Two-way quantum communication: Generalization of secure quantum information exchange to quantum network

The idea of secure quantum information exchange (SQIE) [J. Phys. B: At. Mol. Opt. Phys.44, 115504 (2011)] is introduced for the secure exchange of single qubit information states between two legitimate users, Alice and Bob. In the present paper, we extend this original SQIE protocol by presenting a scheme, which enables the secure exchange of n-single qubit information states among the n nodes of a quantum network, with the aid of a special kind of 4n-qubit entangled state and the classical assistance of an extra participant Charlie. For experimental realization of our extended SQIE protocol, we suggest an efficient scheme for the generation of a special kind of 4n-qubit entangled state using the interaction between highly detuned Λ-type three-level atoms and optical coherent field. Further, by discussing the various experimental parameters, we show that the special kind 4n-qubit entangled state can be generated with the presently available technology.     

Avalanche transmission and critical behaviour in load-bearing hierarchical networks

The strength and stability properties of hierarchical load-bearing networks and their strengthened variants have been discussed in a recent work. Here, we study the avalanche time distributions on these load-bearing networks. The avalanche time distributions of the V-lattice, a unique realization of the networks, show power-law behaviour when tested with certain fractions of its trunk weights. All other avalanche distributions show Gaussian peaked behaviour. Thus the V-lattice is the critical case of the network. We discuss the implications of this result.     

Dielectric relaxation study of pyridine-alcohol mixtures using time domain reflectometry

Time domain reflectometry is applied to dielectric relaxation measurements on pyridine-alcohol (methanol, ethanol, propan- 1-o1 and butan-1 -o1) mixtures over the entire concentration range and over the frequency range 10MHz-10GHz at 5, 15, 25 and 35°C. From the data, static permittivity and the dielectric relaxation time are extracted using a bilinear calibration method and a nonlinear least-squares fit method. These mixtures exhibit a principal dispersion of the Debye type at microwave frequencies. The Kirkwood correlation factor, which contains information regarding solute-solvent interaction and corresponding structural information, was obtained for these systems, and the excess inverse relaxation time and molar energy of activation for all these systems were determined. The values of the static permittivity, the relaxation time and the Kirkwood correlation factor decrease with increased pyridine concentration in alcohol. The static permittivity of the mixtures fits the modified Brugemann model well.     

Exact solutions of certain nonlinear chemotaxis diffusion reaction equations

Using the auxiliary equation method, we obtain exact solutions of certain nonlinear chemotaxis diffusion reaction equations in the presence of a stimulant. In particular, we account for the nonlinearities arising not only from the density-dependent source terms contributed by the particles and the stimulant but also from the coupling term of the stimulant. In addition to this, the diffusion of the stimulant and the effect of long-range interactions are also accounted for in the constructed coupled differential equations. The results obtained here could be useful in the studies of several biological systems and processes, e.g., in bacterial infection, chemotherapy, etc.     

Certain variants of multipermutohedron ideals

Multipermutohedron ideals have rich combinatorial properties. An explicit combinatorial formula for the multigraded Betti numbers of a multipermutohedron ideal and their Alexander duals are known. Also, the dimension of the Artinian quotient of an Alexander dual of a multipermutohedron ideal is the number of generalized parking functions. In this paper, monomial ideals which are certain variants of multipermutohedron ideals are studied. Multigraded Betti numbers of these variant monomial ideals and their Alexander duals are obtained. Further, many interesting combinatorial properties of multipermutohedron ideals are extended to these variant monomial ideals.     

Femto-Second Transform Limited Pulse Generation with Higher Order Dispersion Effects for Dispersion-Shifted Optical Communication System

The paper deals with the influence of higher-order effects of dispersion on the femto-second transform limited pulse generation by compensating for linear chirp of self-phase modulation spectra in the dispersion-shifted fibers. It has been shown that the minimum propagation length with first-order dispersion term is 23 m, as reported earlier. If the higher-order dispersion effects are taken into consideration, this length is reduced to 11.5 m. With compensation of the first-order dispersion term, this length can be enhanced to 6.8161 × 10³ km. This length can further be improved to 6.0343 × 10⁹ km by compensation of first- and second-order dispersion terms together. The minimum pulse width and linewidth product without dispersion, with dispersion including higher-order dispersion effects, and with dispersion compensation, is found to be 0.44, 0.4418, and 0.4411, respectively.     

A generalization based on quantitative inadequacy of Archimedes principle in balloon experiments

One consequence of Archimedes' principle is that the mass which a balloon supports in a fluid is independent of the shape of the balloon and depends only upon its volume. For air-filled floating balloons in water some deviations from this result have been observed in first-stage experiments. The dependence of mass on the shape of the balloon which is supported in water has been clearly observed in various observations. It is evident from the first-stage experiments that for floating balloons the principle is only true for particular shapes. The deviations from the principle and contradictions can be explained if the definition of the principle is empirically modified i.e. it is assumed that the upthrust experienced by body is proportional to the weight of the fluid displaced. The constant of proportionality also accounts for shape of body and other relevant factors that were not accounted for by the principle.