The D(D-3)-anyon chain: integrable boundary conditions and excitation spectra

Chains of interacting non-Abelian anyons with local interactions invariant under the action of the Drinfeld double of the dihedral group D-3 are constructed. Formulated as a spin chain the Hamiltonians are generated from commuting transfer matrices of an integrable vertex model for periodic and braided as well as open boundaries. A different anyonic model with the same local Hamiltonian is obtained within the fusion path formulation. This model is shown to be related to an integrable fusion interaction round the face model. Bulk and surface properties of the anyon chain are computed from the Bethe equations for the spin chain. The low-energy effective theories and operator content of the models (in both the spin chain and fusion path formulation) are identified from analytical and numerical studies of the finite-size spectra. For all boundary conditions considered the continuum theory is found to be a product of two conformal field theories. Depending on the coupling constants the factors can be a Z(4) parafermion or a M-(5,M-6) minimal model.

Bosonization and entanglement spectrum for one-dimensional polar bosons on disordered lattices

Ultra cold polar bosons in a disordered lattice potential, described by the extended Bose-Hubbard model, display a rich phase diagram. In the case of uniform random disorder one finds two insulating quantum phases-the Mott-insulator and the Haldane insulator-in addition to a superfluid and a Bose glass phase. In the case of a quasiperiodic potential, further phases are found, e.g. the incommensurate density wave, adiabatically connected to the Haldane insulator. For the case of weak random disorder we determine the phase boundaries using a perturbative bosonization approach. We then calculate the entanglement spectrum for both types of disorder, showing that it provides a good indication of the various phases.

Resonant five-body recombination in an ultracold gas of bosonic atoms

We combine theory and experiment to investigate five-body recombination in an ultracold gas of atomic cesium at negative scattering length. A refined theoretical model, in combination with extensive laboratory tunability of the interatomic interactions, enables the five-body resonant recombination rate to be calculated and measured. The position of the new observed recombination feature agrees with a recent theoretical prediction and supports the prediction of a family of universal cluster states at negative a that are tied to an Efimov trimer.

Truncation identities for the small polaron fusion hierarchy

We study a one-dimensional lattice model of interacting spinless fermions. This model is integrable for both periodic and open boundary conditions; the latter case includes the presence of Grassmann valued non-diagonal boundary fields breaking the bulk U(1) symmetry of the model. Starting from the embedding of this model into a graded Yang-Baxter algebra, an infinite hierarchy of commuting transfer matrices is constructed by means of a fusion procedure. For certain values of the coupling constant related to anisotropies of the underlying vertex model taken at roots of unity, this hierarchy is shown to truncate giving a finite set of functional equations for the spectrum of the transfer matrices. For generic coupling constants, the spectral problem is formulated in terms of a functional (or TQ-)equation which can be solved by Bethe ansatz methods for periodic and diagonal open boundary conditions. Possible approaches for the solution of the model with generic non-diagonal boundary fields are discussed.

Causal structure of the entanglement renormalization ansatz

We show that the multiscale entanglement renormalization ansatz (MERA) can be reformulated in terms of a causality constraint on discrete quantum dynamics. This causal structure is that of de Sitter space with a flat space-like boundary, where the volume of a spacetime region corresponds to the number of variational parameters it contains. This result clarifies the nature of the ansatz, and suggests a generalization to quantum field theory. It also constitutes an independent justification of the connection between MERA and hyperbolic geometry which was proposed as a concrete implementation of the AdS-CFT correspondence.

Equality of opportunity, cultural diversity and claims for fairness

The present paper examines some of the tensions, problems and challenges associated with claims for equality of opportunity (the fairness argument). The introductory part identifies three separate forms of justification for public education, including the argument associated with equality of opportunity. Part II examines in detail two questions that reveal part of the anatomy of equality of opportunity: (1) what an opportunity is, and (2) when individuals’ opportunities are equal. This is followed by a presentation of the two basic principles of equality of opportunity: (1) the principle of non-discrimination, and (2) the “levelling the playing field” principle. The next part takes up the multiculturalist hypothesis advanced by minority groups for the accommodation and recognition of cultural diversity. This is followed by the identification of a set of claims comprising the “fairness argument”. The last section focuses on the “currency problem” associated with cultural diversity as a form of “unfair disadvantage”. Part V examines two of the major shortcomings associated with the multicultural conception of equality of opportunity, while the concluding part discusses some of the questions that must be answered by any conception of equal opportunities. (DIPF/Orig.)

Asymptotic scattering and duality in the one-dimensional three-state quantum Potts model on a lattice

We determine numerically the single-particle and the two-particle spectrum of the three-state quantum Potts model on a lattice by using the density matrix renormalization group method, and extract information on the asymptotic (small momentum) S-matrix of the quasiparticles. The low energy part of the finite size spectrum can be understood in terms of a simple effective model introduced in a previous work, and is consistent with an asymptotic S-matrix of an exchange form below a momentum scale p*. This scale appears to vanish faster than the Compton scale, mc, as one approaches the critical point, suggesting that a dangerously irrelevant operator may be responsible for the behaviour observed on the lattice.

Coleman’s third report

The article analyses the (third) Coleman Report on private and public schools. The report scrutinises the relationship between private and public schools and shows that private school students show better academic achievement. Coleman concluded that these findings provided a strong argument in favour of public financial support for private schools. However, he identified a number of school characteristics that he believed to be related to student achievement. According to his analysis, these characteristics were not limited to private schools; public schools exhibiting the same characteristics also had good results. Coleman interpreted the available data in favour of financial aid to private schools, although this was not the only possible interpretation. An alternative conclusion would have been to encourage these characteristics in public schools. Why did Coleman disregard this possibility? Why did he deviate from his usual scientific rigour? The present article suggests that there appear to be two reasons for the narrow interpretation of the relationship between public and private schools in Coleman's third report. The first lies in Coleman's notion of contemporary society as a constructed system in which every individual actor holds a place in the structure and requires incentives in order to act to the benefit of society. In the case of education, the goal of the institution is to ensure the high cognitive achievement of students, and the incentive is related to choice and competition. The second reason is related to Coleman's vision of sociology as a discipline aiding the construction of an effective society. (DIPF/Orig.)

A representation-free description of the Kasevich-Chu interferometer: a resolution of the redshift controversy

Motivated by a recent claim by Muller et al (2010 Nature 463 926-9) that an atom interferometer can serve as an atom clock to measure the gravitational redshift with an unprecedented accuracy, we provide a representation-free description of the Kasevich-Chu interferometer based on operator algebra. We use this framework to show that the operator product determining the number of atoms at the exit ports of the interferometer is a c-number phase factor whose phase is the sum of only two phases: one is due to the acceleration of the phases of the laser pulses and the other one is due to the acceleration of the atom. This formulation brings out most clearly that this interferometer is an accelerometer or a gravimeter. Moreover, we point out that in different representations of quantum mechanics such as the position or the momentum representation the phase shift appears as though it originates from different physical phenomena. Due to this representation dependence conclusions concerning an enhanced accuracy derived in a specific representation are unfounded.

Tomographic readout of an opto-mechanical interferometer

The quantum state of light changes its nature when being reflected off a mechanical oscillator due to the latter's susceptibility to radiation pressure. As a result, a coherent state can transform into a squeezed state and can get entangled with the motion of the oscillator. Full information of the state of light can only be gathered by a tomographic measurement. Here we demonstrate a tomographic interferometer readout by measuring arbitrary quadratures of the light field exiting a Michelson-Sagnac interferometer that contains a thermally excited high-quality silicon nitride membrane. A readout noise of 1.9 x 10(-16) mHz(-1/2) around the membrane's fundamental oscillation mode at 133 kHz has been achieved, going below the peak value of the standard quantum limit by a factor of 8.2 (9 dB). The readout noise was entirely dominated by shot noise in a rather broad frequency range around the mechanical resonance.

The age of studies and reports: selected elements concerning the background of encounters defining the power of education

In the present paper, we discuss the time before the “age of reports”. Besides the Coleman Report in the period of Coleman, the Lady Plowden Report also appeared, while there were important studies in France (Bourdieu & Passeron, 1964; Peyre, 1959) and studies that inaugurated comprehensive education in Nordic countries. We focus on the period after the World War II, which was marked by rising economic nationalism, on the one hand, and by the second wave of mass education, on the other, bearing the promise of more equality and a reduction of several social inequalities, both supposed to be ensured by school. It was a period of great expectations related to the power of education and the rise of educational meritocracy. On this background, in the second part of the paper, the authors attempt to explore the phenomenon of the aforementioned reports, which significantly questioned the power of education and, at the same time, enabled the formation of evidence-based education policies. In this part of the paper, the central place is devoted to the case of socialist Yugoslavia/Slovenia and its striving for more equality and equity through education. Through the socialist ideology of more education for all, socialist Yugoslavia, with its exaggerated stress on the unified school and its overemphasised belief in simple equality, overstepped the line between relying on comprehensive education as an important mechanism for increasing the possibility of more equal and just education, on the one hand, and the myth of the almighty unified school capable of eradicating social inequalities, especially class inequalities, on the other. With this radical approach to the reduction of inequalities, socialist policy in the then Yugoslavia paradoxically reduced the opportunity for greater equality, and even more so for more equitable education. (DIPF/Orig.)

Exciton-mediated photothermal cooling in GaAs membranes

Cooling of the mechanical motion of a GaAs nano-membrane using the photothermal effect mediated by excitons was recently demonstrated by some of the authors (Usami et al 2012 Nature Phys. 8 168) and provides a clear example of the use of thermal forces to cool down mechanical motion. Here, we report on a single-free-parameter theoretical model to explain the results of this experiment which matches the experimental data remarkably well.

Social capital and educational achievements: Coleman vs. Bourdieu

The influence of social capital on an individual’s educational achievements is the subject of numerous scientific papers. Research on social capital is most frequently based on Coleman’s (1988) or Bourdieu’s (1986) theories of capital, which are related to different paradigms of social theory: whereas Coleman’s approach has its roots in structural functionalism, Bourdieu’s approach contains elements of conflict theory. A number of authors, starting with Bourdieu, attempt to explain and prove that, when connected with the education of individuals, the activity of social capital facilitates social reproduction. Other authors support the notion that social capital is, in fact, a powerful weapon that encourages social mobility. A third group of researchers emphasise that neither of these approaches in isolation can entirety explain the influences of social capital on an individual’s education (Ho, 2003). The present paper offers a review of research focusing on the influences of social capital on educational achievements, while outlining the fundamental differences between the two theoretical approaches that are most frequently used for research of this topic. The aim of the paper is to explain the influence of social capital on an individual’s educational achievements under Bourdieu’s and Coleman’s theoretical concepts, and to establish whether combining the approaches is possible. The conclusion and arguments show that it is legitimate to use all three theoretical approaches. (DIPF/Orig.)

A proposal for self-correcting stabilizer quantum memories in 3 dimensions (or slightly less)

We propose a family of local CSS stabilizer codes as possible candidates for self-correcting quantum memories in 3D. The construction is inspired by the classical Ising model on a Sierpinski carpet fractal, which acts as a classical self-correcting memory. Our models are naturally defined on fractal subsets of a 4D hypercubic lattice with Hausdorff dimension less than 3. Though this does not imply that these models can be realized with local interactions in R3, we also discuss this possibility. The X and Z sectors of the code are dual to one another, and we show that there exists a finite temperature phase transition associated with each of these sectors, providing evidence that the system may robustly store quantum information at finite temperature.

Disentangling the magnetic force noise contribution in LISA Pathfinder

Magnetically-induced forces on the inertial masses on-board LISA Path finder are expected to be one of the dominant contributions to the mission noise budget, accounting for up to 40%. The origin of this disturbance is the coupling of the residual magnetization and susceptibility of the test masses with the environmental magnetic field. In order to fully understand this important part of the noise model, a set of coils and magnetometers are integrated as a part of the diagnostics subsystem. During operations a sequence of magnetic excitations will be applied to precisely determine the coupling of the magnetic environment to the test mass displacement using the on-board magnetometers. Since no direct measurement of the magnetic field in the test mass position will be available, an extrapolation of the magnetic measurements to the test mass position will be carried out as a part of the data analysis activities. In this paper we show the first results on the magnetic experiments during an end-to-end LISA Path finder simulation, and we describe the methods under development to map the magnetic field on-board.