional systems super-diffusively, which leads to a size dependent thermal conductivity. In other words, Fourier's law is breakdown in low dimensional structures

Three independently deleted regions at chromosome arm 16q in human prostate cancer: allelic loss at 16q24.1–q24.2 is associated with aggressive behaviour of the disease, recurrent growth, poor differentiation of the tumour and poor prognosis for the patient

Loss of heterozygosity at chromosome arm 16q is a frequent event in human prostate cancer. In this study, loss of heterozygosity at 16q was studied in 44 prostate cancer patients exhibiting various clinical features. Fifteen polymorphic polymerase chain reaction (PCR) markers were used to identify the separately deleted areas and the findings were compared with clinicopathological variables and 5-year survival of the patients. The results indicated that there are at least three independently deleted regions at 16q. Allelic losses at the central and distal areas were associated significantly with aggressive behaviour of the disease (16q24.1–q24.2, P< 0.01, and 16q24.3–qter, P< 0.05), and the central area of deletion was further significantly associated with poorly differentiated tumour cells (P< 0.05) and with recurrent (P< 0.01) growth of the tumour. During the follow-up period, 28% of the patients initially with M0 disease developed distant metastases. Of the patients showing allelic loss at 16q24.1–q24.2, distant metastasis were found in 45% during the 5-year follow-up period, and 31% of the patients showing loss at 16q21.1 also developed distant metastases. After the 5-year follow-up period, 14 (32%) of the patients remained alive, whereas 19 (43%) had died because of their prostate cancer. The overall survival rate of the patients showing allelic loss at 16q21.1 or 16q24.1–q24.2 was significantly lower than that of the patients with retained heterozygosity. © 1999 Cancer Research Campaig

Parenteral oestrogen in the treatment of prostate cancer: a systematic review

The objectives of this study were to assess the effectiveness and safety of parenteral oestrogen in the treatment of prostate cancer, and to examine any dose relationship. A systematic review was undertaken. Electronic databases, published paper and internet resources were searched to locate published and unpublished studies with no restriction by language or publication date. Studies included were randomised controlled trials of parenteral oestrogen in patients with prostate cancer; other study designs were also included to examine dose–response. Study selection, appraisal, data extraction and quality assessment were performed by one reviewer and independently checked by another. Twenty trials were included in the review. The trials differed with regard to the included patients, formulation and dose of parenteral oestrogen, comparator used, outcome measures reported and the duration of follow-up. The results provide no evidence to suggest that parenteral oestrogen, in doses sufficient to produce castrate levels of testosterone, is less effective than luteinising hormone-releasing hormone (LHRH) or orchidectomy in controlling prostate cancer, or that it is consistently associated with an increase in cardiovascular mortality. Further well-conducted trials of parenteral oestrogen are required. A pilot randomised controlled trial comparing transdermal oestrogen to LHRH analogues in men with locally advanced or metastatic prostate cancer is underway in the United Kingdom