Condensed Matter Theory

Abstract:

We consider a hypothetical topological quantum computer composed of either Ising or Fibonacci anyons. For each case, we calculate the time and number of qubits (space) necessary to execute the most computationally expensive step of Shor's algorithm, modular exponentiation. For Ising anyons, we apply Bravyi's distillation method which combines topological and nontopological operations to allow for universal quantum computation. With reasonable restrictions on the physical parameters we find that factoring a 128-bit number requires approximately 103 Fibonacci anyons versus at least 3×109 Ising anyons. Other distillation algorithms could reduce the resources for Ising anyons substantially. © 2010 The American Physical Society.

Abstract:

Division in Staphylococci occurs equatorially and on specific sequentially orthogonal planes in three dimensions, resulting, after incomplete cell separation, in the 'bunch of grapes' cluster organization that defines the genus. The shape of Staphylococci is principally maintained by peptidoglycan. In this study, we use Atomic Force Microscopy (AFM) and fluorescence microscopy with vancomycin labelling to examine purified peptidoglycan architecture and its dynamics in Staphylococcus aureus and correlate these with the cell cycle. At the presumptive septum, cells were found to form a large belt of peptidoglycan in the division plane before the centripetal formation of the septal disc; this often had a 'piecrust' texture. After division, the structures remain as orthogonal ribs, encoding the location of past division planes in the cell wall. We propose that this epigenetic information is used to enable S. aureus to divide in sequentially orthogonal planes, explaining how a spherical organism can maintain division plane localization with fidelity over many generations.

Abstract:

We study the consequences of disorder in the Kitaev honeycomb model, considering both site dilution and exchange randomness. We show that a single vacancy binds a flux and induces a local moment. This moment is polarized by an applied field h: in the gapless phase, for small h the local susceptibility diverges as χ(h)∼ln(1/h); for a pair of nearby vacancies on the same sublattice, this even increases to χ(h)∼1/(h[ln(1/h)](3/2)). By contrast, weak exchange randomness does not qualitatively alter the susceptibility but has its signature in the heat capacity, which in the gapless phase is power law in temperature with an exponent dependent on disorder strength.

Abstract:

The Casimir-Lifshitz interaction between metamaterials is studied using a model that takes into account the structural heterogeneity of the dielectric and magnetic properties of the bodies. A recently developed perturbation theory for the Casimir-Lifshitz interaction between arbitrary material bodies is generalized to include non-uniform magnetic permeability profiles, and used to study the interaction between the magneto-dielectric heterostructures within the leading order. The metamaterials are modeled as two dimensional arrays of domains with varying permittivity and permeability. In the case of two semi-infinite bodies with flat boundaries, the patterned structure of the material properties is found to cause the normal Casimir-Lifshitz force to develop an oscillatory behavior when the distance between the two bodies is comparable to the wavelength of the patterned features in the metamaterials. The non-uniformity also leads to the emergence of lateral Casimir-Lifshitz forces, which tend to strengthen as the gap size becomes smaller. Our results suggest that the recent studies on Casimir-Lifshitz forces between metamaterials, which have been performed with the aim of examining the possibility of observing the repulsive force, should be revisited to include the effect of the patterned structure at the wavelength of several hundred nanometers that coincides with the relevant gap size in the experiments.