Initial value problem of the Whitham equations for the Camassa-Holm equation

We study the Whitham equations for the Camassa-Holm equation. The equations are neither strictly hyperbolic nor genuinely nonlinear. We are interested in the initial value problem of the Whitham equations. When the initial values are given by a step function, the Whitham solution is self-similar. When the initial values are given by a smooth function, the Whitham solution exists within a cusp in the x-t plane. On the boundary of the cusp, the Whitham solution matches the Burgers solution, which exists outside the cusp.     

Andreev states near short-ranged pairing potential impurities

We study Andreev states near atomic scale modulations in the pairing potential in both s- and d-wave superconductors with short coherence lengths. For a moderate reduction of the local gap, the states exist only close to the gap edge. If one allows for local sign changes of the order parameter, however, resonances can occur at energies close to the Fermi level. The local density of states (LDOS) around such pairing potential defects strongly resembles the patterns observed by tunneling measurements around Zn impurities in Bi2Sr2CaCu2O8+x (BSCCO). We discuss how this phase impurity model of the Zn LDOS pattern can be distinguished from other proposals experimentally.     

Surface Polaritons in GaAs/CdTe/PbTe Multilayer Structures

JETP Letters - Infrared spectra of reflection and attenuated total reflection of PbTe thin films deposited by molecular beam epitaxy on a GaAs/CdTe substrate have been measured. The high-frequency...     

Manifestation of outgoing resonance in stokes and anti-stokes spectra of ZnTe and ZnMgTe quantum wires

The spectra of resonant light scattering by ZnTe quantum wires have been measured at excitation energies of 2.18–2.72 eV. The quantum wires have been grown on Si(100) and GaAs(100) substrates by molecular beam epitaxy. The effect of outgoing resonance with the electron transition energy E ₀ on the intensity of phonon lines of the Stokes spectrum and on the intensity ratio of the Stokes and anti-Stokes spectral lines has been studied. The energy E ₀ has been determined in ZnTe and ZnMgTe quantum wires from the edge luminescence spectra.     

Design of two-dimensional random surfaces with specified scattering properties

A method is proposed for designing a two-dimensional randomly rough Dirichlet surface that, when illuminated at normal incidence, scatters a scalar plane wave with a specified angular distribution of its intensity. The method is validated by computer simulation calculations.     

Recording and decay of transient gratings in a system of saturable three-level centers

The kinetics of formation and relaxation of transient holographic gratings recorded in a system of saturable three-level centers is studied. Distortions in the shape of the profile of recorded and decaying structures of population and of the refractive index are taken into account. The analysis of the time dependences of diffraction efficiencies of different orders is performed for phase (thermal) and amplitude (concentration) gratings.     

The role of interdiffusion and spatial confinement in the formation of resonant raman spectra of Ge/Si(100) heterostructures with quantum-dot arrays

The phonon modes of self-assembled Ge/Si quantum dots grown by molecular-beam epitaxy in an apparatus integrated with a chamber of the scanning tunneling microscope into a single high-vacuum system are investigated using Raman spectroscopy. It is revealed that the Ge-Ge and Si-Ge vibrational modes are considerably enhanced upon excitation of excitons between the valence band Λ₃ and the conduction band Λ₁ (the E ₁ and E ₁ + Δ₁ transitions). This makes it possible to observe the Raman spectrum of very small amounts of germanium, such as one layer of quantum dots with a germanium layer thickness of ≈10 Å. The enhancement of these modes suggests a strong electron-phonon interaction of the vibrational modes with the E ₁ and E ₁ + Δ₁ excitons in the quantum dot. It is demonstrated that the frequency of the Ge-Ge mode decreases by 10 cm^?1 with a decrease in the thickness of the Ge layer from 10 to 6 Å due to the spatial-confinement effect. The optimum thickness of the Ge layer for which the size dispersion of quantum dots is minimum is determined.     

Influence of the thickness of CdTe and ZnTe layers on cathodoluminescence spectra of strained CdTe/ZnTe superlattices with quantum-dot layers

The influence of the thickness of ZnTe barrier layers on the cathodoluminescence spectra of strained CdTe/ZnTe superlattices containing layers of quantum dots with an average lateral size of approximately 3 nm has been investigated. In samples with thick barrier layers (30, 15 nm), the cathodoluminescence spectra of quantum dots exhibit one band with a maximum at E = 2.03 eV. It has been revealed that, at a barrier layer thickness of ∼3 nm, the luminescence band is split. However, at a ZnTe layer thickness of 1.5 nm, the luminescence spectrum also contains one band. The experimental results have been interpreted with allowance made for the influence of elastic biaxial strains on the energy states of light and heavy holes in the CdTe and ZnTe layers. For the CdTe/ZnTe heterostructure with quantum dots in which the thickness of the deposited CdTe layer is 1.5 monolayers and the thickness of the barrier layer is 100 monolayers, the cathodoluminescence spectrum contains 2LO-phonon replicas. This effect has been explained by the resonance between two-phonon LO states and the difference between the energy states in the electronic spectrum of wetting layer fragments.     

From the Solution of the Tsarev System to the Solution of the Whitham Equations

We study the Cauchy problem for the Whitham modulation equations for increasing smooth initial data. The Whitham equations are a collection of one-dimensional quasi-linear hyperbolic systems. This collection of systems is enumerated by the genus g=0,1,2, ... of the corresponding hyperelliptic Riemann surface. Each of these systems can be integrated by the so-called hodograph transformation introduced by Tsarev. A key step in the integration process is the solution of the Tsarev linear overdetermined system. For each g>0, we construct the unique solution of the Tsarev system, which matches the genus g+1 and g–1 solutions on the transition boundaries.