We formulate the topological characteristics of lattice Dirac operators in the context of the index and the chiral anomaly, and illustrate this concept by explicit examples. PACS numbers: 11.15.Ha, 11.30.Rd, 11.30.Fs In continuum, the Dirac operator of massless fermions in a smooth background gauge field with nonzero topological charge Q has zero eigenvalues and the corresponding eigenfunctions...

We realize an experimental control over the topological stability of three-lobe discrete vortex solitons by modifying the symmetry of a hexagonal photonic lattice optically induced in a photorefractive crystal. By continuously deforming the lattice wave in one transverse direction, we manipulate the coupling between lattice sites and induce or inhibit the reversal of soliton vorticity.

Let E be a Banach lattice and let M be a norm-closed and Dedekind σ-complete ideal of E. If E contains a lattice-isometric copy of ∞ , then E/M contains such a copy as well, or M contains a lattice copy of ∞. This is one of the consequences of more general results presented in this paper. 1. Introduction. Let E be a locally solid linear lattice (Riesz space), for example , a Banach lattice, let...

In theoretical chemistry, -modified Wiener index is a graph invariant topological index to analyze the chemical properties of molecular structure. In this note, we determine the minimum -modified Wiener index of graph with fixed connectivity or edge-connectivity. Our results also present the sufficient and necessary condition for reaching the lower bound.

We construct the Wess-Zumino-Witten (WZW) term in lattice gauge theory by using a Dirac operator which obeys the Ginsparg-Wilson relation. Topological properties of the WZW term known in the continuum are reproduced on the lattice as a consequence of a non-trivial topological structure of the space of admissible lattice gauge fields. In the course of this analysis, we observe that the gauge ano...

The index bundle of the Overlap lattice Dirac operator over the orbit space of lattice gauge fields is introduced and studied. Obstructions to the vanishing of gauge anomalies in the Overlap formulation of lattice chiral gauge theory have a natural description in this context. Our main result is a formula for the topological charge (Pontryargin number) of the index bundle over evendimensional s...

The index bundle of the Overlap lattice Dirac operator over the orbit space of lattice gauge fields is introduced and studied. Obstructions to the vanishing of gauge anomalies in the Overlap formulation of lattice chiral gauge theory have a natural description in this context. Our main result is a formula for the topological charge (integrated Chern character) of the index bundle over evendimen...

The index bundle of the Overlap lattice Dirac operator over the orbit space of lattice gauge fields is introduced and studied. Obstructions to the vanishing of gauge anomalies in the Overlap formulation of lattice chiral gauge theory have a natural description in this context. Our main result is a formula for the topological charge (Pontryargin number) of the index bundle over evendimensional s...

The influence of topological constraints on the local dynamics in crosslinked polymer melts and their contribution to the elastic properties of rubber elastic systems are long standing problems in statistical mechanics. Polymer networks with diamond lattice connectivity are idealized model systems which isolate the effect of topology conservation from other sources of quenched disorder. By stud...