A note on the Fröhlich dynamics in the strong coupling limit

We revise a previous result about the Fröhlich dynamics in the strong coupling limit obtained in Griesemer (Rev Math Phys 29(10):1750030, 2017). In the latter it was shown that the Fröhlich time evolution applied to the initial state $$\varphi _0 \otimes \xi _\alpha $$ φ 0 ⊗ ξ α , where $$\varphi _0$$ φ 0 is the electron ground state of the Pekar energy functional and $$\xi _\alpha $$ ξ α the associated coherent state of the phonons, can be approximated by a global phase for times small compared to $$\alpha ^2$$ α 2 . In the present note we prove that a similar approximation holds for $$t=O(\alpha ^2)$$ t = O ( α 2 ) if one includes a nontrivial effective dynamics for the phonons that is generated by an operator proportional to $$\alpha ^{-2}$$ α - 2 and quadratic in creation and annihilation operators. Our result implies that the electron ground state remains close to its initial state for times of order $$\alpha ^2$$ α 2 , while the phonon fluctuations around the coherent state $$\xi _\alpha $$ ξ α can be described by a time-dependent Bogoliubov transformation.

Энергетический спектр и волновые функции электронов в туннельно-связанных сферических квантовых точках InAs/GaAs

The results of numerical calculation of the electron ground state energy and electron density in tunneled InAs/GaAs quantum dots forming a simple cubic superlattice are presented. The calculation is carried out in the framework of a modified effective mass method, taking into account the microscopic (atomic) structure of individual quantum dots, without taking into account the spin-orbit interaction and deformation effects. The dependence of the electron binding energy on the radius of the quantum dot R. It is shown that in the region R < 27 Å the electron binding energy is proportional to R in degree three.

Response to: Comment on “Does the Equivalence between Gravitational Mass and Energy Survive for a Composite Quantum Body?”

We have recently shown that both passive and active gravitational masses of a composite body are not equivalent to its energy due to some quantum effects. We have also suggested idealized and more realistic experiments to detect the above-mentioned inequivalence for a passive gravitational mass. The suggested idealized effect is as follows. A spacecraft moves protons of a macroscopic ensemble of hydrogen atoms with constant velocity in the Earth’s gravitational field. Due to nonhomogeneous squeezing of space by the field, electron ground state wave function experiences time-dependent perturbation in each hydrogen atom. This perturbation results in the appearance of a finite probability for an electron to be excited at higher energy levels and to emit a photon. The experimental task is to detect such photons from the ensemble of the atoms. More realistic variants of such experiment can be realized in solid crystals and nuclei, as first mentioned by us. In his recent comment on our paper, Crowell has argued that the effect, suggested by us, contradicts the existing experiments and, in particular, astronomic data. We show here that this conclusion is incorrect and based on the so-called “free fall” experiments, where our effect does not have to be observed.

Electronic States and Optical Gap of Phosphorus-Doped Silicon Nanocrystals Embedded in a Silica Host Matrix

Using the envelope-function approximation the electronic states and the optical gap of silicon nanocrystals heavily doped with phosphorus have been calculated. Assuming the uniform impurity distribution over the crystallite volume we have found the fine structure of the electron ground state (induced by the valley-orbit interaction) and the optical gap as a function of the crystallite size and donor concentration. It is shown that the energy of the ground singlet state decreases almost linearly as the concentration increases, while the valley-orbit splitting increases nonlinearly. Phosphorus doping also results in the decrease of the nanocrystal gap with increasing the impurity concentration.

Electron energy structure of self-assembled In(Ga)As nanostructures probed by capacitance-voltage spectroscopy and one-dimensional numerical simulation

The electron energy structure of self-assembled In(Ga)As/GaAs nanostructures, quantum dots, and quantum rings was studied with capacitance-voltage spectroscopy and one-dimensional numerical simulation using Poisson/Schrödinger equations. The electron energy levels in the quantum dots and quantum rings with respect to the electron ground state of the wetting layer were determined directly from capacitance-voltage measurements with a linear lever arm approximation. In the regime where the linear lever arm approximation was not valid anymore (after the charging of the wetting layer), the energy difference between the electron ground state of the wetting layer and the GaAs conduction band edge was obtained indirectly from a numerical simulation of the conduction band under different gate voltages, which led to the erection of complete electron energy levels of the nanostructures in the conduction band.

Experimental and theoretical investigations of optical properties of GaN/AlGaN MQW nanostructures. Impact of built-in polarization fields

We report the results from detailed optical spectroscopy from MOCVD grown GaN/AlGaN multiple quantum wells (MQWs), as opposed to most previous studies where MBE was employed by means of photoluminescence (PL) technique. In this paper we will present theoretical and experimental results demonstrating how polarization induced electric fields and bound interface charges in GaN/AlGaN MQWs affect the emission peak energy, PL line shape, as well as the emission line width. Theoretically estimated fields in this work are consistent with experimental data. Transition energy of the heavy hole and electron ground state Ee-hh in GaN/AlGaN MQWs were calculated and it is found that it stays in good agreement with the experimental data.