Spin Chains as Perfect Quantum State Mirrors

Quantum information transfer is an important part of quantum information processing. Several proposals for quantum information transfer along linear arrays of nearest-neighbor coupled qubits or spins were made recently. Perfect transfer was shown to exist in two models with specifically designed strongly inhomogeneous couplings. We show that perfect transfer occurs in an entire class of chains, including systems whose nearest-neighbor couplings vary only weakly along the chain. The key to these observations is the Jordan-Wigner mapping of spins to noninteracting lattice fermions which display perfectly periodic dynamics if the single-particle energy spectrum is appropriate. After a half-period of that dynamics any state is transformed into its mirror image with respect to the center of the chain. The absence of fermion interactions preserves these features at arbitrary temperature and allows for the transfer of nontrivially entangled states of several spins or qubits.Comment: Abstract extended, introduction shortened, some clarifications in the text, one new reference. Accepted by Phys. Rev. A (Rapid Communications

Breakup reaction models for two- and three-cluster projectiles

Breakup reactions are one of the main tools for the study of exotic nuclei, and in particular of their continuum. In order to get valuable information from measurements, a precise reaction model coupled to a fair description of the projectile is needed. We assume that the projectile initially possesses a cluster structure, which is revealed by the dissociation process. This structure is described by a few-body Hamiltonian involving effective forces between the clusters. Within this assumption, we review various reaction models. In semiclassical models, the projectile-target relative motion is described by a classical trajectory and the reaction properties are deduced by solving a time-dependent Schroedinger equation. We then describe the principle and variants of the eikonal approximation: the dynamical eikonal approximation, the standard eikonal approximation, and a corrected version avoiding Coulomb divergence. Finally, we present the continuum-discretized coupled-channel method (CDCC), in which the Schroedinger equation is solved with the projectile continuum approximated by square-integrable states. These models are first illustrated by applications to two-cluster projectiles for studies of nuclei far from stability and of reactions useful in astrophysics. Recent extensions to three-cluster projectiles, like two-neutron halo nuclei, are then presented and discussed. We end this review with some views of the future in breakup-reaction theory.Comment: Will constitute a chapter of "Clusters in Nuclei - Vol.2." to be published as a volume of "Lecture Notes in Physics" (Springer

Global persistence exponent of the two-dimensional Blume-Capel model

The global persistence exponent $\theta_g$ is calculated for the two-dimensional Blume-Capel model following a quench to the critical point from both disordered states and such with small initial magnetizations. Estimates are obtained for the nonequilibrium critical dynamics on the critical line and at the tricritical point. Ising-like universality is observed along the critical line and a different value $\theta_g =1.080(4)$ is found at the tricritical point.Comment: 7 pages with 3 figure

Random-cluster representation of the Blume-Capel model

The so-called diluted-random-cluster model may be viewed as a random-cluster representation of the Blume--Capel model. It has three parameters, a vertex parameter $a$, an edge parameter $p$, and a cluster weighting factor $q$. Stochastic comparisons of measures are developed for the `vertex marginal' when $q\in[1,2]$, and the `edge marginal' when q\in[1,\oo). Taken in conjunction with arguments used earlier for the random-cluster model, these permit a rigorous study of part of the phase diagram of the Blume--Capel model

Low temperature relaxational dynamics of the Ising chain in a transverse field

We present asymptotically exact results for the real time order parameter correlations of a class of d=1 Ising models in a transverse field at low temperatures (T) on both sides of the quantum critical point. The correlations are a product of a T-independent factor determined by quantum effects, and a T-dependent relaxation function which comes from a classical theory. We confirm our predictions by a no-free-parameter comparison with numerical studies on the nearest neighbor spin-1/2 model.Comment: Final version to be published in Physical Review Letters. The postscript file is also available by anonymous ftp at ftp://chopin.ucsc.edu/pub/dynamics.ps.g

Universality and scaling study of the critical behavior of the two-dimensional Blume-Capel model in short-time dynamics

In this paper we study the short-time behavior of the Blume-Capel model at the tricritical point as well as along the second order critical line. Dynamic and static exponents are estimated by exploring scaling relations for the magnetization and its moments at early stage of the dynamic evolution. Our estimates for the dynamic exponents, at the tricritical point, are $z= 2.215(2)$ and $\theta= -0.53(2)$.Comment: 12 pages, 9 figure

Impurity spin relaxation in S=1/2 XX chains

Dynamic autocorrelations $$ (\alpha=x,z) of an isolated impurity spin in a S=1/2 XX chain are calculated. The impurity spin, defined by a local change in the nearest-neighbor coupling, is either in the bulk or at the boundary of the open-ended chain. The exact numerical calculation of the correlations employs the Jordan-Wigner mapping from spin operators to Fermi operators; effects of finite system size can be eliminated. Two distinct temperature regimes are observed in the long-time asymptotic behavior. At T=0 only power laws are present. At high T the x correlation decays exponentially (except at short times) while the z correlation still shows an asymptotic power law (different from the one at T=0) after an intermediate exponential phase. The boundary impurity correlations follow power laws at all T. The power laws for the z correlation and the boundary correlations can be deduced from the impurity-induced changes in the properties of the Jordan-Wigner fermion states.Comment: Final version to be published in Phys. Rev. B. Three references added, extended discussion of relation to previous wor

Extended gaussian ensemble solution and tricritical points of a system with long-range interactions

The gaussian ensemble and its extended version theoretically play the important role of interpolating ensembles between the microcanonical and the canonical ensembles. Here, the thermodynamic properties yielded by the extended gaussian ensemble (EGE) for the Blume-Capel (BC) model with infinite-range interactions are analyzed. This model presents different predictions for the first-order phase transition line according to the microcanonical and canonical ensembles. From the EGE approach, we explicitly work out the analytical microcanonical solution. Moreover, the general EGE solution allows one to illustrate in details how the stable microcanonical states are continuously recovered as the gaussian parameter $\gamma$ is increased. We found out that it is not necessary to take the theoretically expected limit $\gamma \to \infty$ to recover the microcanonical states in the region between the canonical and microcanonical tricritical points of the phase diagram. By analyzing the entropy as a function of the magnetization we realize the existence of unaccessible magnetic states as the energy is lowered, leading to a treaking of ergodicity.Comment: 8 pages, 5 eps figures. Title modified, sections rewritten, tricritical point calculations added. To appear in EPJ

Primary physical education, coaches and continuing professional development

This is an Author's Accepted Manuscript of an article published in Sport, Education and Society, 16(4), 485 - 505, 2011, copyright @ Taylor & Francis, available online at: http://www.tandfonline.com/10.1080/13573322.2011.589645.Physical education (PE) in primary schools has traditionally been taught by qualified primary teachers. More recently, some teaching of PE in primary schools has been undertaken by coaches (mostly football coaches). These coaches hold national governing body awards but do not hold teaching qualifications. Thus, coaches may not be adequately prepared to teach PE in curriculum time. The purpose of this study was to evaluate the perceptions of a group of community-based football coaches working in primary schools for the impact of a Continuing Professional Development (CPD) programme on their ability to undertake ‘specified work’ to cover PE in primary schools. The programme focused on four areas identified as important to enable coaches to cover specified work: short- and medium-term planning, pedagogy, knowledge of the curriculum and reflection. Results showed that for the majority of coaches the CPD programme had made them more aware of the importance of these four areas and had helped to develop their knowledge and ability to put this into practice in covering planning, preparation and assessment time. However, further input is still required to develop coaches’ knowledge and understanding in all four areas, but especially their curriculum knowledge, as well as their ability to put these into practice consistently. These findings are discussed in relation to the implications of employing coaches to cover the teaching of PE in primary schools and, if employed, what CPD coaches need to develop the necessary knowledge, skill and understanding for covering specified work in schools

Geometric invariant theory approach to the determination of ground states of D-wave condensates in isotropic space

A complete and rigorous determination of the possible ground states for D-wave pairing Bose condensates is presented, using a geometrical invariant theory approach to the problem. The order parameter is argued to be a vector, transforming according to a ten dimensional real representation of the group $G=${\bf O}$_3\otimes${\bf U}$_1\times$. We determine the equalities and inequalities defining the orbit space of this linear group and its symmetry strata, which are in a one-to-one correspondence with the possible distinct phases of the system. We find 15 allowed phases (besides the unbroken one), with different symmetries, that we thoroughly determine. The group-subgroup relations between bordering phases are pointed out. The perturbative sixth degree corrections to the minimum of a fourth degree polynomial $G$-invariant free energy, calculated by Mermin, are also determined.Comment: 27 revtex pages, 2 figures, use of texdraw; minor changes in the bibliography and in Table II