Indifferent electromagnetic modes: bound states and topology

At zero energy the Dirac equation has interesting behaviour. The asymmetry in the number of spin up and spin down modes is determined by the topology of both space and the gauge field in which the system sits. An analogous phenomenon also occurs in electromagnetism. Writing Maxwell's equations in a Dirac-like form, we identify cases where a material parameter plays the role of energy. At zero energy we thus find electromagnetic modes that are indifferent to local changes in the material parameters, depending only on their asymptotic values at infinity. We give several examples, and show that this theory has implications for non-Hermitian media, where it can be used to construct permittivity profiles that are either reflectionless, or act as coherent perfect absorbers, or lasers.Comment: 10 pages, 6 figure

Unidirectional wave propagation in media with complex principal axes

In an anisotropic medium, the refractive index depends on the direction of propagation. Zero index in a fixed direction implies a stretching of the wave to uniformity along that axis, reducing the effective number of dimensions by one. Here we investigate two dimensional gyrotropic media where the refractive index is zero in a complex valued direction, finding that the wave becomes an analytic function of a single complex variable z. For simply connected media this analyticity implies unidirectional propagation of electromagnetic waves, similar to the edge states that occur in photonic 'topological insulators'. For a medium containing holes the propagation is no longer unidirectional. We illustrate the sensitivity of the field to the topology of the space using an exactly solvable example. To conclude we provide a generalization of transformation optics where a complex coordinate transformations can be used to relate ordinary anisotropic media to the recently highlighted gyrotropic ones supporting one-way edge states.Comment: 21 pages, 4 figure

Transport Coefficients of Quark Gluon Plasma for Pure Gauge Models

The transport coefficients of quark gluon plasma are calculated on a lattice 16**3X8, with the pure gauge models. Matsubara Green's functions of energy momentum tensors have very large fluctuations and about a few million MC sweeps are needed to reduce the errors reasonably small in the case of the standard action. They are much suppressed if Iwasaki's improved action is employed. Preliminary results show that the transport coefficients roughly depend on the coupling constant as a**(-3)(g) in the case of SU(2).Comment: Talk presented at LATTICE96(finite temperature), 3 pages in latex, 4 Postscript figure