Algebraic Rainich conditions for the tensor V

Algebraic conditions on the Ricci tensor in the Rainich-Misner-Wheeler unified field theory are known as the Rainich conditions. Penrose and more recently Bergqvist and Lankinen made an analogy from the Ricci tensor to the Bel-Robinson tensor $B_{\alpha\beta\mu\nu}$, a certain fourth rank tensor quadratic in the Weyl curvature, which also satisfies algebraic Rainich-like conditions. However, we found that not only does the tensor $B_{\alpha\beta\mu\nu}$ fulfill these conditions, but so also does our recently proposed tensor $V_{\alpha\beta\mu\nu}$, which has many of the desirable properties of $B_{\alpha\beta\mu\nu}$. For the quasilocal small sphere limit restriction, we found that there are only two fourth rank tensors $B_{\alpha\beta\mu\nu}$ and $V_{\alpha\beta\mu\nu}$ which form a basis for good energy expressions. Both of them have the completely trace free and causal properties, these two form necessary and sufficient conditions. Surprisingly either completely traceless or causal is enough to fulfill the algebraic Rainich conditions. Furthermore, relaxing the quasilocal restriction and considering the general fourth rank tensor, we found two remarkable results: (i) without any symmetry requirement, the algebraic Rainich conditions only require totally trace free; (ii) with a symmetry requirement, we recovered the same result as in the quasilocal small sphere limit.Comment: 17 page

Gravitational energy from a combination of a tetrad expression and Einstein's pseudotensor

The energy-momentum for a gravitating system can be considered by the tetard teleparalle gauge current in orthonormal frames. Whereas the Einstein pseudotensor used holonomic frames. Tetrad expression itself gives a better result for gravitational energy than Einstein's. Inspired by an idea of Deser, we found a gravitational energy expression which enjoys the positive energy property by combining the tetrad expression and the Einstein pseudotensor, i.e., the connection coefficient has a form appropriate to a suitable intermediate between orthonormal and holonomic frames.Comment: 5 page

Gravitational energy in a small region for the modified Einstein and Landau-Lifshitz pseudotensors

The purpose of the classical Einstein and Landau-Lifshitz pseudotensors is for determining the gravitational energy. Neither of them can guarantee a positive energy in holonomic frames. In the small sphere approximation, it has been required that the quasilocal expression for the gravitational energy-momentum density should be proportional to the Bel-Robinson tensor $B_{\alpha\beta\mu\nu}$. However, we propose a new tensor $V_{\alpha\beta\mu\nu}$ which is the sum of certain tensors $S_{\alpha\beta\mu\nu}$ and $K_{\alpha\beta\mu\nu}$, it has certain properties so that it gives the same gravitational "energy-momentum" content as $B_{\alpha\beta\mu\nu}$ does. Moreover, we show that a modified Einstein pseudotensor turns out to be one of the Chen-Nester quasilocal expressions, while the modified Landau-Lifshitz pseudotensor becomes the Papapetrou pseudotensor; these two modified pseudotensors have positive gravitational energy in a small region.Comment:

New positive small vacuum region gravitational energy expressions

We construct an infinite number of new holonomic quasi-local gravitational energy-momentum density pseudotensors with good limits asymptotically and in small regions, both materially and in vacuum. For small vacuum regions they are all a positive multiple of the Bel-Robinson tensor and consequently have positive energy.Comment: 4 page

Detection of Sugar-Lectin Interactions by Multivalent Dendritic Sugar Functionalized Single-Walled Carbon Nanotubes

We show that single walled carbon nanotubes (SWNT) decorated with sugar functionalized poly (propyl ether imine) (PETIM) dendrimer is a very sensitive platform to quantitatively detect carbohydrate recognizing proteins, namely, lectins. The changes in electrical conductivity of SWNT in field effect transistor device due to carbohydrate - protein interactions form the basis of present study. The mannose sugar attached PETIM dendrimers undergo charge - transfer interactions with the SWNT. The changes in the conductance of the dendritic sugar functionalized SWNT after addition of lectins in varying concentrations were found to follow the Langmuir type isotherm, giving the concanavalin A (Con A) - mannose affinity constant to be 8.5 x 106 M-1. The increase in the device conductance observed after adding 10 nM of Con A is same as after adding 20 \muM of a non - specific lectin peanut agglutinin, showing the high specificity of the Con A - mannose interactions. The specificity of sugar-lectin interactions was characterized further by observing significant shifts in Raman modes of the SWNT.Comment: 12 pages, 3 figure

Quantifying the Dynamics of Bacterial Secondary Metabolites by Spectral Multiphoton Microscopy

Phenazines, a group of fluorescent small molecules produced by the bacterium Pseudomonas aeruginosa, play a role in maintaining cellular redox homeostasis. Phenazines have been challenging to study in vivo due to their redox activity, presence both intra- and extracellularly, and their diverse chemical properties. Here, we describe a noninvasive in vivo optical technique to monitor phenazine concentrations within bacterial cells using time-lapsed spectral multiphoton fluorescence microscopy. This technique enables simultaneous monitoring of multiple weakly fluorescent molecules (phenazines, siderophores, NAD(P)H) expressed by bacteria in culture. This work provides the first in vivo measurements of reduced phenazine concentration as well as the first description of the temporal dynamics of the phenazine-NAD(P)H redox system in Pseudomonas aeruginosa, illuminating an unanticipated role for 1-hydroxyphenazine. Similar approaches could be used to study the abundance and redox dynamics of a wide range of small molecules within bacteria, both as single cells and in communities

Nonequilibrium quantum criticality in open electronic systems

A theory is presented of quantum criticality in open (coupled to reservoirs) itinerant electron magnets, with nonequilibrium drive provided by current flow across the system. Both departures from equilibrium at conventional (equilibrium) quantum critical points and the physics of phase transitions induced by the nonequilibrium drive are treated. Nonequilibrium-induced phase transitions are found to have the same leading critical behavior as conventional thermal phase transitions.Comment: 5 pages, 1 figur

Topological superconductivity and Majorana fermions in hybrid structures involving cuprate high-T_c superconductors

The possibility of inducing topological superconductivity with cuprate high-temperature superconductors (HTSC) is studied for various heterostructures. We first consider a ballistic planar junction between a HTSC and a metallic ferromagnet. We assume that inversion symmetry breaking at the tunnel barrier gives rise to Rashba spin-orbit coupling in the barrier and allows equal-spin triplet superconductivity to exist in the ferromagnet. Bogoliubov-de Gennes equations are obtained by explicitly modeling the barrier, and taking account of the transport anisotropy in the HTSC. By making use of the self-consistent boundary conditions and solutions for the barrier and HTSC regions, an effective equation of motion for the ferromagnet is obtained where Andreev scattering at the barrier is incorporated as a boundary condition for the ferromagnetic region. For a ferromagnet layer deposited on a (100) facet of the HTSC, triplet p-wave superconductivity is induced. For the layer deposited on a (110) facet, the induced gap does not have the p-wave orbital character, but has an even orbital symmetry and an odd dependence on energy. For the layer on the (001) facet, an exotic f-wave superconductivity is induced. We also consider the induced triplet gap in a one-dimensional half-metallic nanowire deposited on a (001) facet of a HTSC. We find that for a wire axis along the a-axis, a robust triplet p-wave gap is induced. For a wire oriented 45 degrees away from the a-axis the induced triplet p-wave gap vanishes. For the appropriately oriented wire, the induced p-wave gap should give rise to Majorana fermions at the ends of the half-metallic wire. Based on our result, topological superconductivity in a semi-conductor nanowire may also be possible given that it is oriented along the a-axis of the HTSC.Comment: 14 pages, 4 figure

Kaplan-Narayanan-Neuberger lattice fermions pass a perturbative test

We test perturbatively a recent scheme for implementing chiral fermions on the lattice, proposed by Kaplan and modified by Narayanan and Neuberger, using as our testing ground the chiral Schwinger model. The scheme is found to reproduce the desired form of the effective action, whose real part is gauge invariant and whose imaginary part gives the correct anomaly in the continuum limit, once technical problems relating to the necessary infinite extent of the extra dimension are properly addressed. The indications from this study are that the Kaplan--Narayanan--Neuberger (KNN) scheme has a good chance at being a correct lattice regularization of chiral gauge theories.Comment: LaTeX 18 pages, 3 figure

On the energy of homogeneous cosmologies

An energy for the homogeneous cosmological models is presented. More specifically, using an appropriate natural prescription, we find the energy within any region with any gravitational source for a large class of gravity theories--namely those with a tetrad description--for all 9 Bianchi types. Our energy is given by the value of the Hamiltonian with homogeneous boundary conditions; this value vanishes for all regions in all Bianchi class A models, and it does not vanish for any class B model. This is so not only for Einstein's general relativity but, moreover, for the whole 3-parameter class of tetrad-teleparallel theories. For the physically favored one parameter subclass, which includes the teleparallel equivalent of Einstein's theory as an important special case, the energy for all class B models is, contrary to expectation, negative.Comment: 11 pages, reformated with minor change