Stochastic evolutions in superspace and superconformal field theory

Some stochastic evolutions of conformal maps can be described by SLE and may be linked to conformal field theory via stochastic differential equations and singular vectors in highest-weight modules of the Virasoro algebra. Here we discuss how this may be extended to superconformal maps of N=1 superspace with links to superconformal field theory and singular vectors of the N=1 superconformal algebra in the Neveu-Schwarz sector.Comment: 13 pages, LaTe

Combined hamartoma of the retina and retinal pigment epithelium associated with optic coloboma

The authors relate an uncommon case of combined hamartoma of the retina and retinal pigment epithelium associated with optic coloboma

Note on SLE and logarithmic CFT

It is discussed how stochastic evolutions may be linked to logarithmic conformal field theory. This introduces an extension of the stochastic Loewner evolutions. Based on the existence of a logarithmic null vector in an indecomposable highest-weight module of the Virasoro algebra, the representation theory of the logarithmic conformal field theory is related to entities conserved in mean under the stochastic process.Comment: 10 pages, LaTeX, v2: version to be publishe

Bulk and surface magnetoinductive breathers in binary metamaterials

We study theoretically the existence of bulk and surface discrete breathers in a one-dimensional magnetic metamaterial comprised of a periodic binary array of split-ring resonators. The two types of resonators differ in the size of their slits and this leads to different resonant frequencies. In the framework of the rotating-wave approximation (RWA) we construct several types of breather excitations for both the energy-conserved and the dissipative-driven systems by continuation of trivial breather solutions from the anticontinuous limit to finite couplings. Numerically-exact computations that integrate the full model equations confirm the quality of the RWA results. Moreover, it is demonstrated that discrete breathers can spontaneously appear in the dissipative-driven system as a results of a fundamental instability.Comment: 10 pages, 16 figure

On the optical properties of carbon nanotubes--Part I. A general formula for the dynamical optical conductivity

This paper is the first one of a series of two articles in which we revisit the optical properties of single-walled carbon nanotubes (SWNT). Produced by rolling up a graphene sheet, SWNT owe their intriguing properties to their cylindrical quasi-one-dimensional (quasi-1D) structure (the ratio length/radius is experimentally of order of 10^3). We model SWNT by circular cylinders of small diameters on the surface of which the conduction electron gas is confined by the electric field generated by the fixed carbon ions. The pair-interaction potential considered is the 3D Coulomb potential restricted to the cylinder. To reflect the quasi-1D structure, we introduce a 1D effective many-body Hamiltonian which is the starting-point of our analysis. To investigate the optical properties, we consider a perturbation by a uniform time-dependent electric field modeling an incident light beam along the longitudinal direction. By using Kubo's method, we derive within the linear response theory an asymptotic expansion in the low-temperature regime for the dynamical optical conductivity at fixed density of particles. The leading term only involves the eigenvalues and associated eigenfunctions of the (unperturbed) 1D effective many-body Hamiltonian, and allows us to account for the sharp peaks observed in the optical absorption spectrum of SWNT.Comment: Comments: 24 pages. Revised version. Accepted for publication in J.M.

Architectural Engineering Approach to Developing a Matrix for Planning in Extreme Environments

Extreme environments on Earth share similar facilities and operations, design and planning challenges. Each environment presents special lessons regarding housing design, crew/staff operations and training, and equipment and logistical requirements for human activities. The paper discusses these challenges and lessons. Recurrent and specific to environment and conditions events are outlined and categorized based on case studies reviews and literature summary. Understanding of relationships and influences between different facets of human society and architecture can help to find a design approach which would optimize needs and requirements for various types of people living in different environments, societies and cultures. Environmental conditions affecting architectural requirements include form developing factors, site orientation and circulation, and budget considerations. They have to be addressed at the programming design stage in order to avoid costly adjustments at later development stages. It is even more critical in case of designing for challenging environments

Superconductor-Nanowire Devices from Tunneling to the Multichannel Regime: Zero-Bias Oscillations and Magnetoconductance Crossover

We present transport measurements in superconductor-nanowire devices with a gated constriction forming a quantum point contact. Zero-bias features in tunneling spectroscopy appear at finite magnetic fields, and oscillate in amplitude and split away from zero bias as a function of magnetic field and gate voltage. A crossover in magnetoconductance is observed: Magnetic fields above ~ 0.5 T enhance conductance in the low-conductance (tunneling) regime but suppress conductance in the high-conductance (multichannel) regime. We consider these results in the context of Majorana zero modes as well as alternatives, including Kondo effect and analogs of 0.7 structure in a disordered nanowire.Comment: Supplemental Material here: https://dl.dropbox.com/u/1742676/Churchill_Supplemental.pd

SLE-type growth processes and the Yang-Lee singularity

The recently introduced SLE growth processes are based on conformal maps from an open and simply-connected subset of the upper half-plane to the half-plane itself. We generalize this by considering a hierarchy of stochastic evolutions mapping open and simply-connected subsets of smaller and smaller fractions of the upper half-plane to these fractions themselves. The evolutions are all driven by one-dimensional Brownian motion. Ordinary SLE appears at grade one in the hierarchy. At grade two we find a direct correspondence to conformal field theory through the explicit construction of a level-four null vector in a highest-weight module of the Virasoro algebra. This conformal field theory has central charge c=-22/5 and is associated to the Yang-Lee singularity. Our construction may thus offer a novel description of this statistical model.Comment: 12 pages, LaTeX, v2: thorough revision with corrections, v3: version to be publishe