Classification of Electron States in a Thin Film in an External Longitudinal Magnetic Field

This research was supported as part of Project CPBP-01.12 of the Polish Academy of SciencesThe electron energy spectrum is considered for a simple model of a thin film in an external longitudinal magnetic field. A systematic classification of the electron states in the thin film is carried out.Zadanie pt. „Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki” nr 885/P-DUN/2014 zostało dofinansowane ze środków MNiSW w ramach działalności upowszechniającej naukę

Spectra of Harmonium in a magnetic field using an initial value representation of the semiclassical propagator

For two Coulombically interacting electrons in a quantum dot with harmonic confinement and a constant magnetic field, we show that time-dependent semiclassical calculations using the Herman-Kluk initial value representation of the propagator lead to eigenvalues of the same accuracy as WKB calculations with Langer correction. The latter are restricted to integrable systems, however, whereas the time-dependent initial value approach allows for applications to high-dimensional, possibly chaotic dynamics and is extendable to arbitrary shapes of the potential.Comment: 11 pages, 1 figur

The boundary integral method for magnetic billiards

We introduce a boundary integral method for two-dimensional quantum billiards subjected to a constant magnetic field. It allows to calculate spectra and wave functions, in particular at strong fields and semiclassical values of the magnetic length. The method is presented for interior and exterior problems with general boundary conditions. We explain why the magnetic analogues of the field-free single and double layer equations exhibit an infinity of spurious solutions and how these can be eliminated at the expense of dealing with (hyper-)singular operators. The high efficiency of the method is demonstrated by numerical calculations in the extreme semiclassical regime.Comment: 28 pages, 12 figure

Two Electrons in a Quantum Dot: A Unified Approach

Low-lying energy levels of two interacting electrons confined in a two-dimensional parabolic quantum dot in the presence of an external magnetic field have been revised within the frame of a novel model. The present formalism, which gives closed algebraic solutions for the specific values of magnetic field and spatial confinement length, enables us to see explicitly individual effects of the electron correlation.Comment: 14 page

Temperature Dependence of the Electron Raman Light Scattering in Normal Metals and Superconductors

Within the anisotropic BCS model the temperature dependence of the electron Raman light scattering in normal metals and superconductors is investigated. In either case analytical expressions describing the intensity of scattered light as a function of the Raman frequency and temperature are derived

Fano Resonance in a Coupled Electron-Phonon System

Raman light scattering with excitation of electron-hole continuum and a phonon is investigated theoretically. The effect of a surface and screening of the electron-photon coupling and of the deformation potential as a result of the Coulomb interaction of the electrons is taken into account. The parameters of the 340 cm$\text{}^{-1}$ resonance line in superconducting YBaCuO are estimated by comparing with experimental data