Renormalization group approach to chiral symmetry breaking in graphene

We investigate the development of a gapped phase in the field theory of Dirac fermions in graphene with long-range Coulomb interaction. In the large-N approximation, we show that the chiral symmetry is only broken below a critical number of two-component Dirac fermions $N_c = 32/\pi^2$, that is exactly half the value found in quantum electrodynamics in 2+1 dimensions. Adopting otherwise a ladder approximation, we give evidence of the existence of a critical coupling at which the anomalous dimension of the order parameter of the transition diverges. This result is consistent with the observation that chiral symmetry breaking may be driven by the long-range Coulomb interaction in the Dirac field theory, despite the divergent scaling of the Fermi velocity in the low-energy limit.Comment: 6 pages, 4 figures, extended version with technical detail

Exploring Vortex Dynamics in the Presence of Dissipation: Analytical and Numerical Results

In this paper, we systematically examine the stability and dynamics of vortices under the effect of a phenomenological dissipation used as a simplified model for the inclusion of the effect of finite temperatures in atomic Bose-Einstein condensates. An advantage of this simplified model is that it enables an analytical prediction that can be compared directly (and favorably) to numerical results. We then extend considerations to a case of considerable recent experimental interest, namely that of a vortex dipole and observe good agreement between theory and numerical computations in both the stability properties (eigenvalues of the vortex dipole stationary states) and the dynamical evolution of such configurations.Comment: 12 pages, 5 figures, accepted by PR

Electron-induced rippling in graphene

We show that the interaction between flexural phonons, when corrected by the exchange of electron-hole excitations, may place the graphene sheet very close to a quantum critical point characterized by the strong suppression of the bending rigidity of the membrane. Ripples arise then due to spontaneous symmetry breaking, following a mechanism similar to that responsible for the condensation of the Higgs field in relativistic field theories. In the presence of membrane tensions, ripple condensation may be reinforced or suppressed depending on the sign of the tension, following a zero-temperature buckling transition in which the order parameter is given essentially by the square of the gradient of the flexural phonon field.Comment: 4 pages, 3 figure

Beyond A/B Testing: Sequential Randomization for Developing Interventions in Scaled Digital Learning Environments

Randomized experiments ensure robust causal inference that are critical to effective learning analytics research and practice. However, traditional randomized experiments, like A/B tests, are limiting in large scale digital learning environments. While traditional experiments can accurately compare two treatment options, they are less able to inform how to adapt interventions to continually meet learners' diverse needs. In this work, we introduce a trial design for developing adaptive interventions in scaled digital learning environments -- the sequential randomized trial (SRT). With the goal of improving learner experience and developing interventions that benefit all learners at all times, SRTs inform how to sequence, time, and personalize interventions. In this paper, we provide an overview of SRTs, and we illustrate the advantages they hold compared to traditional experiments. We describe a novel SRT run in a large scale data science MOOC. The trial results contextualize how learner engagement can be addressed through inclusive culturally targeted reminder emails. We also provide practical advice for researchers who aim to run their own SRTs to develop adaptive interventions in scaled digital learning environments

On the regularity of the covariance matrix of a discretized scalar field on the sphere

We present a comprehensive study of the regularity of the covariance matrix of a discretized field on the sphere. In a particular situation, the rank of the matrix depends on the number of pixels, the number of spherical harmonics, the symmetries of the pixelization scheme and the presence of a mask. Taking into account the above mentioned components, we provide analytical expressions that constrain the rank of the matrix. They are obtained by expanding the determinant of the covariance matrix as a sum of determinants of matrices made up of spherical harmonics. We investigate these constraints for five different pixelizations that have been used in the context of Cosmic Microwave Background (CMB) data analysis: Cube, Icosahedron, Igloo, GLESP and HEALPix, finding that, at least in the considered cases, the HEALPix pixelization tends to provide a covariance matrix with a rank closer to the maximum expected theoretical value than the other pixelizations. The effect of the propagation of numerical errors in the regularity of the covariance matrix is also studied for different computational precisions, as well as the effect of adding a certain level of noise in order to regularize the matrix. In addition, we investigate the application of the previous results to a particular example that requires the inversion of the covariance matrix: the estimation of the CMB temperature power spectrum through the Quadratic Maximum Likelihood algorithm. Finally, some general considerations in order to achieve a regular covariance matrix are also presented.Comment: 36 pages, 12 figures; minor changes in the text, matches published versio

Dynamics and Manipulation of Matter-Wave Solitons in Optical Superlattices

We analyze the existence and stability of bright, dark, and gap matter-wave solitons in optical superlattices. Then, using these properties, we show that (time-dependent) ``dynamical superlattices'' can be used to controllably place, guide, and manipulate these solitons. In particular, we use numerical experiments to displace solitons by turning on a secondary lattice structure, transfer solitons from one location to another by shifting one superlattice substructure relative to the other, and implement solitonic ``path-following'', in which a matter wave follows the time-dependent lattice substructure into oscillatory motion.Comment: 6 pages, revtex, 6 figures, to appear in Physics Letters A; minor modifications from last versio

Confinement of electrons in layered metals

We analyze the out of plane hopping in models of layered systems where the in--plane properties deviate from Landau's theory of a Fermi liquid. We show that the hopping term acquires a non trivial energy dependence, due to the coupling to in plane excitations, and can be either relevant or irrelevant at low energies or temperatures. The latter is always the case if the Fermi level lies close to a saddle point in the dispersion relation.Comment: 4 pages, 1 eps figur

Beating dark-dark solitons in Bose-Einstein condensates

Motivated by recent experimental results, we study beating dark-dark solitons as a prototypical coherent structure that emerges in two-component Bose-Einstein condensates. We showcase their connection to dark- bright solitons via SO(2) rotation, and infer from it both their intrinsic beating frequency and their frequency of oscillation inside a parabolic trap. We identify them as exact periodic orbits in the Manakov limit of equal inter- and intra-species nonlinearity strengths with and without the trap and showcase the persistence of such states upon weak deviations from this limit. We also consider large deviations from the Manakov limit illustrating that this breathing state may be broken apart into dark-antidark soliton states. Finally, we consider the dynamics and interactions of two beating dark-dark solitons in the absence and in the presence of the trap, inferring their typically repulsive interaction.Comment: 13 pages, 14 figure

Vortex Structures Formed by the Interference of Sliced Condensates

We study the formation of vortices, vortex necklaces and vortex ring structures as a result of the interference of higher-dimensional Bose-Einstein condensates (BECs). This study is motivated by earlier theoretical results pertaining to the formation of dark solitons by interfering quasi one-dimensional BECs, as well as recent experiments demonstrating the formation of vortices by interfering higher-dimensional BECs. Here, we demonstrate the genericity of the relevant scenario, but also highlight a number of additional possibilities emerging in higher-dimensional settings. A relevant example is, e.g., the formation of a "cage" of vortex rings surrounding the three-dimensional bulk of the condensed atoms. The effects of the relative phases of the different BEC fragments and the role of damping due to coupling with the thermal cloud are also discussed. Our predictions should be immediately tractable in currently existing experimental BEC setups.Comment: 8 pages, 6 figures (low res). To appear in Phys. Rev. A. Full resolution preprint available at: http://www-rohan.sdsu.edu/~rcarrete/publications