Abstract:
This paper explores several aspects of the adiabatic quantum computation model. We first show a way that directly maps any arbitrary circuit in the standard quantum computing model to an adiabatic algorithm of the same depth. Specifically, we look for a smooth time-dependent Hamiltonian whose unique ground state slowly changes from the initial state of the circuit to its final state. Since this construction requires in general an n-local Hamiltonian, we will study whether approximation is possible using previous results on ground state entanglement and perturbation theory. Finally we will point out how the adiabatic model can be relaxed in various ways to allow for 2-local partially adiabatic algorithms as well as 2-local holonomic quantum algorithms.

Abstract:
We introduce the idea of using adiabatic rotation to generate superpositions of a large class of quantum states. For quantum computing this is an interesting alternative to the well-studied "straight line" adiabatic evolution. In ways that complement recent results, we show how to efficiently prepare three types of states: Kitaev's toric code state, the cluster state of the measurement-based computation model and the history state used in the adiabatic simulation of quantum circuit. We also show that the method, when adapted for quantum search, provides quadratic speedup as other optimal methods do with the advantages that the problem Hamiltonian is time-independent and that the energy gap above the ground state is strictly nondecreasing with time. Likewise the method can be used for optimization as an alternative to the usual adiabatic algorithm.

Abstract:
We propose a bootstrap method for approximating the long-range terms in the Contractor Renormalization (CORE) method. The idea is tested on the 2-D Heisenberg antiferromagnet and the frustrated J_2-J_1 model. We obtain renormalization group flows that directly reveal the Neel phase of the unfrustrated HAF and the existence of a phase transition in the J_2-J_1 model for weak frustration. However, we find that this bootstrap method is dependent on blocking and truncation schemes. For this reason, we discuss these dependencies and unresolved issues that researchers who use this approach must consider.

Abstract:
A low mass Standard Model Higgs boson should be visible at the Large Hadron Collider through its production via gluon-gluon fusion and its decay to two photons. We compute the interference of this resonant process, gg -> H -> gamma gamma, with the continuum QCD background, gg -> gamma gamma induced by quark loops. Helicity selection rules suppress the effect, which is dominantly due to the imaginary part of the two-loop gg -> gamma gamma scattering amplitude. The interference is destructive, but only of order 5% in the Standard Model, which is still below the 10-20% present accuracy of the total cross section prediction. We comment on the potential size of such effects in other Higgs models.

Abstract:
Contractor Renormalization (CORE) is a numerical renormalization method for Hamiltonian systems that has found applications in particle and condensed matter physics. There have been few studies, however, on further understanding of what exactly it does and its convergence properties. The current work has two main objectives. First, we wish to investigate the convergence of the cluster expansion for a two-dimensional Heisenberg Antiferromagnet(HAF). This is important because the linked cluster expansion used to evaluate this formula non-perturbatively is not controlled by a small parameter. Here we present a study of three different blocking schemes which reveals some surprises and in particular, leads us to suggest a scheme for defining successive terms in the cluster expansion. Our second goal is to present some new perspectives on CORE in light of recent developments to make it accessible to more researchers, including those in Quantum Information Science. We make some comparison to entanglement-based approaches and discuss how it may be possible to improve or generalize the method.

Abstract:
When a substance that shrinks in volume as it solidifies (for example, lead) is melted in a container and then cooled, a deep hole is often found in the center after resolidification. We use a simple model to describe the shape of the pipe and compare it with experimental results.

Abstract:
The views of patients (with a variety of LTCs) on family doctors in Hong Kong were explored. Two groups of participants were interviewed; a) those who considered themselves as having a family doctor, b) those who considered themselves as not having a family doctor (either with a regular primary care doctor but not a family doctor or with no regular primary care doctor). In-depth individual semi-structured interviews were carried out with 28 participants (10 with a family doctor, 10 with a regular doctor, and 8 with no regular doctor) and analysed using the constant comparative method.Participants who did not have a family doctor were familiar with the concept but regarded it as a 'luxury item' for the rich within the private healthcare system. Those with a regular family doctor (all private) regarded having one as important to their and their family's health. Participants in both groups felt that as well as the more usual family medicine specialist or general practitioner, traditional Chinese medicine practitioners also had the potential to be family doctors. However most participants attended the public healthcare system for management of their LTCs whether they had a family doctor or not. Cost, perceived need, quality, trust, and choice were all barriers to the use of family doctors for the management of their LTCs.Important barriers to the adoption of a 'family doctor' model of management of LTCs exist in Hong Kong. Effective policy implementation seems unlikely unless these complex barriers are addressed.Effective primary health care is regarded as essential for a high quality, equitable, and cost-effective health care system [1] and a variety of models of primary care are in place around the world [2]. The rising incidence of long-term conditions globally, linked to the changing demographic profiles (with more people living to a greater age) is an important driver for the development of more effective primary care services [3].In Hong Kong, like many other Asia

Abstract:
We compare three attempts that have been made to decompose the angular momentum of the electromagnetic field into components of an “orbital” and “spin” nature. All three expressions are different, and there seems to be no reason to prefer one to another. It appears, on the basis of classical electrodynamics, that there is no unique way of decomposing the angular momentum of the electromagnetic field into orbital and spin components, even in a fixed inertial frame. 1. Introduction The total angular momentum of the electromagnetic field is given (in SI units) [1] by Henceforth, we will suppress the time coordinate of the fields, all of which depend on time, and also the factor. There has been debate for a long time over whether the total angular moment of the electromagnetic field can be decomposed into an orbital part and a spin part so that Some authors [2] argue that on the basis of the first principles it is not possible to do this; others [3–5] show that forms can be demonstrated that appear to be, at least algebraically, of a spin and orbital nature. By means of partial integration Ohanian [4] effected a decomposition with , where is the vector potential and is the gradient operator that operates on functions of . Ohanian assumed that the electric charge density was zero and deemed (3) and (4) to be the spin and orbital components, respectively, of the electromagnetic field on the basis that the integrand of (3) was not explicitly linear in the coordinate whereas the integrand of (4) was. When the charge density is not zero, a bound term , considered also to be of an orbital nature is obtained on whose form all writers agree [6]. Although the sum of (3) and (4) and (5) is gauge invariant, the individual terms are not and so have no physical interpretation until the gauge of the vector potential is fixed completely. Cohen-Tannoudji et al. [3] used the Coulomb (or transverse) gauge, defined by the gauge condition , which gives The bound component remains the same as (8). It will be shown in Section 2 that the terms that involve the scalar potential in (6) and (7) cancel so that in (6), (7), and (8) and in (9), (10), and (8) but in (6) differs from in (9) and in (7) differs from in (10). The forms of (9) and (10) have also been used by van Enk and Nienhuis [5]. The general explicit form for , given in (13), was not specified by these writers. On the other hand, Stewart [7] found a decomposition from decomposing the electric field by the Helmholtz theorem [8]: This decomposition uses the and fields throughout so no issues of gauge arbitrariness arise.

Abstract:
exact expressions for the wavelengths where maxima occur in the spectral distribution curves of blackbody radiation for a number of diferent dispersion rules are given in terms of the lambert w function. these dispersion rule dependent "wien peaks" are compared to those wavelengths obtained in a setting independent of the dispersion rule chosen where the "peak" wavelengths are taken to be those obtained on dividing the total radiation intensity emitted from a blackbody into a given percentile. the account provides a simple yet accessible example of the growing applicability of the lambert w function in physics.

Abstract:
the ready availability of very strong permanent magnets in the form of rare-earth magnetic alloys such as neodymium-iron-boron has lead to renewed interest in one of the oldest types of electric motors - the homopolar motor. the ease with which a demonstration homopolar motor can now be built and operated when neodymium magnets are used is quite remarkable. in this paper some simple homopolar motors employing neodymium magnets suitable for demonstrational purposes are described and discussed.