Comment on "Wave Refraction in Negative-Index Materials: Always Positive and Very Inhomogeneous"
Wave refraction in negative-index media is always negative.
cond-mat↗
arXiv subjects
W. T. Lu
Publications and source records attributed to W. T. Lu.
Sinai billiards, Ruelle zeta-functions and Ruelle resonances: microwave experiments
We discuss the impact of recent developments in the theory of chaotic dynamical systems, particularly the results of Sinai and Ruelle, on microwave experiments designed to study quantum chaos. The properties of closed Sinai billiard microwave cavities are discussed in terms of universal predictions from random matrix theory, as well as periodic orbit contributions which manifest as `scars' in eigenfunctions. The semiclassical and classical Ruelle zeta-functions lead to quantum and classical resonances, both of which are observed in microwave experiments on n-disk hyperbolic billiards.
nlin.CD↗
Dimer statistics on the Möbius strip and the Klein bottle
Closed-form expressions are obtained for the generating function of close-packed dimers on a $2M \times 2N$ simple quartic lattice embedded on a Möbius strip and a Klein bottle. Finite-size corrections are also analyzed and compared with those under cylindrical and free boundary conditions. Particularly, it is found that, for large lattices of the same size and with a square symmetry, the number of dimer configurations on a Möbius strip is 70.2% of that on a cylinder. We also establish two identities relating dimer generating functions for Möbius strips and cylinders.
cond-mat.stat-mech↗
On the rooted Tutte polynomial
The Tutte polynomial is a generalization of the chromatic polynomial of graph colorings. Here we present an extension called the rooted Tutte polynomial, which is defined on a graph where one or more vertices are colored with prescribed colors. We establish a number of results pertaining to the rooted Tutte polynomial, including a duality relation in the case that all roots reside around a single face of a planar graph. The connection with the Potts model is also reviewed.
cond-mat.stat-mech↗