General decay of the solution for a viscoelastic wave equation with a time-varying delay term in the internal feedback

In this paper we consider a viscoelastic wave equation with a time-varying delay term, the coefficient of which is not necessarily positive. By introducing suitable energy and Lyapunov functionals, under suitable assumptions, we establish a general energy decay result from which the exponential and polynomial types of decay are only special cases.Comment: 11 page

Solitons in tunnel-coupled repulsive and attractive condensates

We study solitons in the condensate trapped in a double-well potential with far-separated wells, when the s-wave scattering length has different signs in the two parts of the condensate. By employing the coupled-mode approximation it is shown that there are unusual stable bright solitons in the condensate, with the larger share of atoms being gathered in the repulsive part. Such unusual solitons derive their stability from the quantum tunneling and correspond to the strong coupling between the parts of the condensate. The ground state of the system, however, corresponds to weak coupling between the condensate parts, with the larger share of atoms being gathered in the attractive part of the condensate.Comment: LaTex, 23 pages, 6 figures; revised version; to appear in Physical Review

Vandermonde-subspace Frequency Division Multiplexing for Two-Tiered Cognitive Radio Networks

Vandermonde-subspace frequency division multiplexing (VFDM) is an overlay spectrum sharing technique for cognitive radio. VFDM makes use of a precoder based on a Vandermonde structure to transmit information over a secondary system, while keeping an orthogonal frequency division multiplexing (OFDM)-based primary system interference-free. To do so, VFDM exploits frequency selectivity and the use of cyclic prefixes by the primary system. Herein, a global view of VFDM is presented, including also practical aspects such as linear receivers and the impact of channel estimation. We show that VFDM provides a spectral efficiency increase of up to 1 bps/Hz over cognitive radio systems based on unused band detection. We also present some key design parameters for its future implementation and a feasible channel estimation protocol. Finally we show that, even when some of the theoretical assumptions are relaxed, VFDM provides non-negligible rates while protecting the primary system.Comment: 9 pages, accepted for publication in IEEE Transactions on Communication

Uniform semiclassical approximation in quantum statistical mechanics

We present a simple method to deal with caustics in the semiclassical approximation to the partition function of a one-dimensional quantum system. The procedure, which makes use of complex trajectories, is applied to the quartic double-well potential.Comment: 5 pages, 1 figure, Latex. Contribution to the Proceedings of the XXI Brazilian National Meeting on Particles and Fields (Sao Lourenco, October 23-27, 2000

Multipartite entanglement percolation

We present percolation strategies based on multipartite measurements to propagate entanglement in quantum networks. We consider networks spanned on regular lattices whose bonds correspond to pure but non-maximally entangled pairs of qubits, with any quantum operation allowed at the nodes. Despite significant effort in the past, improvements over naive (classical) percolation strategies have been found for only few lattices, often with restrictions on the initial amount of entanglement in the bonds. In contrast, multipartite entanglement percolation outperform the classical percolation protocols, as well as all previously known quantum ones, over the entire range of initial entanglement and for every lattice that we considered.Comment: revtex4, 4 page