Screened Coulomb interaction in insulators with strong disorder.

We study the effect of disorder on the excitons in a semiconductor with screened Coulomb interaction. Examples are polymeric semiconductors and/or van der Waals structures. In the screened hydrogenic problem, we consider the disorder phenomenologically using the so-called fractional Scrödinger equation. Our main finding is that joint action of screening and disorder either destroys the exciton (strong screening) or enhances the bounding of electron and hole in an exciton, leading to its collapse in the extreme case. Latter effects may also be related to the quantum manifestations of chaotic exciton behavior in the above semiconductor structures. Hence, they should be considered in device applications, where the interplay between dielectric screening and disorder is important. Our theoretical results permit one to predict the various excitonic properties in semiconductor samples with different degrees of disorder and Coulomb interaction screenings.

1D solitons in cubic-quintic fractional nonlinear Schrödinger model.

We examine the properties of a soliton solution of the fractional Schrö dinger equation with cubic-quintic nonlinearity. Using analytical (variational) and numerical arguments, we have shown that the substitution of the ordinary Laplacian in the Schrödinger equation by its fractional counterpart with Lévy index [Formula: see text] permits to stabilize the soliton texture in the wide range of its parameters (nonlinearity coefficients and [Formula: see text]) values. Our studies of [Formula: see text] dependence ([Formula: see text] is soliton frequency and N its norm) permit to acquire the regions of existence and stability of the fractional soliton solution. For that we use famous Vakhitov-Kolokolov (VK) criterion. The variational results are confirmed by numerical solution of a one-dimensional cubic-quintic nonlinear Schrödinger equation. Direct numerical simulations of the linear stability problem of soliton texture gives the same soliton stability boundary as within variational method. Thus we confirm that simple variational approach combined with VK criterion gives reliable information about soliton structure and stability in our model. Our results may be relevant to both optical solitons and Bose-Einstein condensates in cold atomic gases.

Stabilization of 1D solitons by fractional derivatives in systems with quintic nonlinearity.

We study theoretically the properties of a soliton solution of the fractional Schrödinger equation with quintic nonlinearity. Under "fractional" we understand the Schrödinger equation, where ordinary Laplacian (second spatial derivative in 1D) is substituted by its fractional counterpart with Lévy index [Formula: see text]. We speculate that the latter substitution corresponds to phenomenological account for disorder in a system. Using analytical (variational and perturbative) and numerical arguments, we have shown that while in the case of Schrödinger equation with the ordinary Laplacian (corresponding to Lévy index [Formula: see text]), the soliton is unstable, even infinitesimal difference [Formula: see text] from 2 immediately stabilizes the soliton texture. Our analytical and numerical investigations of [Formula: see text] dependence ([Formula: see text] is soliton frequency and N its mass) show (within the famous Vakhitov-Kolokolov criterion) the stability of our soliton texture in the fractional [Formula: see text] case. Direct numerical analysis of the linear stability problem of soliton texture also confirms this point. We show analytically and numerically that fractional Schrödinger equation with quintic nonlinearity admits the existence of (stable) soliton textures at [Formula: see text], which is in accord with existing literature data. These results may be relevant to both Bose-Einstein condensates in cold atomic gases and optical solitons in the disordered media.

Lévy distributions and disorder in excitonic spectra.

We study analytically the spectrum of excitons in disordered semiconductors like transition metal dichalcogenides, which are important for photovoltaic and spintronic applications. We show that ambient disorder exerts a strong influence on the exciton spectra. For example, in such a case, the well-known degeneracy of the hydrogenic problem (related to Runge-Lenz vector conservation) is lifted so that the exciton energy starts to depend on both the principal quantum number n and orbital l. We model the disorder phenomenologically substituting the ordinary Laplacian in the corresponding Schrödinger equation by the fractional one with Lévy index µ, characterizing the degree of disorder. Our variational treatment (corroborated by numerical results) shows that an exciton exists for 1 < µ≤ 2. The case µ = 2 corresponds to the "ordered" hydrogenic problem, while in the opposite case µ = 1 the exciton collapses. The exciton spectrum is dominated by the sample areas with moderate disorder. Our theory permits controlled predictions to be made of the excitonic properties in semiconductor samples with different degrees of disorder.

Experimental and theoretical Stark broadening studies of the hydrogen Paschen beta line.

Experimental and theoretical Stark broadening studies of the Paschen beta line of hydrogen (lambda=1.28 microm) are reported. Line shape measurements were performed at electron densities of the plasma between 3.5 x 10(15) cm(-3) and 7.5 x 10(15) cm(-3), applying as the light source a wall-stabilized arc operated at atmospheric pressure in a helium-hydrogen gas mixture. The radiation of the plasma, emitted from nearly homogeneous plasma layers in the end-on direction, was registered with the use of a grating spectrometer equipped with a charge coupled device detector. The measured light outputs were calibrated against signals obtained from a tungsten strip radiation standard. The experimentally determined line profiles are compared with results of new Stark broadening calculations based on simulation techniques. The measured broadening, shift, and asymmetry parameters are also compared with results of previous Stark broadening calculations and other experimental data obtained at electron densities higher as well as lower than ours.