RESUMEN
We revisit the problem of constructing one-dimensional acoustic black holes. Instead of considering the Euler-Bernoulli beam theory, we use Timoshenko's approach, which is known to be more realistic at higher frequencies. Our goal is to minimize the reflection coefficient under a constraint imposed on the normalized wavenumber variation. We use the calculus of variations to derive the corresponding Euler-Lagrange equation analytically and then use numerical methods to solve this equation to find the "optimal" height profile for different frequencies. We then compare these profiles to the corresponding ones previously found using the Euler-Bernoulli beam theory and see that in the lower range of the dimensionless frequency Ω (defined using the largest height of the plate), the optimal profiles almost coincide, as expected.
RESUMEN
The Stark effect in confined geometries is sensitive to boundary conditions. The vanishing wave function required on the boundary of nanostructures described by the infinite-barrier Schrödinger equation means that such states are only weakly polarizable. In contrast, materials described by the Dirac equation are characterized by much less restrictive boundary conditions. Focusing on honeycomb-lattice armchair nanoribbons, we demonstrate an enhancement by more than an order of magnitude. This result follows from an exact Dirac polarizability valid for arbitrary mass, momentum and ribbon width. Moreover, an exact expression for the frequency-dependent dynamic polarizability has been derived. Our analytic Dirac results have been validated by comparison to numerical results from atomistic models.
RESUMEN
Calculus of variations is used to determine a profile shape for an acoustic black hole without a layer of viscoelastic dampening material with fixed parameters of geometry (i.e., length, maximal and minimal thickness), which minimizes the reflection coefficient, without violating the underlying assumptions of existence for acoustic black holes. The additional constraint imposed by keeping the normalized wave number variation (NWV) small everywhere in the acoustic black hole is handled by the use of Lagrange multipliers. From this method, closed-form expressions for the optimal profile, its reflection coefficient, and the NWV are derived. Additionally, it is shown that in the special case where only the NWV (and not the reflection coefficient) is considered, the optimal profile reduces to the well-known thickness profile for acoustic black holes, h(x)=ϵx2. We give a numerical example of the difference between an acoustic black hole with optimal profile and classical profile, h(x)=ϵxm, m > 2. For close to identical reflection coefficients, the optimal profile vastly outperforms the classical profile in terms of having low NWV at a large range of frequencies.
RESUMEN
The linear optical properties of semiconducting carbon nanotubes are dominated by quasi-one-dimensional excitons formed by single electron-hole pairs. Hence, the nonlinear response at high pump levels most likely leads to the formation of exciton complexes involving several electron-hole pairs. Such complexes would therefore play an important role in, e.g., lasing applications. We demonstrate here that the biexciton complex is surprisingly stable for nanotubes in a wide diameter range. Theoretical predictions for the signature of such states in pump-probe spectroscopy are presented.
