An improved perturbation approach to the 2D Edwards polymer -- corrections to scaling

We present the results of a new perturbation calculation in polymer statistics which starts from a ground state that already correctly predicts the long chain length behaviour of the mean square end--to--end distance $\langle R_N^2 \rangle\$, namely the solution to the 2~dimensional~(2D) Edwards model. The $\langle R_N^2 \rangle$ thus calculated is shown to be convergent in $N$, the number of steps in the chain, in contrast to previous methods which start from the free random walk solution. This allows us to calculate a new value for the leading correction--to--scaling exponent~$\Delta$. Writing $\langle R_N^2 \rangle = AN^{2\nu}(1+BN^{-\Delta} + CN^{-1}+...)$, where $\nu = 3/4$ in 2D, our result shows that $\Delta = 1/2$. This value is also supported by an analysis of 2D self--avoiding walks on the {\em continuum}.Comment: 17 Pages of Revtex. No figures. Submitted to J. Phys.

Improving zero-error classical communication with entanglement

Given one or more uses of a classical channel, only a certain number of messages can be transmitted with zero probability of error. The study of this number and its asymptotic behaviour constitutes the field of classical zero-error information theory, the quantum generalisation of which has started to develop recently. We show that, given a single use of certain classical channels, entangled states of a system shared by the sender and receiver can be used to increase the number of (classical) messages which can be sent with no chance of error. In particular, we show how to construct such a channel based on any proof of the Bell-Kochen-Specker theorem. This is a new example of the use of quantum effects to improve the performance of a classical task. We investigate the connection between this phenomenon and that of ``pseudo-telepathy'' games. The use of generalised non-signalling correlations to assist in this task is also considered. In this case, a particularly elegant theory results and, remarkably, it is sometimes possible to transmit information with zero-error using a channel with no unassisted zero-error capacity.Comment: 6 pages, 2 figures. Version 2 is the same as the journal version plus figure 1 and the non-signalling box exampl

ATP allosterically activates the human 5-lipoxygenase molecular mechanism of arachidonic acid and 5(S)-hydroperoxy-6(E),8(Z),11(Z),14(Z)-eicosatetraenoic acid.

5-Lipoxygenase (5-LOX) reacts with arachidonic acid (AA) to first generate 5(S)-hydroperoxy-6(E),8(Z),11(Z),14(Z)-eicosatetraenoic acid [5(S)-HpETE] and then an epoxide from 5(S)-HpETE to form leukotriene A4, from a single polyunsaturated fatty acid. This work investigates the kinetic mechanism of these two processes and the role of ATP in their activation. Specifically, it was determined that epoxidation of 5(S)-HpETE (dehydration of the hydroperoxide) has a rate of substrate capture (Vmax/Km) significantly lower than that of AA hydroperoxidation (oxidation of AA to form the hydroperoxide); however, hyperbolic kinetic parameters for ATP activation indicate a similar activation for AA and 5(S)-HpETE. Solvent isotope effect results for both hydroperoxidation and epoxidation indicate that a specific step in its molecular mechanism is changed, possibly because of a lowering of the dependence of the rate-limiting step on hydrogen atom abstraction and an increase in the dependency on hydrogen bond rearrangement. Therefore, changes in ATP concentration in the cell could affect the production of 5-LOX products, such as leukotrienes and lipoxins, and thus have wide implications for the regulation of cellular inflammation

Quantum data compression, quantum information generation, and the density-matrix renormalization group method

We have studied quantum data compression for finite quantum systems where the site density matrices are not independent, i.e., the density matrix cannot be given as direct product of site density matrices and the von Neumann entropy is not equal to the sum of site entropies. Using the density-matrix renormalization group (DMRG) method for the 1-d Hubbard model, we have shown that a simple relationship exists between the entropy of the left or right block and dimension of the Hilbert space of that block as well as of the superblock for any fixed accuracy. The information loss during the RG procedure has been investigated and a more rigorous control of the relative error has been proposed based on Kholevo's theory. Our results are also supported by the quantum chemistry version of DMRG applied to various molecules with system lengths up to 60 lattice sites. A sum rule which relates site entropies and the total information generated by the renormalization procedure has also been given which serves as an alternative test of convergence of the DMRG method.Comment: 8 pages, 7 figure

Photoelectrochemical water splitting: silicon photocathodes for hydrogen evolution

The development of low cost, scalable, renewable energy technologies is one of today's most pressing scientific challenges. We report on progress towards the development of a photoelectrochemical water-splitting system that will use sunlight and water as the inputs to produce renewable hydrogen with oxygen as a by-product. This system is based on the design principle of incorporating two separate, photosensitive inorganic semiconductor/liquid junctions to collectively generate the 1.7-1.9 V at open circuit needed to support both the oxidation of H_2O (or OH^-) and the reduction of H^+ (or H_2O). Si microwire arrays are a promising photocathode material because the high aspect-ratio electrode architecture allows for the use of low cost, earth-abundant materials without sacrificing energy-conversion efficiency, due to the orthogonalization of light absorption and charge-carrier collection. Additionally, the high surfacearea design of the rod-based semiconductor array inherently lowers the flux of charge carriers over the rod array surface relative to the projected geometric surface of the photoelectrode, thus lowering the photocurrent density at the solid/liquid junction and thereby relaxing the demands on the activity (and cost) of any electrocatalysts. Arrays of Si microwires grown using the Vapor Liquid Solid (VLS) mechanism have been shown to have desirable electronic light absorption properties. We have demonstrated that these arrays can be coated with earth-abundant metallic catalysts and used for photoelectrochemical production of hydrogen. This development is a step towards the demonstration of a complete artificial photosynthetic system, composed of only inexpensive, earth-abundant materials, that is simultaneously efficient, durable, and scalable

Structures and Electromagnetic Properties of New Metal-Ordered Manganites; RBaMn_{2}O_{6} (R = Y and Rare Earth Elements)

New metal-ordered manganites RBaMn_{2}O_{6} have been synthesized and investigated in the structures and electromagnetic properties. RBaMn_{2}O_{6} can be classified into three groups from the structural and electromagnetic properties. The first group (R = La, Pr and Nd) has a metallic ferromagnetic transition, followed by an A-type antiferromagnetic transition in PrBaMn_{2}O_{6}. The second group (R = Sm, Eu and Gd) exhibits a charge-order transition, followed by an antiferromagnetic long range ordering. The third group (R = Tb, Dy and Ho) shows successive three phase transitions, the structural, charge/orbital-order and magnetic transitions, as observed in YBaMn_{2}O_{6}. Comparing to the metal-disordered manganites (R^{3+}_{0.5}A^{2+}_{0.5})MnO_{3}, two remarkable features can be recognized in RBaMn_{2}O_{6}; (1) relatively high charge-order transition temperature and (2) the presence of structural transition above the charge-order temperature in the third group. We propose a possible orbital ordering at the structural transition, that is a possible freezing of the orbital, charge and spin degrees of freedom at the independent temperatures in the third group. These features are closely related to the peculiar structure that the MnO_{2} square-lattice is sandwiched by the rock-salt layers of two kinds, RO and BaO with extremely different lattice-sizes.Comment: 5 pages, 4 figures, submitted to J. Phys. Soc. Jp

Information Content of Spontaneous Symmetry Breaking

We propose a measure of order in the context of nonequilibrium field theory and argue that this measure, which we call relative configurational entropy (RCE), may be used to quantify the emergence of coherent low-entropy configurations, such as time-dependent or time-independent topological and nontopological spatially-extended structures. As an illustration, we investigate the nonequilibrium dynamics of spontaneous symmetry-breaking in three spatial dimensions. In particular, we focus on a model where a real scalar field, prepared initially in a symmetric thermal state, is quenched to a broken-symmetric state. For a certain range of initial temperatures, spatially-localized, long-lived structures known as oscillons emerge in synchrony and remain until the field reaches equilibrium again. We show that the RCE correlates with the number-density of oscillons, thus offering a quantitative measure of the emergence of nonperturbative spatiotemporal patterns that can be generalized to a variety of physical systems.Comment: LaTeX, 9 pages, 5 figures, 1 tabl

Specific protein-protein binding in many-component mixtures of proteins

Proteins must bind to specific other proteins in vivo in order to function. The proteins must bind only to one or a few other proteins of the of order a thousand proteins typically present in vivo. Using a simple model of a protein, specific binding in many component mixtures is studied. It is found to be a demanding function in the sense that it demands that the binding sites of the proteins be encoded by long sequences of bits, and the requirement for specific binding then strongly constrains these sequences. This is quantified by the capacity of proteins of a given size (sequence length), which is the maximum number of specific-binding interactions possible in a mixture. This calculation of the maximum number possible is in the same spirit as the work of Shannon and others on the maximum rate of communication through noisy channels.Comment: 13 pages, 3 figures (changes for v2 mainly notational - to be more in line with notation in information theory literature