Quantum doubles from a class of noncocommutative weak Hopf algebras

The concept of biperfect (noncocommutative) weak Hopf algebras is introduced and their properties are discussed. A new type of quasi-bicrossed products is constructed by means of weak Hopf skew-pairs of the weak Hopf algebras which are generalizations of the Hopf pairs introduced by Takeuchi. As a special case, the quantum double of a finite dimensional biperfect (noncocommutative) weak Hopf algebra is built. Examples of quantum doubles from a Clifford monoid as well as a noncommutative and noncocommutative weak Hopf algebra are given, generalizing quantum doubles from a group and a noncommutative and noncocommutative Hopf algebra, respectively. Moreover, some characterizations of quantum doubles of finite dimensional biperfect weak Hopf algebras are obtained. (C) 2004 American Institute of Physics.

Partial regularity of weak solutions of the liquid crystal equilibrium system

For a parameter, we consider the modified relaxed energy of the liquid crystal system. Each minimizer of the modified relaxed energy is a weak solution to the liquid crystal equilibrium system. We prove the partial regularity of minimizers of the modified relaxed energy. We also prove the existence of infinitely many weak solutions for the special boundary value x.

Measurement of quantum weak values of photon polarization

We experimentally determine weak values for a single photon's polarization, obtained via a weak measurement that employs a two-photon entangling operation, and postselection. The weak values cannot be explained by a semiclassical wave theory, due to the two-photon entanglement. We observe the variation in the size of the weak value with measurement strength, obtaining an average measurement of the S-1 Stokes parameter more than an order of magnitude outside of the operator's spectrum for the smallest measurement strengths.

Particle bed charge decay behaviour under high tension roll separation

A new theory of particle discharge in high tension roll (HTR) separation is presented. The discharge dynamics of an isolated charged particle resting on a conducting surface are studied first. The analysis is extended to particle discharge in a homogenous particle bed. Finally, the paper looks at the more realistic scenario of particle discharge in a non-homogenous particle bed. The consequences of the resulting theory on HTR separation are discussed. Predictions from the new theory are tested against experimental HTR separations at the pilot scale. (c) 2005 Elsevier Ltd. All rights reserved.

Using weak nonlinearity under decoherence for macroscopic entanglement generation and quantum computation

Recently, there have been several suggestions that weak Kerr nonlinearity can be used for generation of macroscopic superpositions and entanglement and for linear optics quantum computation. However, it is not immediately clear that this approach can overcome decoherence effects. Our numerical study shows that nonlinearity of weak strength could be useful for macroscopic entanglement generation and quantum gate operations in the presence of decoherence. We suggest specific values for real experiments based on our analysis. Our discussion shows that the generation of macroscopic entanglement using this approach is within the reach of current technology.

Features of nitrogen adsorption on nonporous carbon and silica surfaces in the framework of classical density functional theory

Equilibrium adsorption data of nitrogen on a series of nongraphitized carbon blacks and nonporous silica at 77 K were analyzed by means of classical density functional theory to determine the solid-fluid potential. The behavior of this potential profile at large distance is particularly considered. The analysis of nitrogen adsorption isotherms seems to indicate that the adsorption in the first molecular layer is localized and controlled mainly by short-range forces due to the surface roughness, crystalline defects, and functional groups. At distances larger than approximately 1.3-1.5 molecular diameters, the adsorption is nonlocalized and appears as a thickening of the adsorbed film with increasing bulk pressure in a relatively weak adsorption potential field. It has been found that the asymptotic decay of the potential obeys the power law with the exponent being -3 for carbon blacks and -4 for silica surface, which signifies that in the latter case the adsorption potential is mainly exerted by surface oxygen atoms. In all cases, the absolute value of the solid-fluid potential is much smaller than that predicted by the Lennard-Jones pair potential with commonly used solid-fluid molecular parameters. The effect of surface heterogeneity on the heat of adsorption is also discussed.

Optical Bloch equations and enhanced decay of Rabi oscillations in strong driving fields

Optical Bloch equations are widely used for describing dynamics in a system consisting molecules, electromagnetic waves, and a thermal bath. We analyze applicability of these equations to a single molecule imbedded in a solid matrix. Classical Bloch equations and the limits of their applicability are derived from more general master equations. Simple and intuitively appealing picture based on stochastic Bloch equations shows that at low temperatures, contrary to common believes, a strong driving field can not only suppress but can also increase decay rates of Rabi oscillations. A physical system where predicted effects can be observed experimentally is suggested. (c) 2005 Elsevier B.V. All rights reserved.

Orbital currents and charge density waves in a generalized Hubbard ladder

We study a generalized Hubbard model on the two-leg ladder at zero temperature, focusing on a parameter region with staggered flux (SF)/d-density wave (DDW) order. To guide our numerical calculations, we first investigate the location of a SF/DDW phase in the phase diagram of the half-filled weakly interacting ladder using a perturbative renormalization group (RG) and bosonization approach. For hole doping 6 away from half-filling, finite-system density-matrix renormalizationgroup (DMRG) calculations are used to study ladders with up to 200 rungs for intermediate-strength interactions. In the doped SF/DDW phase, the staggered rung current and the rung electron density both show periodic spatial oscillations, with characteristic wavelengths 2/delta and 1/delta, respectively, corresponding to ordering wavevectors 2k(F) and 4k(F) for the currents and densities, where 2k(F) = pi(1 - delta). The density minima are located at the anti-phase domain walls of the staggered current. For sufficiently large dopings, SF/DDW order is suppressed. The rung density modulation also exists in neighboring phases where currents decay exponentially. We show that most of the DMRG results can be qualitatively understood from weak-coupling RG/bosonization arguments. However, while these arguments seem to suggest a crossover from non-decaying correlations to power-law decay at a length scale of order 1/delta, the DMRG results are consistent with a true long-range order scenario for the currents and densities. (c) 2005 Elsevier Inc. All rights reserved.

Strong and weak lifespan extension: What is most feasible and likely?

Recent advances in biomedical science indicate that it may eventually be possible to intervene in the biological process of human ageing. This paper overviews the current state of the science of lifespan extension and promising future directions. It is uncertain whether 'strong' lifespan extension - the extension of human life beyond the maximum 122 years so far observed - will become a reality. It is more likely that cumulative effects of numerous scientific and biomedical advances in the treatment of common disease will produce 'weak' lifespan extension - the extension of average life expectancy. The practical application of molecular, genetic and nanomaterials research may also lead to advances in life expectancy. It is not too early to begin to consider the policy implications of either form of lifespan extension.

Television satire, decmocracy and the decay of public language: John Clarke's verbal caricature

This paper examines the contributions of John Clarke to the field of political satire through his interviews with straight-man Bryan Dawe on ABC TV’s The 7.30 Report. Clarke’s work represents one of the last vestiges of what was once a vigorous satiric tradition in TV comedy, specifically the practice of political caricature. There was The Mavis Bramston Show in the 1960s and The Naked Vicar Show in the 1970s, while The Gillies Report in the 1980s was probably the best example of sustained political caricature in television comedy. Even in later sketch-based shows such as Fast Forward and The Late Show in the early 1990s, political caricature was a significant component of the material, whereas it seems to have all but disappeared from current television comedy. The paper investigates the disappearance of this type of comedy from Australian television screens and also discusses why the longevity, consistency, not to mention accuracy, of Clarke’s satire is so important in the current political climate. Clarke’s political caricature is almost entirely language-based, expertly parodying the spin-doctored rhetoric of our elected representatives and business leaders. This leads to a secondary focus of the paper, which is a discussion of Clarke’s unique form of satire in the context of what an historian (and former satirist) identifies as ‘the decay of public language’.

Quantum computation using weak nonlinearities: Robustness against decoherence

We investigate decoherence effects in the recently suggested quantum-computation scheme using weak nonlinearities, strong probe coherent fields, detection, and feedforward methods. It is shown that in the weak-nonlinearity-based quantum gates, decoherence in nonlinear media can be made arbitrarily small simply by using arbitrarily strong probe fields, if photon-number-resolving detection is used. On the contrary, we find that homodyne detection with feedforward is not appropriate for this scheme because in this case decoherence rapidly increases as the probe field gets larger.