Non-Hermitian photonic lattices combine the peculiar consequences of energy non-conservation with physics bandstructures, giving rise to a variety exotic properties not found in conventional materials or metamaterials. In this tutorial, we introduce key concepts design and implementation non-Hermitian lattices, including general features lattice Hamiltonians their role symmetries, topological c...

The paper deals with special types of $L$-ordered sets, $L$-fuzzy complete lattices, and fuzzy directed complete posets.First, a theorem for constructing monotone maps is proved, a characterization for monotone maps on an $L$-fuzzy complete lattice is obtained, and it's proved that if $f$ is a monotone map on an $L$-fuzzy complete lattice $(P;e)$, then the least fixpoint of $f$ is meet of a spe...

We propose a definition for the entropy of capacities defined on lattices. Classical capacities are monotone set functions and can be seen as a generalization of probability measures. Capacities on lattices address the general case where the family of subsets is not necessarily the Boolean lattice of all subsets. Our definition encompasses the classical definition of Shannon for probability mea...

We study localized traveling waves and chaotic states in strongly nonlinear one-dimensional Hamiltonian lattices. We show that the solitary waves are superexponentially localized and present an accurate numerical method allowing one to find them for an arbitrary nonlinearity index. Compactons evolve from rather general initially localized perturbations and collide nearly elastically. Neverthele...

We investigate the dispersion curves of coupled waveguides in hexagonal lattices. We show that hexagonal PCW lattices have coupling coefficients that change magnitude and sign along the BZ. It is also shown that the modes of these structures no longer form odd and even modes but are superposed in a more general sense. OCIS codes: (130.5296) Photonic crystal waveguides; (130.2790) Guided waves; ...

In this paper we study representations of conformal nets associated with positive definite even lattices and their orbifolds with respect to isometries of the lattices. Using previous general results on orbifolds, we give a list of all irreducible representations of the orbifolds, which generate a unitary modular tensor category. 2000MSC:81R15, 17B69. Supported in part by NSF and a research gra...

We relate notions of complementarity in three layers of quantum mechanics: (i) von Neumann algebras, (ii) Hilbert spaces, and (iii) orthomodular lattices. Taking a more general categorical perspective of which the above are instances, we consider dagger monoidal kernel categories for (ii), so that (i) become (sub)endohomsets and (iii) become subobject lattices. By developing a ‘point-free’ defi...

By examining the behaviour of the “SLAC” lattice derivative operators, it is found that lattices with an even number of sites have a somewhat strange self-consistency requirement for extra structure in the spatial derivative operator, which is not needed by lattices having an odd number of sites, and which is not at all obvious from a firstprinciples derivation. The general implications of this...

To express wider uncertainty, B?hounek and Da?ková studied fuzzy partial logic function. At the same time, Borzooei generalized t-norms put forward concept of when studying lattice valued quantum effect algebras. Based on t-norms, Zhang et al. residuated implications (PRIs) proposed lattices (PRLs). In this paper, we mainly study related algebraic structure logic. First, provide definitions reg...

Based on the notion of $Q$-sup-lattices (a fuzzy counterpart of complete join-semilattices valuated in a commutative quantale), we present the concept of $Q$-sup-algebras -- $Q$-sup-lattices endowed with a collection of finitary operations compatible with the fuzzy joins. Similarly to the crisp case investigated in cite{zhang-laan}, we characterize their subalgebras and quotients, and following...