On the large N limit, W_\infty Strings, Star products, AdS/CFT Duality, Nonlinear Sigma Models on AdS spaces and Chern-Simons p-branes

It is shown that the large $N$ limit of SU(N) YM in $curved$ $m$-dim backgrounds can be subsumed by a higher $m+n$ dimensional gravitational theory which can be identified to an $m$-dim generally invariant gauge theory of diffs $N$, where $N$ is an $n$-dim internal space (Cho, Sho, Park, Yoon). Based on these findings, a very plausible geometrical interpretation of the $AdS/CFT$ correspondence could be given. Conformally invariant sigma models in $D=2n$ dimensions with target non-compact SO(2n,1) groups are reviewed. Despite the non-compact nature of the SO(2n,1), the classical action and Hamiltonian are positive definite. Instanton field configurations are found to correspond geometrically to conformal ``stereographic'' mappings of $R^{2n}$ into the Euclidean signature $AdS_{2n}$ spaces. The relation between Self Dual branes and Chern-Simons branes, High Dimensional Knots, follows. A detailed discussion on $W_\infty$ symmetry is given and we outline the Vasiliev procedure to construct an action involving higher spin massless fields in $AdS_4$. This $AdS_4$ spacetime higher spin theory should have a one-to-one correspondence to noncritical $W_\infty$ strings propagating on $AdS_4 \times S^7$.Comment: 43 pages, Tex fil

Dirac Fermion Confinement in Graphene

We study the problem of Dirac fermion confinement in graphene in the presence of a perpendicular magnetic field B. We show, analytically and numerically, that confinement leads to anomalies in the electronic spectrum and to a magnetic field dependent crossover from \sqrt{B}, characteristic of Dirac-Landau level behavior, to linear in B behavior, characteristic of confinement. This crossover occurs when the radius of the Landau level becomes of the order of the width of the system. As a result, we show that the Shubnikov-de Haas oscillations also change as a function of field, and lead to a singular Landau plot. We show that our theory is in excellent agreement with the experimental data.Comment: 4 pages, 6 figure

A qualitative exploration of care homes workers' views and training needs in relation to the use of socially assistive humanoid robots in their workplace

Aim: The study aimed to explore the views and attitudes of care home workers about the socially assistive robot that was trialled in their workplace, in order to identify training needs in relation to the hypothetical future use of these robots in their workplace. Background: Care home workers face challenging workload conditions which may require the exploration of new solutions such as the use of socially assistive robots (SARs). Methods: This is a qualitative descriptive study which used semi-structured interviews. Care home workers (n = 23) in the UK participated in the study, and data collection took place between October 2019 and January 2020. NVivo software was used for data management, and a thematic inductive analysis was conducted. Results: Findings indicated that many participants were open to the use of robots and valued the potential usefulness of SARs in the care setting. However, some participants showed resistance to the use of robots and did not feel comfortable with the idea of working alongside them. Participants wished to receive technical training that would enable them to be competent in using SARs. Participants took seriously their duty of care to the older people and thus wanted to ensure that the use of the SAR would not negatively impact on the care being provided. Robots were viewed as having potential to be supplementary to human carers, such as sharing the workload and improving upon the care already being provided. Conclusions: Care home workers express both positive and negative views in relation to the hypothetical future deployment of socially assistive humanoid robots in their workplace. Implications for practice: The findings highlighted the importance of values around person-centred care which should be taken into account when planning for the implementation of robots in social care settings and training care home workers in how to work with robots

Topological Defects and the Spin Glass Phase of Cuprates

We propose that the spin glass phase of cuprates is due to the proliferation of topological defects of a spiral distortion of the antiferromagnet order. Our theory explains straightforwardly the simultaneous existence of short range incommensurate magnetic correlations and complete a-b symmetry breaking in this phase. We show via a renormalization group calculation that the collinear O(3)/O(2) symmetry is unstable towards the formation of local non-collinear correlations. A critical disorder strength is identified beyond which topological defects proliferate already at zero temperature.Comment: 7 pages, 2 figures. Final version with some changes and one replaced figur

Applications of quantum integrable systems

We present two applications of quantum integrable systems. First, we predict that it is possible to generate high harmonics from solid state devices by demostrating that the emission spectrum for a minimally coupled laser field of frequency $\omega$ to an impurity system of a quantum wire, contains multiples of the incoming frequency. Second, evaluating expressions for the conductance in the high temperature regime we show that the caracteristic filling fractions of the Jain sequence, which occur in the fractional quantum Hall effect, can be obtained from quantum wires which are described by minimal affine Toda field theories.Comment: 25 pages of LaTex, 4 figures, based on talk at the 6-th international workshop on conformal field theories and integrable models, (Chernogolovka, September 2002

New convolutions weighted by Hermite functions and their applications

We introduce eight new convolutions weighted by multi-dimensional Hermite functions, prove two Young-type inequalities, and exhibit their applications in different subjects. One application consists in the study of the solvability of a very general class of integral equations whose kernel depends on four different functions. Necessary and sufficient conditions for the unique solvability of such integral equations are here obtained.publishe

On integral operators and equations generated by cosine and sine Fourier transforms

In this paper, we study some properties of a class of integral operators that depends on the cosine and sine Fourier transforms. In particular, we will exhibit properties related with their invertibility, the spectrum, Parseval type identities and involutions. Moreover, a new convolution will be proposed and consequent integral equations will be also studied in detail. Namely, we will characterize the solvability of two integral equations which are associated with the integral operator under study. Moreover, under appropriate conditions, the unique solutions of those two equations are also obtained in a constructive way.publishe

Edge States of Monolayer and Bilayer Graphene Nanoribbons

On the basis of tight-binding lattice model, the edge states of monolayer and bilayer graphene nanoribbons (GNRs) with different edge terminations are studied. The effects of edge-hopping modulation, spin-orbital coupling (SOC), and bias voltage on bilayer GNRs are discussed. We observe the following: (i) Some new extra edge states can be created by edge-hopping modulation for monolayer GNRs. (ii) Intralayer Rashba SOC plays a role in depressing the band energy gap $E_g$ opened by intrinsic SOC for both monolayer and bilayer GNRs. An almost linear dependent relation, i.e., $E_g\sim \lambda_R$, is found. (iii) Although the bias voltage favors a bulk energy gap for bilayer graphene without intrinsic SOC, it tends to reduce the gap induced by intrinsic SOC. (iv) The topological phase of the quantum spin Hall effect can be destroyed completely by interlayer Rashba SOC for bilayer GNRs.Comment: 6 pages, 6 figure

SAMBA: Stochastic Analytical Model with a Bayesian Approach

We develop and estimate a DSGE model for the Brazilian economy, to be used as part of the macroeconomic modeling framework at the Central Bank of Brazil. The model combines the building blocks of standard DSGE models (e.g., price and wage rigidities and adjustment costs) with the following features that better describe the Brazilian economy: (i) a fiscal authority pursuing an explicit target for the primary surplus; (ii) administered or regulated prices as part of consumer prices; (iii) external finance for imports, amplifying the effects of changes in external financial conditions on the economy; and (iv) imported goods used in the production function of differentiated goods. It also includes the presence of financially constrained households. We estimate the model with Bayesian techniques, using data starting in 1999, when inflation targeting was implemented. Model evaluation, based on impulse response functions, moment conditions, variance error decomposition and initial forecasting exercises, suggests that the model can be a useful tool for policy analysis and forecasting.

Infrared properties of Mg1−x_{1-x}Alx(_x(B1−y_{1-y}Cy_{y})2_2 single crystals in the normal and superconducting state

The reflectivity $R (\omega)$ of $ab$-oriented Mg$_{1-x}$Al$_x$(B$_{1-y }$C$_y$)$_2$ single crystals has been measured by means of infrared microspectroscopy for $1300<\omega<17000$ cm$^{-1}$. An increase with doping of the scattering rates in the $\pi$ and $\sigma$ bands is observed, being more pronounced in the C doped crystals. The $\sigma$-band plasma frequency also changes with doping due to the electron doping, while the $\pi$-band one is almost unchanged. Moreover, a $\sigma\to\sigma$ interband excitation, predicted by theory, is observed at $\omega_{IB} \simeq 0.47$ eV in the undoped sample, and shifts to lower energies with doping. By performing theoretical calculation of the doping dependence $\omega_{IB}$, the experimental observations can be explained with the increase with electron doping of the Fermi energy of the holes in the $\sigma$-band. On the other hand, the $\sigma$ band density of states seems not to change substantially. This points towards a $T_c$ reduction driven mainly by disorder, at least for the doping level studied here. The superconducting state has been also probed by infrared synchrotron radiation for $30<\omega<150$ cm$^{-1}$ in one pure and one C-doped sample. In the undoped sample ($T_c$ = 38.5 K) a signature of the $\pi$-gap only is observed. At $y$ = 0.08 ($T_c$ = 31.9 K), the presence of the contribution of the $\sigma$-gap indicates dirty-limit superconductivity in both bands.Comment: 12 pages, 9 figure