Quantum Blobs

Quantum blobs are the smallest phase space units of phase space compatible with the uncertainty principle of quantum mechanics and having the symplectic group as group of symmetries. Quantum blobs are in a bijective correspondence with the squeezed coherent states from standard quantum mechanics, of which they are a phase space picture. This allows us to propose a substitute for phase space in quantum mechanics. We study the relationship between quantum blobs with a certain class of level sets defined by Fermi for the purpose of representing geometrically quantum states.Comment: Prepublication. Dedicated to Basil Hile

Clifford Algebras in Symplectic Geometry and Quantum Mechanics

The necessary appearance of Clifford algebras in the quantum description of fermions has prompted us to re-examine the fundamental role played by the quaternion Clifford algebra, C(0,2). This algebra is essentially the geometric algebra describing the rotational properties of space. Hidden within this algebra are symplectic structures with Heisenberg algebras at their core. This algebra also enables us to define a Poisson algebra of all homogeneous quadratic polynomials on a two-dimensional sub-space, Fa of the Euclidean three-space. This enables us to construct a Poisson Clifford algebra, H(F), of a finite dimensional phase space which will carry the dynamics. The quantum dynamics appears as a realization of H(F) in terms of a Clifford algebra consisting of Hermitian operators.Comment: 17 page

A Method for Measuring the Weak Value of Spin for Metastable Atoms

A method for measuring the weak value of spin for atoms is proposed using a variant of the original Stern–Gerlach apparatus. A full simulation of an experiment for observing the real part of the weak value using the impulsive approximation has been carried out. Our predictions show a displacement of the beam of helium atoms in the metastable 2 3S1 state, ∆w, that is within the resolution of conventional microchannel plate detectors indicating that this type of experiment is feasible. Our analysis also determines the experimental parameters that will give an accurate determination of the weak value of spin. Preliminary experimental results are shown for helium, neon and argon in the 23S1 and 3P2 metastable states, respectivel

Size and area of square lattice polygons

We use the finite lattice method to calculate the radius of gyration, the first and second area-weighted moments of self-avoiding polygons on the square lattice. The series have been calculated for polygons up to perimeter 82. Analysis of the series yields high accuracy estimates confirming theoretical predictions for the value of the size exponent, $\nu=3/4$, and certain universal amplitude combinations. Furthermore, a detailed analysis of the asymptotic form of the series coefficients provide the firmest evidence to date for the existence of a correction-to-scaling exponent, $\Delta = 3/2$.Comment: 12 pages 3 figure

Symplectically Covariant Schr\"{o}dinger Equation in Phase Space

A classical theorem of Stone and von Neumann says that the Schr\"{o}dinger representation is, up to unitary equivalences, the only irreducible representation of the Heisenberg group on the Hilbert space of square-integrable functions on configuration space. Using the Wigner-Moyal transform we construct an irreducible representation of the Heisenberg group on a certain Hilbert space of square-integrable functions defined on phase space. This allows us to extend the usual Weyl calculus into a phase-space calculus and leads us to a quantum mechanics in phase space, equivalent to standard quantum mechanics. We also briefly discuss the extension of metaplectic operators to phase space and the probabilistic interpretation of the solutions of the phase space Schr\"{o}dinger equationComment: To appear in J Phys

Feasibility of a multicentre, randomised controlled trial of laparoscopic versus open colorectal surgery in the acute setting: the LaCeS feasibility trial protocol.

Introduction Acute colorectal surgery forms a significant proportion of emergency admissions within the National Health Service. There is limited evidence to suggest minimally invasive surgery may be associated with improved clinical outcomes in this cohort of patients. Consequently, there is a need to assess the clinical effectiveness and cost-effectiveness of laparoscopic surgery in the acute colorectal setting. However,emergency colorectal surgical trials have previously been difficult to conduct due to issues surrounding recruitment and equipoise. The LaCeS (randomised controlled trial of Laparoscopic versus open Colorectal Surgery in the acute setting) feasibility trial will determine the feasibility of conducting a definitive, phase III trial of laparoscopic versus open acute colorectal resection. Methods and analysis The LaCeS feasibility trial is a prospective, multicentre, single-blinded, parallel group, pragmatic randomised controlled feasibility trial. Patients will be randomised on a 1:1 basis to receive either laparoscopic or open surgery. The trial aims to recruit at least 66 patients from five acute general surgical units across the UK. Patients over the age of 18 with a diagnosis of acute colorectal pathology requiring resection on clinical and radiological/endoscopic investigations, with a National Confidential Enquiry into Patient Outcome and Death classification of urgent will be considered eligible for participation. The primary outcome is recruitment. Secondary outcomes include assessing the safety profile of laparoscopic surgery using intraoperative and postoperative complication rates, conversion rates and patient-safety indicators as surrogate markers. Clinical and patient-reported outcomes will also be reported. The trial will contain an embedded qualitative study to assess clinician and patient acceptability of trial processes. Ethics and dissemination The LaCeS feasibility trial is approved by the Yorkshire and The Humber, Bradford Leeds Research Ethics Committee (REC reference: 15/ YH/0542). The results from the trial will be presented at national and international colorectal conferences and will be submitted for publication to peer-reviewed journals. Trial registration number ISRCTN15681041; Pre-results

Imprints of the Quantum World in Classical Mechanics

The imprints left by quantum mechanics in classical (Hamiltonian) mechanics are much more numerous than is usually believed. We show Using no physical hypotheses) that the Schroedinger equation for a nonrelativistic system of spinless particles is a classical equation which is equivalent to Hamilton's equations.Comment: Paper submitted to Foundations of Physic

Perturbation and Variational Methods in Nonextensive Tsallis Statistics

A unified presentation of the perturbation and variational methods for the generalized statistical mechanics based on Tsallis entropy is given here. In the case of the variational method, the Bogoliubov inequality is generalized in a very natural way following the Feynman proof for the usual statistical mechanics. The inequality turns out to be form-invariant with respect to the entropic index $q$. The method is illustrated with a simple example in classical mechanics. The formalisms developed here are expected to be useful in the discussion of nonextensive systems.Comment: revte

Changes in the Management of Patients having Radical Radiotherapy for Lung Cancer during the First Wave of the COVID-19 Pandemic in the UK.

AIMS: In response to the COVID-19 pandemic, guidelines on reduced fractionation for patients treated with curative-intent radiotherapy were published, aimed at reducing the number of hospital attendances and potential exposure of vulnerable patients to minimise the risk of COVID-19 infection. We describe the changes that took place in the management of patients with stage I-III lung cancer from April to October 2020. MATERIALS AND METHODS: Lung Radiotherapy during the COVID-19 Pandemic (COVID-RT Lung) is a prospective multicentre UK cohort study. The inclusion criteria were: patients with stage I-III lung cancer referred for and/or treated with radical radiotherapy between 2nd April and 2nd October 2020. Patients who had had a change in their management and those who continued with standard management were included. Data on demographics, COVID-19 diagnosis, diagnostic work-up, radiotherapy and systemic treatment were collected and reported as counts and percentages. Patient characteristics associated with a change in treatment were analysed using multivariable binary logistic regression. RESULTS: In total, 1553 patients were included (median age 72 years, 49% female); 93 (12%) had a change to their diagnostic investigation and 528 (34%) had a change to their treatment from their centre's standard of care as a result of the COVID-19 pandemic. Age ≥70 years, male gender and stage III disease were associated with a change in treatment on multivariable analysis. Patients who had their treatment changed had a median of 15 fractions of radiotherapy compared with a median of 20 fractions in those who did not have their treatment changed. Low rates of COVID-19 infection were seen during or after radiotherapy, with only 21 patients (1.4%) developing the disease. CONCLUSIONS: The COVID-19 pandemic resulted in changes to patient treatment in line with national recommendations. The main change was an increase in hypofractionation. Further work is ongoing to analyse the impact of these changes on patient outcomes