Quantum random walk of two photons in separable and entangled state

We discuss quantum random walk of two photons using linear optical elements. We analyze the quantum random walk using photons in a variety of quantum states including entangled states. We find that for photons initially in separable Fock states, the final state is entangled. For polarization entangled photons produced by type II downconverter, we calculate the joint probability of detecting two photons at a given site. We show the remarkable dependence of the two photon detection probability on the quantum nature of the state. In order to understand the quantum random walk, we present exact analytical results for small number of steps like five. We present in details numerical results for a number of cases and supplement the numerical results with asymptotic analytical results

Mass-Gaps and Spin Chains for (Super) Membranes

We present a method for computing the non-perturbative mass-gap in the theory of Bosonic membranes in flat background spacetimes with or without background fluxes. The computation of mass-gaps is carried out using a matrix regularization of the membrane Hamiltonians. The mass gap is shown to be naturally organized as an expansion in a 'hidden' parameter, which turns out to be $\frac{1}{d}$: d being the related to the dimensionality of the background space. We then proceed to develop a large $N$ perturbation theory for the membrane/matrix-model Hamiltonians around the quantum/mass corrected effective potential. The same parameter that controls the perturbation theory for the mass gap is also shown to control the Hamiltonian perturbation theory around the effective potential. The large $N$ perturbation theory is then translated into the language of quantum spin chains and the one loop spectra of various Bosonic matrix models are computed by applying the Bethe ansatz to the one-loop effective Hamiltonians for membranes in flat space times. Apart from membranes in flat spacetimes, the recently proposed matrix models (hep-th/0607005) for non-critical membranes in plane wave type spacetimes are also analyzed within the paradigm of quantum spin chains and the Bosonic sectors of all the models proposed in (hep-th/0607005) are diagonalized at the one-loop level.Comment: 36 Page

Outcomes and complications of fibular head resection

The fibular head is often used as donor graft material for reconstruction of defects of the distal radius. However little is known on the safety of such a procedure. This report describes the long-term donor-site morbidity following the procedure. Fourteen patients who underwent simple or marginal resections of the proximal fibula between 1990 and 2007 were reviewed. Subjective donor-site morbidity, knee and ankle range of motion and instability, presence of sensory or motor function loss, gait and fibular regeneration were assessed. The mean age at surgery was 25 years; six were male, eight were female and the mean follow-up was 11 years. Abnormal clinical findings were present in 10 patients (71.4 %): nine patients (64.3 %) had Grade 2 varus laxity at the knee confirmed by stress radiographs; one had sensory loss in the distribution of the superficial peroneal nerve. Patients with varus laxity had significantly higher mean age at surgery than those without varus laxity (p = 0.001). None had deformity at the knee or ankle. The range of joint movements was normal. All had a normal tibiotalar angle and none had proximal migration of the fibula. One patient demonstrated near-complete regeneration of the fibula. Donor-site morbidity following simple and marginal resection of the proximal fibula is acceptable. Older patients had a higher risk of demonstrable varus laxity at the knee but proximal fibula resection in children appears to be safe

Off Resonant Pumping for Transition from Continuous to Discrete Spectrum and Quantum Revivals in Systems in Coherent States

We show that in parametrically driven systems and, more generally, in systems in coherent states, off-resonant pumping can cause a transition from a continuum energy spectrum of the system to a discrete one, and result in quantum revivals of the initial state. The mechanism responsible for quantum revivals in the present case is different from that in the non-linear wavepacket dynamics of systems such as Rydberg atoms. We interpret the reported phenomena as an optical analog of Bloch oscillations realized in Fock space and propose a feasible scheme for inducing Bloch oscillations in trapped ions.Comment: 5 pages, 4 figures, submitted to Jnl. of Optics

Trajectory-Based Dynamic Map Labeling

In this paper we introduce trajectory-based labeling, a new variant of dynamic map labeling, where a movement trajectory for the map viewport is given. We define a general labeling model and study the active range maximization problem in this model. The problem is NP-complete and W[1]-hard. In the restricted, yet practically relevant case that no more than k labels can be active at any time, we give polynomial-time algorithms. For the general case we present a practical ILP formulation with an experimental evaluation as well as approximation algorithms.Comment: 19 pages, 7 figures, extended version of a paper to appear at ISAAC 201

Mass Deformations of Super Yang-Mills Theories in D= 2+1, and Super-Membranes: A Note

Mass deformations of supersymmetric Yang-Mills theories in three spacetime dimensions are considered. The gluons of the theories are made massive by the inclusion of a non-local gauge and Poincare invariant mass term due to Alexanian and Nair, while the matter fields are given standard Gaussian mass-terms. It is shown that the dimensional reduction of such mass deformed gauge theories defined on $R^3$ or $R\times T^2$ produces matrix quantum mechanics with massive spectra. In particular, all known massive matrix quantum mechanical models obtained by the deformations of dimensional reductions of minimal super Yang-Mills theories in diverse dimensions are shown also to arise from the dimensional reductions of appropriate massive Yang-Mills theories in three spacetime dimensions. Explicit formulae for the gauge theory actions are provided.Comment: 20 Page

Apparent Molal Volume of Tetraalkylammonium Iodides in Dioxane-Water Mixtures of Varying Dielectric Constants

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`Commerciality` in International Commercial Arbitration

Enterprises, the world over, now conduct business on a dramatically more international scale. The growth of world economies is directly connected with millions of commercial contracts, which are becoming more international in character owing to global integration. Commercial arbitration has been hailed as the most efficient form of dispute settlement available to participants in international trade. As the purpose of the commercial arbitration is to resolve commercial disputes, often issues have been raised whether a particular dispute is commercial or not. With globalisation and seamless trade the aspirations of global business community, it would be of immense importance to understand the meaning of ‘commercial’ as construed in ‘international commercial arbitration’ in some of the major jurisdictions of the world.