Quantum Harmonic Oscillators with Nonlinear Effective Masses in the weak density approximation

We study the eigen-energy and eigen-function of a quantum particle acquiring the probability density-dependent effective mass (DDEM) in harmonic oscillators. Instead of discrete eigen-energies, continuous energy spectra are revealed due to the introduction of a nonlinear effective mass. Analytically, we map this problem into an infinite discrete dynamical system and obtain the stationary solutions in the weak density approximation, along with the proof on the monotonicity in the perturbed eigen-energies. Numerical results not only give agreement to the asymptotic solutions stemmed from the expansion of Hermite-Gaussian functions, but also unveil a family of peakon-like solutions without linear counterparts. As nonlinear Schr ¨odinger wave equation has served as an important model equation in various sub-fields in physics, our proposed generalized quantum harmonic oscillator opens an unexplored area for quantum particles with nonlinear effective masses.

К модельному описанию электронного спектра графеноподобных Янус-структур

Model of C – AB – D Janus structure as the compound formed by the interacting through atoms А and В dimers А – С and В – D, where А and В atoms are in the sites of two-dimensional hexagonal lattice and C and D atoms are on the opposite sides from AB list is proposed. In the scope of tight-binding theory and Green’s function method general equation for the dispersion low is obtained. The particular cases of C – AА – D и А – AB – В compounds are considered and analytical expressions for their electronic spectra is fulfilled. The effect of the external mechanical deformation on the band parameters including effective masses is examined. Problem of the magnetic states in Janus compounds is discussed.

Optical properties of semiconductor “anisotropic” quantum dot

The optical properties of an “anisotropic” semiconductor nanodot – a nanoscale object in the form of a rectangular parallelepiped - with sides a ≠ b ≠ c are considered. Such dimensions are closely related to the values of the effective masses of the electron. The analysis of the spectral dependence of the absorption coefficient a(w) under different degrees of "anisotropy" and under different polarizations of the electromagnetic wave is carried out. The cases of the most intense optical transitions, i.e. between electronic states separated by the Fermi level, are analyzed. The obtained results indicate that 1) a(w) is of line structure, and 2) the positions of the peaks of a(w) in identical optical transitions in the isotropic nanodot and in the “anisotropic” ones coincide qualitatively. However, different masses in the “anisotropic” nanodot lead to a shift to the left or right of the peaks relative to identical peaks in the isotropic nanodot with simultaneous splitting of its degenerate peaks. Such shifts and their magnitudes are determined both by the degree of anisotropy (i.e. by the ratio between the effective masses), and by the polarization of light. It is pointed out that modern achievements in the creation of ordered semiconductor materials with nanoobjects of different shapes and sizes in nanostructures allows us to consider polarized electromagnetic wave as an effective factor in achieving the desired physical characteristics.

Improved tight-binding parameters of III-V semiconductor alloys and their application to type-II superlattices

A simple tight-binding method for ternary semiconductor alloys is generalized to calculate the properties of the semiconductor alloys accurately. Specifically independently adjustable parameters, which represent compositional disorder, are incorporated in all the ternary tight-binding parameters. Energy levels and effective masses agree well with the reference values only by the proposed method. We have applied the method to calculate the band gaps and a spectrum of the absorption coefficient of (InAs)/(GaInSb) type-II superlattices. The calculated band-gaps agree well with the experimental ones and we could well reproduce the shape of the absorption coefficient spectrum calculated by an empirical pseudopotential scheme.

Light-induced electron pairing in two-dimensional systems

The mechanism of electron pairing induced by a circularly polarized off-resonant electromagnetic field is suggested and examined theoretically for various two-dimensional (2D) nanostructures. Particularly, it is demonstrated that such a pairing can exist in 2D systems containing charge carriers with different effective masses. As a result of the pairing, the optically induced hybrid Bose-Fermy system appears. The elementary excitation in the system are analyzed and the possible Bose-Einstein condensation of the paired electrons and the related light-induced superconductivity are discussed.

Horizon acoustics of the GHS black hole and the spectrum of AdS2

We uncover a novel structure in Einstein-Maxwell-dilaton gravity: an AdS2 × S2 solution in string frame, which can be obtained by a near-horizon limit of the extreme GHS black hole with dilaton coupling λ ≠ 1. Unlike the Bertotti-Robinson spacetime, our solution has independent length scales for the AdS2 and S2, with ratio controlled by λ. We solve the perturbation problem for this solution, finding the independently propagating towers of states in terms of superpositions of gravitons, photons, and dilatons and their associated effective potentials. These potentials describe modes obeying conformal quantum mechanics, with couplings that we compute, and can be recast as giving the spectrum of the effective masses of the modes. By dictating the conformal weights of boundary operators, this spectrum provides crucial data for any future construction of a holographic dual to these AdS2 × S2 configurations.

Seeds don’t sink: even massive black hole ‘seeds’ cannot migrate to galaxy centres efficiently

ABSTRACT Possible formation scenarios of supermassive black holes (BHs) in the early universe include rapid growth from less massive seed BHs via super-Eddington accretion or runaway mergers, yet both of these scenarios would require seed BHs to efficiently sink to and be trapped in the Galactic Centre via dynamical friction. This may not be true for their complicated dynamics in clumpy high-z galaxies. In this work, we study this ‘sinking problem’ with state-of-the-art high-resolution cosmological simulations, combined with both direct N-body integration of seed BH trajectories and post-processing of randomly generated test particles with a newly developed dynamical friction estimator. We find that seed BHs less massive than $10^8\, \mathrm{M}_\odot$ (i.e. all but the already-supermassive seeds) cannot efficiently sink in typical high-z galaxies. We also discuss two possible solutions: dramatically increasing the number of seeds such that one seed can end up trapped in the Galactic Centre by chance, or seed BHs being embedded in dense structures (e.g. star clusters) with effective masses above the mass threshold. We discuss the limitations of both solutions.