C. A. A. de Carvalho

Plasmon polaritons in photonic superlattices containing a left-handed material

We analyze one-dimensional photonic superlattices which alternate layers of air and a left-handed material. We assume Drude-type dispersive responses for the dielectric permittivity and magnetic permeability of the left-handed material. Maxwells equations and the transfer-matrix technique are used to derive the dispersion relation and transmission spectra for the propagation of obliquely incident optical fields. The photonic dispersion indicates that the growth direction component of the electric (or magnetic) field leads to the propagation of electric (or magnetic) plasmon polaritons, for either TE or TM configurations. Furthermore, we show that if the plasma frequency is chosen within the photonic n(ω)=0 zeroth-order bandgap, the coupling of light with plasmons weakens considerably. As light propagation is forbidden in that particular frequency region, the plasmon-polariton mode reduces to a pure plasmon mode.

Semiclassical Series at Finite Temperature

Abstract We derive the semiclassical series for the partition function of a one-dimensional quantum-mechanical system consisting of a particle in a single-well potential. We do this by applying the method of steepest descent to the path-integral representation of the partition function, and we present a systematic procedure to generate the terms of the series using the minima of the Euclidean action as the only input. For the particular case of a quartic anharmonic oscillator, we compute the first two terms of the series, and investigate their high and low temperature limits. We also exhibit the nonperturbative character of the terms, as each corresponds to sums over infinite subsets of perturbative graphs. We illustrate the power of such resummations by extracting from the first term an accurate nonperturbative estimate of the ground-state energy of the system and a curve for the specific heat. We conclude by pointing out possible extensions of our results which include field theories with spherically symmetric classical solutions.

Tunneling Catastrophes of the Partition Function

We use path-integrals to derive a general expression for the semiclassical approximation to the partition function of a one-dimensional quantum-mechanical system. Our expression depends solely on ordinary integrals which involve the potential. For high temperatures, the semiclassical expression is dominated by single closed paths. As we lower the temperature, new closed paths may appear, including tunneling paths. The transition from single to multiple-path regime corresponds to well-defined catastrophes. Tunneling sets in whenever they occur. Our formula fully accounts for this feature

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. Maxwells 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.

ELECTRON LOCALIZATION BY A MAGNETIC VORTEX

We study the problem of an electron in two dimensions in the presence of a magnetic vortex with a step-like profile. Dependending on the values of the effective mass and gyromagnetic factor of the electron, it may be trapped by the vortex. The bound state spectrum is obtained numerically, and some limiting cases are treated analytically.

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.

Focal decomposition, renormalization and semiclassical physics

We review some recent results concerning a connection between focal decomposition, renormalization and semiclassical physics. The dynamical behaviour of a family of mechanical systems which includes the pendulum at small neighbourhoods of the equilibrium but after long intervals of time can be characterized through a renormalization scheme acting on the dynamics of this family. We have proved that the asymptotic limit of this renormalization scheme is universal: it is the same for all the elements in the considered class of mechanical systems. As a consequence, we have obtained an asymptotic universal focal decomposition for this family of mechanical systems which can now be used to compute estimates for propagators in semiclassical physics.

Polarons as nucleation droplets in nondegenerate polymers

We present a study of the nucleation mechanism that allows the decay of the metastable phase (trans-cisoid) to the stable phase (cis-transoid) in quasi-one-dimensional nondegenerate polymers within the continuum electron-phonon model. The electron-phonon configurations that lead to the decay, i.e., the critical droplets (or transition state), are identified as polarons of the metastable phase. We obtain an estimate for the decay rate via thermal activation within a range of parameters consistent with experimental values for the gap of the cis configuration. It is pointed out that, upon doping, the activation barriers of the excited states are quite smaller and the decay rate is greatly enhanced. Typical activation energies for electron or hole polarons are \ensuremath{\approxeq}0.1 eV and the typical size for a critical droplet (polaron) is about 20 \AA{}. Decay via quantum nucleation is also studied and it is found that the crossover temperature between quantum nucleation and thermal activation is of order

The electromagnetic response of a relativistic Fermi gas at finite temperatures: Applications to condensed-matter systems

{\mathit{T}}_{\mathit{c}}

An asymptotic universal focal decomposition for non-isochronous potentials

\ensuremath{\le}40 K. Metastable configurations of nondegenerate polymers may provide examples for mesoscopic quantum tunneling.