Effective Magnetic Fields in Graphene Superlattices

We demonstrate that the electronic spectrum of graphene in a one-dimensional periodic potential will develop a Landau level spectrum when the potential magnitude varies slowly in space. The effect is related to extra Dirac points generated by the potential whose positions are sensitive to its magnitude. We develop an effective theory that exploits a chiral symmetry in the Dirac Hamiltonian description with a superlattice potential, to show that the low energy theory contains an effective magnetic field. Numerical diagonalization of the Dirac equation confirms the presence of Landau levels. Possible consequences for transport are discussed.Comment: 4 pages (+ 2 pages of supplementary material), 3 figure

Entanglement between two fermionic atoms inside a cylindrical harmonic trap

We investigate quantum entanglement between two (spin-1/2) fermions inside a cylindrical harmonic trap, making use of the von Neumann entropy for the reduced single particle density matrix as the pure state entanglement measure. We explore the dependence of pair entanglement on the geometry and strength of the trap and on the strength of the pairing interaction over the complete range of the effective BCS to BEC crossover. Our result elucidates an interesting connection between our model system of two fermions and that of two interacting bosons.Comment: to appear in PR

Distribution of extremes in the fluctuations of two-dimensional equilibrium interfaces

We investigate the statistics of the maximal fluctuation of two-dimensional Gaussian interfaces. Its relation to the entropic repulsion between rigid walls and a confined interface is used to derive the average maximal fluctuation $\sim \sqrt{2/(\pi K)} \ln N$ and the asymptotic behavior of the whole distribution $P(m) \sim N^2 e^{-{\rm (const)} N^2 e^{-\sqrt{2\pi K} m} - \sqrt{2\pi K} m}$ for $m$ finite with $N^2$ and $K$ the interface size and tension, respectively. The standardized form of $P(m)$ does not depend on $N$ or $K$, but shows a good agreement with Gumbel's first asymptote distribution with a particular non-integer parameter. The effects of the correlations among individual fluctuations on the extreme value statistics are discussed in our findings.Comment: 4 pages, 4 figures, final version in PR

Zero-field magnetization reversal of two-body Stoner particles with dipolar interaction

Nanomagnetism has recently attracted explosive attention, in particular, because of the enormous potential applications in information industry, e.g. new harddisk technology, race-track memory[1], and logic devices[2]. Recent technological advances[3] allow for the fabrication of single-domain magnetic nanoparticles (Stoner particles), whose magnetization dynamics have been extensively studied, both experimentally and theoretically, involving magnetic fields[4-9] and/or by spin-polarized currents[10-20]. From an industrial point of view, important issues include lowering the critical switching field $H_c$, and achieving short reversal times. Here we predict a new technological perspective: $H_c$ can be dramatically lowered (including $H_c=0$) by appropriately engineering the dipole-dipole interaction (DDI) in a system of two synchronized Stoner particles. Here, in a modified Stoner-Wohlfarth (SW) limit, both of the above goals can be achieved. The experimental feasibility of realizing our proposal is illustrated on the example of cobalt nanoparticles.Comment: 5 pages, 4 figure

Gather-Excite: Exploiting Feature Context in Convolutional Neural Networks

While the use of bottom-up local operators in convolutional neural networks (CNNs) matches well some of the statistics of natural images, it may also prevent such models from capturing contextual long-range feature interactions. In this work, we propose a simple, lightweight approach for better context exploitation in CNNs. We do so by introducing a pair of operators: gather, which efficiently aggregates feature responses from a large spatial extent, and excite, which redistributes the pooled information to local features. The operators are cheap, both in terms of number of added parameters and computational complexity, and can be integrated directly in existing architectures to improve their performance. Experiments on several datasets show that gather-excite can bring benefits comparable to increasing the depth of a CNN at a fraction of the cost. For example, we find ResNet-50 with gather-excite operators is able to outperform its 101-layer counterpart on ImageNet with no additional learnable parameters. We also propose a parametric gather-excite operator pair which yields further performance gains, relate it to the recently-introduced Squeeze-and-Excitation Networks, and analyse the effects of these changes to the CNN feature activation statistics.Comment: NeurIPS 201

Energy Gap Induced by Impurity Scattering: New Phase Transition in Anisotropic Superconductors

It is shown that layered superconductors are subjected to a phase transition at zero temperature provided the order parameter (OP) reverses its sign on the Fermi-surface but its angular average is finite. The transition is regulated by an elastic impurity scattering rate $1/\tau$. The excitation energy spectrum, being gapless at the low level of scattering, develops a gap as soon as the scattering rate exceeds some critical value of $1/\tau_\star$.Comment: Revtex, 11 page