Spin 1 inversion: a Majorana tensor force for deuteron alpha scattering

We demonstrate, for the first time, successful S-matrix to potential inversion for spin one projectiles with non-diagonal $S^j_{ll'}$ yielding a $T_{\rm R}$ interaction. The method is a generalization of the iterative-perturbative, IP, method. We present a test case indicating the degree of uniqueness of the potential. The method is adapted, using established procedures, into direct observable to potential inversion, fitting $\sigma$, ${\rm i}T_{11}$, $T_{20}$, $T_{21}$ and $T_{22}$ for d + alpha scattering over a range of energies near 10 MeV. The $T_{\rm R}$ interaction which we find is very different from that proposed elsewhere, both real and imaginary parts being very different for odd and even parity channels.Comment: 7 pages Revtex, 4 ps figure

Hearing the grass grow. Emotional and epistemological challenges of practice-near research

This paper discusses the concept of practice-near research in terms of the emotional and epistemological challenges that arise from the researcher coming 'near' enough to other people for psychological processes to ensue. These may give rise in the researcher to confusion, anxiety and doubt about who is who and what is what; but also to the possibility of real emotional and relational depth in the research process. Using illustrations from three social work doctoral research projects undertaken by students at the Tavistock Clinic and the University of East London the paper examines four themes that seem to the author to be central to meaningful practice-near research undertaken in a spirit of true emotional and epistemological open-mindedness: the smell of the real; losing our minds; the inevitability of personal change; and the discovery of complex particulars

Stable Topological Superfluid Phase of Ultracold Polar Fermionic Molecules

We show that single-component fermionic polar molecules confined to a 2D geometry and dressed by a microwave field, may acquire an attractive $1/r^3$ dipole-dipole interaction leading to superfluid p-wave pairing at sufficiently low temperatures even in the BCS regime. The emerging state is the topological $p_x+ip_y$ phase promising for topologically protected quantum information processing. The main decay channel is via collisional transitions to dressed states with lower energies and is rather slow, setting a lifetime of the order of seconds at 2D densities $\sim 10^8$ cm$^{-2}$

Exact and approximate dynamics of the quantum mechanical O(N) model

We study a quantum dynamical system of N, O(N) symmetric, nonlinear oscillators as a toy model to investigate the systematics of a 1/N expansion. The closed time path (CTP) formalism melded with an expansion in 1/N is used to derive time evolution equations valid to order 1/N (next-to-leading order). The effective potential is also obtained to this order and its properties areelucidated. In order to compare theoretical predictions against numerical solutions of the time-dependent Schrodinger equation, we consider two initial conditions consistent with O(N) symmetry, one of them a quantum roll, the other a wave packet initially to one side of the potential minimum, whose center has all coordinates equal. For the case of the quantum roll we map out the domain of validity of the large-N expansion. We discuss unitarity violation in the 1/N expansion; a well-known problem faced by moment truncation techniques. The 1/N results, both static and dynamic, are also compared to those given by the Hartree variational ansatz at given values of N. We conclude that late-time behavior, where nonlinear effects are significant, is not well-described by either approximation.Comment: 16 pages, 12 figrures, revte

Product renovation and shared ownership: sustainable routes to satisfying the world's growing demand for goods

It has been estimated that by 2030 the number of people who are wealthy enough to be considered as middle class consumers will have tripled. This will have a dramatic impact on the demands for primary materials and energy. Much work has been carried out on sustainable ways of meeting the World’s energy demands and some work has been carried out on the sustainable production and consumption of goods. It has been estimated that with improvements in design and manufacturing it is possible to reduce the primary material requirements by 30% to produce the current demand for goods. Whilst this is a crucial step on the production side, there will still be a doubling of primary material requirements by the end of the century because of an absolute rise in demand for goods and services. It is therefore clear that the consumption of products must also be explored. This is a key areas of research for the UK INDEMAND centre, which is investigating ways of reducing the UK’s industrial energy demand and demand for energy intensive materials. Our ongoing work shows that two strategies would result in considerable reductions in the demand for primary materials: product longevity and using goods more intensively (which may requires increased durability). Product longevity and durability are not new ideas, but ones that can be applied across a raft of goods as methods of reducing the consumption of materials. With long life products there is a potential risk of outdated design and obsolescence, consequently there is a need to ensure upgradability and adaptability are incorporated at the design stage. If products last longer, then the production of new products can be diverted to emerging markets rather than the market for replacement goods. There are many goods which are only used occasionally; these goods do not normally wear out. The total demand for such could be drastically reduced if they were shared with other people. Sharing of goods has traditionally been conducted between friends or by hiring equipment. The use of modern communication systems and social media could enable the development of sharing co-ops and swap spaces that will increase the utilisation of goods and hence reduce the demand for new goods. This could also increase access to a range of goods for those on low incomes. From a series of workshops it has been found that the principal challenges are sociological rather than technological. This paper contains a discussion of these challenges and explores possible futures where these two strategies have been adopted. In addition, the barriers and opportunities that these strategies offer for consumers and businesses are identified, and areas where government policy could be instigated to bring about change are highlighted

Stability and dynamical properties of Rosenau-Hyman compactons using Pade approximants

We present a systematic approach for calculating higher-order derivatives of smooth functions on a uniform grid using Pad\'e approximants. We illustrate our findings by deriving higher-order approximations using traditional second-order finite-differences formulas as our starting point. We employ these schemes to study the stability and dynamical properties of K(2,2) Rosenau-Hyman (RH) compactons including the collision of two compactons and resultant shock formation. Our approach uses a differencing scheme involving only nearest and next-to-nearest neighbors on a uniform spatial grid. The partial differential equation for the compactons involves first, second and third partial derivatives in the spatial coordinate and we concentrate on four different fourth-order methods which differ in the possibility of increasing the degree of accuracy (or not) of one of the spatial derivatives to sixth order. A method designed to reduce roundoff errors was found to be the most accurate approximation in stability studies of single solitary waves, even though all derivates are accurate only to fourth order. Simulating compacton scattering requires the addition of fourth derivatives related to artificial viscosity. For those problems the different choices lead to different amounts of "spurious" radiation and we compare the virtues of the different choices.Comment: 12 figure

On the properties of compacton-anticompacton collisions

We study the properties of compacton-anticompacton collision processes. We compare and con- trast results for the case of compacton-anticompacton solutions of the K(l, p) Rosenau-Hyman (RH) equation for l = p = 2, with compacton-anticompacton solutions of the L(l,p) Cooper-Shepard- Sodano (CSS) equation for p = 1 and l = 3. This study is performed using a Pad\'e discretization of the RH and CSS equations. We find a significant difference in the behavior of compacton- anticompacton scattering. For the CSS equation, the scattering can be interpreted as "annihila- tion" as the wake left behind dissolves over time. In the RH equation, the numerical evidence is that multiple shocks form after the collision which eventually lead to "blowup" of the resulting waveform.Comment: 8 pages, 7 figure

Resumming the large-N approximation for time evolving quantum systems

In this paper we discuss two methods of resumming the leading and next to leading order in 1/N diagrams for the quartic O(N) model. These two approaches have the property that they preserve both boundedness and positivity for expectation values of operators in our numerical simulations. These approximations can be understood either in terms of a truncation to the infinitely coupled Schwinger-Dyson hierarchy of equations, or by choosing a particular two-particle irreducible vacuum energy graph in the effective action of the Cornwall-Jackiw-Tomboulis formalism. We confine our discussion to the case of quantum mechanics where the Lagrangian is $L(x,\dot{x}) = (1/2) \sum_{i=1}^{N} \dot{x}_i^2 - (g/8N) [ \sum_{i=1}^{N} x_i^2 - r_0^2 ]^{2}$. The key to these approximations is to treat both the $x$ propagator and the $x^2$ propagator on similar footing which leads to a theory whose graphs have the same topology as QED with the $x^2$ propagator playing the role of the photon. The bare vertex approximation is obtained by replacing the exact vertex function by the bare one in the exact Schwinger-Dyson equations for the one and two point functions. The second approximation, which we call the dynamic Debye screening approximation, makes the further approximation of replacing the exact $x^2$ propagator by its value at leading order in the 1/N expansion. These two approximations are compared with exact numerical simulations for the quantum roll problem. The bare vertex approximation captures the physics at large and modest $N$ better than the dynamic Debye screening approximation.Comment: 30 pages, 12 figures. The color version of a few figures are separately liste

Density waves and supersolidity in rapidly rotating atomic Fermi gases

We study theoretically the low-temperature phases of a two-component atomic Fermi gas with attractive s-wave interactions under conditions of rapid rotation. We find that, in the extreme quantum limit, when all particles occupy the lowest Landau level, the normal state is unstable to the formation of "charge" density wave (CDW) order. At lower rotation rates, when many Landau levels are occupied, we show that the low-temperature phases can be supersolids, involving both CDW and superconducting order.Comment: 4 pages, 1 figure, uses feynmp.st