Local electronic properties of metallic-semiconducting carbon nanotube heterostructures are investigated by studying the behavior of the one-electron local density of states ͑LDOS͒ along the tubes. We determine how these properties change from the metallic to the semiconducting side of a nanotube junction. We show that Friedel oscillations may not always be evident on the metallic side, and we found clear exponential decay of the LDOS on the semiconducting side. The exponential rates of decay as well as the absence of the oscillations are explained in terms of a simple picture that relates the LDOS to the bulk electronic structure of the constituent parts of the heterostructures.

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We quantize the Einstein gravity in the formalism of weak gravitational fields by using the constrained Hamiltonian method. Special emphasis is given to the 2+1 spacetime dimensional case where a (topological) Chern-Simons term is added to the Lagrangian.

Local electronic properties of quantum dot nanotubes modeled by connecting pure semiconducting and metallic nanotubes via appropriate junctions are studied following a single -band tight-binding Hamiltonian. The junctions are formed by introducing pair defects composed of heptagons and pentagons along the axial direction of pure nanotubes. We investigate the dependence of the confined electronic states with the characteristic sizes of the quantum dots taking into account different nanotube-based heterostructures. Quantum-welllike and interface states are characterized by investigating the spatial dependence of the local density of states of the discrete levels. We follow the Green's function formalism and adopt real-space renormalization techniques to calculate local density of states. The conductance of metal/semiconductor͑metal͒/metal carbon heterostructures is also investigated and we found exponentially the decay and oscillatory behaviors that may be associated with the electronic structure of the tube constituents and the details of the junctions.

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