Exciton spectra in disordered quantum wells.

We study the effects of disorder on the exciton spectra in quantum well (QW) semiconductor structures. We model the disorder by introducing the fractional Laplacian into the Schrödinger equations, which describe the exciton spectra of the above QW structures. We calculate the exciton binding energies in its ground state and a few low-lying excited states as a function of the GaAs QW size.

Quantum chaotic features of the spin-orbit coupled excitons in disordered two-dimensional insulators.

We study the synergy between disorder (phenomenologically modeled by the introduction of Riesz fractional derivative in the corresponding Schrödinger equation) and spin-orbit coupling (SOC) on the exciton spectra in two-dimensional (2D) semiconductor structures. We demonstrate that the joint impact of "fractionality" and SOC considerably modifies the spectrum of corresponding "ordinary" (i.e.

Spin-orbit-coupled fractional oscillators and trapped Bose-Einstein condensates.

We study the ensemble of pseudo-spin 1/2 ultracold bosons, performing Lévy flights, confined in a parabolic potential. The (pseudo-) spin-orbit coupling (SOC) is additionally imposed on these particles. We consider the structure and dynamics of macroscopic pseudospin qubits based on Bose-Einstein condensates, obtained from the above "fractional" bosons.

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.

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.