The Asymptotics of Spectral Gaps of a 1D Dirac Operator with Cosine Potential

Letters in Mathematical Physics -     

Quantum effects in submillimetre hot hole semiconductor lasers

The hole dynamics and emission processes in degenerate band semiconductors in strong crossedE B fields were studied both theoretically and experimentally. The Luttinger effective mass Hamiltonian was used to study the Landau level energy spectrum in anisotropic valence bands of Ge. The dependence of the energy spectrum onE,H fields orientation is analysed. The role of quantum effects, such as interaction and mixing of light and heavy hole states in the scattering process and Landau level population is studied. The results of experimental studies of stimulated emission spectra for intersub-band and cyclotron transitions as well as their dependence onE,H field orientation are presented, the experimental data being in good agreement with the quantum model calculations.     

Energy relaxation mechanism in Landau level system of quantum wells

Kinetics of intrasubband energy relaxation of electrons in the system of Landau levels lying below the optical phonon energy is studied. Extraordinary behavior of the relaxation of electronic subsystem excitation energy is detected. Despite the fact that its main channel is optical phonon emission, the total relaxation time exceeds the characteristic times of scattering on optical phonons by several orders of magnitude.     

Spectral triangles of Schrödinger operators with complex potentials

Consider the Schrödinger operator with a complex-valued potential v of period Let and be the eigenvalues of L that are close to respectively, with periodic (for n even), antiperiodic (for n odd), and Dirichelet boundary conditions on [0,1], and let be the diameter of the spectral triangle with vertices We prove the following statement: If then v(x) is a Gevrey function, and moreover      

Nonlinear quantum mode of terahertz electromagnetic wave amplification in resonant tunneling heterostructures

An analysis of high-frequency properties of the resonant tunneling diode (RTD) in a strong microwave electromagnetic field showed that the high-frequency current response increasing with the microwave power significantly more rapidly saturates out in the case of classical amplification mode, than in the case of “quantum” amplification mode. This makes the “quantum” mode even more attractive in comparison with the classical mode from the viewpoint of the possibility of amplification and generation in the range of subterahertz and terahertz frequencies and offers new opportunities to advance towards these frequencies.     

Combinatorial Identities Related to Eigen-Function Decompositions of Hill operators: Open Questions

We formulate three open questions related to enumerative combinatorics, which arise in the spectral analysis of Hill operators with trigonometric polynomial potentials.