Metric-signature topological transitions in dispersive metamaterials.

The metric signature topological transitions associated with the propagation of electromagnetic waves in a dispersive metamaterial with frequency-dependent and anisotropic dielectric and magnetic responses are examined in the present work. The components of the reciprocal-space metric tensor depend upon both the electric permittivity and magnetic permeability of the metamaterial, which are taken as Drude-like dispersive models. A thorough study of the frequency dependence of the metric tensor is presented which leads to the possibility of topological transitions of the isofrequency surface determining the wave dynamics inside the medium, to a diverging photonic density of states at some range of frequencies, and to the existence of large wave vectors' modes propagating through the metamaterial.

Plasmon polaritons in photonic metamaterial superlattices: absorption effects.

We discuss the propagation of electromagnetic waves in layered structures made up of alternate layers of air and metamaterials. The role played by absorption on the existence of electric and magnetic plasmon polaritons is investigated. Results show that plasmon-polariton modes are robust even in the presence of rather large absorption.

Functional density matrix formulation of quantum statistics.

We present a unified formulation for quantum statistical physics based on the representation of the density matrix as a functional integral. For quantum statistical (thermal) field theory, the stochastic variable of the statistical theory is a boundary field configuration. We explore the properties of an effective theory for such boundary configurations and apply it to the computation of the partition function of an interacting one-dimensional quantum-mechanical system at finite temperature. Plots of free energy and specific heat show excellent agreement with more involved semiclassical results. The method of calculation provides an alternative to the usual sum over periodic trajectories: it sums over paths with coincident end points and includes nonvanishing boundary terms. An appropriately modified expansion into modified Matsubara modes is presented.

Absorption effects on plasmon polaritons in quasiperiodic photonic superlattices containing a metamaterial.

Absorption effects on plasmon-polariton excitations in quasiperiodic (Fibonacci and Thue-Morse) one-dimensional stacks composed of layers of right- and left-handed materials are theoretically investigated. A Drude-type dispersive response for both the dielectric permittivity and magnetic permeability of the left-handed layer is considered. Maxwell's equations are solved for oblique incidence by using the transfer matrix formalism, and the reflection coefficient as a function of the frequency and incidence angle is obtained. The Fibonacci (or Thue-Morse) quasiperiodic structure leads to a Cantor-like photonic spectra for the plasmon-polariton modes. Moreover, results for the photonic band structure, density of states and reflection coefficient indicate that plasmon-polariton modes are robust in the presence of low and moderate levels of absorption.

Improved semiclassical density matrix: taming caustics.

We present a simple method to deal with caustics in the semiclassical approximation to the thermal density matrix of a particle moving on the line. For simplicity, only its diagonal elements are considered. The only ingredient we require is the knowledge of the extrema of the Euclidean action. The procedure makes use of complex trajectories, and is applied to the quartic double-well potential.