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Register a new userDiscrete solitons in zigzag waveguide arrays with different types of linear mixing between nearest-neighbor and next-nearest-neighbor couplings
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We study discrete solitons in zigzag discrete waveguide arrays with different types of linear mixing between nearest-neighbor and next-nearest-neighbor couplings. The waveguide array is constructed from two layers of one-dimensional (1D) waveguide arrays arranged in zigzag form. If we alternately label the number of waveguides between the two layers, the cross-layer couplings (which couple one waveguide in one layer with two adjacent waveguides in the other layer) construct the nearestneighbor couplings, while the couplings that couple this waveguide with the two nearest-neighbor waveguides in the same layer, i.e., self-layer couplings, contribute the next-nearest-neighbor couplings. Two families of discrete solitons are found when these couplings feature different types of linear mixing. As the total power is increased, a phase transition of the second kind occurs for discrete solitons in one type of setting, which is formed when the nearest-neighbor coupling and next-nearest-neighbor coupling feature positive and negative linear mixing, respectively. The mobilities and collisions of these two families of solitons are discussed systematically throughout the paper, revealing that the width of the soliton plays an important role in its
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Random walks including non-nearest-neighbor jumps appear in many real situations such as the diffusion of adatoms and have found numerous applications including PageRank search algorithm, however, related theoretical results are much less for this dynamical process. In this paper, we present a study of mixed random walks in a family of fractal scale-free networks, where both nearest-neighbor and next-nearest-neighbor jumps are included. We focus on trapping problem in the network family, which is a particular case of random walks with a perfect trap fixed at the central high-degree node. We derive analytical expressions for the average trapping time (ATT), a quantitative indicator measuring the efficiency of the trapping process, by using two different methods, the results of which are consistent with each other. Furthermore, we analytically determine all the eigenvalues and their multiplicities for the fundamental matrix characterizing the dynamical process. Our results show that although next-nearest-neighbor jumps have no effect on the leading sacling of the trapping efficiency, they can strongly affect the prefactor of ATT, providing insight into better understanding of random-walk process in complex systems.
We calculate the local Green function for a quantum-mechanical particle with hopping between nearest and next-nearest neighbors on the Bethe lattice, where the on-site energies may alternate on sublattices. For infinite connectivity the renormalized perturbation expansion is carried out by counting all non-self-intersecting paths, leading to an implicit equation for the local Green function. By integrating out branches of the Bethe lattice the same equation is obtained from a path integral approach for the partition function. This also provides the local Green function for finite connectivity. Finally, a recently developed topological approach is extended to derive an operator identity which maps the problem onto the case of only nearest-neighbor hopping. We find in particular that hopping between next-nearest neighbors leads to an asymmetric spectrum with additional van-Hove singularities.
It is well known that for linear Gaussian channels, a nearest neighbor decoding rule, which seeks the minimum Euclidean distance between a codeword and the received channel output vector, is the maximum likelihood solution and hence capacity-achieving. Nearest neighbor decoding remains a convenient and yet mismatched solution for general channels, and the key message of this paper is that the performance of the nearest neighbor decoding can be improved by generalizing its decoding metric to incorporate channel state dependent output processing and codeword scaling. Using generalized mutual information, which is a lower bound to the mismatched capacity under independent and identically distributed codebook ensemble, as the performance measure, this paper establishes the optimal generalized nearest neighbor decoding rule, under Gaussian channel input. Several suboptimal but reduced-complexity generalized nearest neighbor decoding rules are also derived and compared with existing solutions. The results are illustrated through several case studies for channels with nonlinear effects, and fading channels with receiver channel state information or with pilot-assisted training.
The subject of this paper are operators represented on Fock spaces whose behavior on one level depends only on two of its neighbors. Our initial objective was to generalize (via a common framework) the results of arXiv:math/0702158, arXiv:0709.4334, arXiv:0812.0895, and arXiv:1003.2998, whose constructions exhibited this behavior. We extend a number of results from these papers to our more general setting. These include the quadratic relation satisfied by the free cumulant generating function (actually by a variant of it), the resolvent form of the generating function for the Wick polynomials, and classification results for the case when the vacuum state on the operator algebra is tracial. We are able to handle the generating functions in infinitely many variables by considering their matrix-valu
We calculate the quantum phase diagram of the {it XXZ} chain with nearest-neighbor (NN) $J_{1}$ and next-NN exchange $J_{2}$ with anisotropies $Delta_{1}$ and $Delta_{2}$ respectively. In particular we consider the case $Delta_{1}=-Delta_{2}$ to interpolate between the {it XX} chain ($% Delta_{i}=0$) and the isotropic model with ferromagnetic $J_{2}$. For $% Delta_{1}<-1$, a ferromagnetic and two antiferromagnetic phases exist. For $| Delta_{i}| <1$, the boundary between the dimer and spin fluid phases is determined by the method of crossing of excitation spectra. For large $J_{2}/J_{1}$, this method seems to indicate the existence of a second spin fluid critical phase. However, an analysis of the spin stiffness and magnetic susceptibility for $Delta_{1}=Delta_{2}=1$ suggest that a small gap is present.
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