Free Energies of Isolated 5- and 7-fold Disclinations in Hexatic Membranes

We examine the shapes and energies of 5- and 7-fold disclinations in low-temperature hexatic membranes. These defects buckle at different values of the ratio of the bending rigidity, $\kappa$, to the hexatic stiffness constant, $K_A$, suggesting {\em two} distinct Kosterlitz-Thouless defect proliferation temperatures. Seven-fold disclinations are studied in detail numerically for arbitrary $\kappa/K_A$. We argue that thermal fluctuations always drive $\kappa/K_A$ into an ``unbuckled'' regime at long wavelengths, so that disclinations should, in fact, proliferate at the {\em same} critical temperature. We show analytically that both types of defects have power law shapes with continuously variable exponents in the ``unbuckled'' regime. Thermal fluctuations then lock in specific power laws at long wavelengths, which we calculate for 5- and 7-fold defects at low temperatures.Comment: LaTeX format. 17 pages. To appear in Phys. Rev.

Orientational order on curved surfaces - the high temperature region

We study orientational order, subject to thermal fluctuations, on a fixed curved surface. We derive, in particular, the average density of zeros of Gaussian distributed vector fields on a closed Riemannian manifold. Results are compared with the density of disclination charges obtained from a Coulomb gas model. Our model describes the disordered state of two dimensional objects with orientational degrees of freedom, such as vector ordering in Langmuir monolayers and lipid bilayers above the hexatic to fluid transition.Comment: final version, 13 Pages, 2 figures, uses iopart.cl

Allowed and forbidden transitions in artificial hydrogen and helium atoms

The strength of radiative transitions in atoms is governed by selection rules. Spectroscopic studies of allowed transitions in hydrogen and helium provided crucial evidence for the Bohr's model of an atom. Forbidden transitions, which are actually allowed by higher-order processes or other mechanisms, indicate how well the quantum numbers describe the system. We apply these tests to the quantum states in semiconductor quantum dots (QDs), which are regarded as artificial atoms. Electrons in a QD occupy quantized states in the same manner as electrons in real atoms. However, unlike real atoms, the confinement potential of the QD is anisotropic, and the electrons can easily couple with phonons of the material. Understanding the selection rules for such QDs is an important issue for the manipulation of quantum states. Here we investigate allowed and forbidden transitions for phonon emission in one- and two-electron QDs (artificial hydrogen and helium atoms) by electrical pump-and-probe experiments, and find that the total spin is an excellent quantum number in artificial atoms. This is attractive for potential applications to spin based information storage.Comment: slightly longer version of Nature 419, 278 (2002

The Geometrical Structure of 2d Bond-Orientational Order

We study the formulation of bond-orientational order in an arbitrary two dimensional geometry. We find that bond-orientational order is properly formulated within the framework of differential geometry with torsion. The torsion reflects the intrinsic frustration for two-dimensional crystals with arbitrary geometry. Within a Debye-Huckel approximation, torsion may be identified as the density of dislocations. Changes in the geometry of the system cause a reorganization of the torsion density that preserves bond-orientational order. As a byproduct, we are able to derive several identities involving the topology, defect density and geometric invariants such as Gaussian curvature. The formalism is used to derive the general free energy for a 2D sample of arbitrary geometry, both in the crystalline and hexatic phases. Applications to conical and spherical geometries are briefly addressed.Comment: 22 pages, LaTeX, 4 eps figures Published versio

The Democratic Biopolitics of PrEP

PrEP (Pre-Exposure Prophylaxis) is a relatively new drug-based HIV prevention technique and an important means to lower the HIV risk of gay men who are especially vulnerable to HIV. From the perspective of biopolitics, PrEP inscribes itself in a larger trend of medicalization and the rise of pharmapower. This article reconstructs and evaluates contemporary literature on biopolitical theory as it applies to PrEP, by bringing it in a dialogue with a mapping of the political debate on PrEP. As PrEP changes sexual norms and subjectification, for example condom use and its meaning for gay subjectivity, it is highly contested. The article shows that the debate on PrEP can be best described with the concepts ‘sexual-somatic ethics’ and ‘democratic biopolitics’, which I develop based on the biopolitical approach of Nikolas Rose and Paul Rabinow. In contrast, interpretations of PrEP which are following governmentality studies or Italian Theory amount to either farfetched or trivial positions on PrEP, when seen in light of the political debate. Furthermore, the article is a contribution to the scholarship on gay subjectivity, highlighting how homophobia and homonormativity haunts gay sex even in liberal environments, and how PrEP can serve as an entry point for the destigmatization of gay sexuality and transformation of gay subjectivity. ‘Biopolitical democratization’ entails making explicit how medical technology and health care relates to sexual subjectification and ethics, to strengthen the voice of (potential) PrEP users in health politics, and to renegotiate the profit and power of Big Pharma

Disclination Asymmetry in Two-Dimensional Nematic Liquid Crystals with Unequal Frank Constants

The behavior of a thin film of nematic liquid crystal with unequal Frank constants is discussed. Distinct Frank constants are found to imply unequal core energies for $+1/2$ and $-1/2$ disclinations. Even so, a topological constraint is shown to ensure that the bulk densities of the two types of disclinations are the same. For a system with free boundary conditions, such as a liquid membrane, unequal core energies simply renormalize the Gaussian rigidity and line tension.Comment: RevTex forma

Signed zeros of Gaussian vector fields-density, correlation functions and curvature

We calculate correlation functions of the (signed) density of zeros of Gaussian distributed vector fields. We are able to express correlation functions of arbitrary order through the curvature tensor of a certain abstract Riemann-Cartan or Riemannian manifold. As an application, we discuss one- and two-point functions. The zeros of a two-dimensional Gaussian vector field model the distribution of topological defects in the high-temperature phase of two-dimensional systems with orientational degrees of freedom, such as superfluid films, thin superconductors and liquid crystals.Comment: 14 pages, 1 figure, uses iopart.cls, improved presentation, to appear in J. Phys.

On the origin of the large scale structures of the universe

We revise the statistical properties of the primordial cosmological density anisotropies that, at the time of matter radiation equality, seeded the gravitational development of large scale structures in the, otherwise, homogeneous and isotropic Friedmann-Robertson-Walker flat universe. Our analysis shows that random fluctuations of the density field at the same instant of equality and with comoving wavelength shorter than the causal horizon at that time can naturally account, when globally constrained to conserve the total mass (energy) of the system, for the observed scale invariance of the anisotropies over cosmologically large comoving volumes. Statistical systems with similar features are generically known as glass-like or lattice-like. Obviously, these conclusions conflict with the widely accepted understanding of the primordial structures reported in the literature, which requires an epoch of inflationary cosmology to precede the standard expansion of the universe. The origin of the conflict must be found in the widespread, but unjustified, claim that scale invariant mass (energy) anisotropies at the instant of equality over comoving volumes of cosmological size, larger than the causal horizon at the time, must be generated by fluctuations in the density field with comparably large comoving wavelength.Comment: New section added; final version to appear in Physical Review D; discussion extended and detailed with new calculations to support the claims of the paper; statistical properties of vacuum fluctuations now discussed in the context of FRW flat universe; new important conclussions adde

Spectroscopy, Interactions and Level Splittings in Au Nanoparticles

We have measured the electronic energy spectra of nm-scale Au particles using a new tunneling spectroscopy configuration. The particle diameters ranged from 5nm to 9nm, and at low energies the spectrum is discrete, as expected by the electron-in-a-box model. The density of tunneling resonances increases rapidly with energy, and at higher energies the resonances overlap forming broad resonances. Near the Thouless energy, the broad resonances merge into a continuum. The tunneling resonances display Zeeman splitting in a magnetic field. Surprisingly, the g-factors (~0.3) of energy levels in Au nano-particles are much smaller than the g-factor (2.1) in bulk gold

The distribution of extremal points of Gaussian scalar fields

We consider the signed density of the extremal points of (two-dimensional) scalar fields with a Gaussian distribution. We assign a positive unit charge to the maxima and minima of the function and a negative one to its saddles. At first, we compute the average density for a field in half-space with Dirichlet boundary conditions. Then we calculate the charge-charge correlation function (without boundary). We apply the general results to random waves and random surfaces. Furthermore, we find a generating functional for the two-point function. Its Legendre transform is the integral over the scalar curvature of a 4-dimensional Riemannian manifold.Comment: 22 pages, 8 figures, corrected published versio