Browsing by Subject "Magnetic-field"

Now showing 1 - 3 of 3

Open Access
Self-consistent computation of electronic and optical properties of a single exciton in a spherical quantum dot via matrix diagonalization method
(American Institute of Physics, 2009-08-21) Sahin, M.; Nizamoglu, S.; Kavruk, A. E.; Demir, Hilmi Volkan
In this study, we develop and demonstrate an efficient self-consistent calculation schema that computes the electronic structure and optical properties of a single exciton in a spherical quantum dot (QD) with an interacting pair of electron and hole wave functions. To observe modifications on bands, wave functions, and energies due to the attractive Coulomb potential, the full numeric matrix diagonalization technique is employed to determine sublevel energy eigenvalues and their wave functions in effective mass approximation. This treatment allows to observe that the conduction and valance band edges bend, that the electron and hole wave functions strongly localize in the QD, and that the excitonic energy level exhibits redshift. In our approach for the Coulomb term between electron and hole, the Poisson-Schrodinger equations are solved self-consistently in the Hartree approximation. Subsequently, exciton binding energies and associated optical properties are computed. The results are presented as a function of QD radii and photon energies. We conclude that all of these numerical results are in agreement with the experimental studies.
Open Access
The Smoluchowski-Kramers limit of stochastic differential equations with arbitrary state-dependent friction
(Springer, 2015) Hottovy, S.; McDaniel, A.; Wehr, J.; Volpe, G.
We study a class of systems of stochastic differential equations describing diffusive phenomena. The Smoluchowski-Kramers approximation is used to describe their dynamics in the small mass limit. Our systems have arbitrary state-dependent friction and noise coefficients. We identify the limiting equation and, in particular, the additional drift term that appears in the limit is expressed in terms of the solution to a Lyapunov matrix equation. The proof uses a theory of convergence of stochastic integrals developed by Kurtz and Protter. The result is sufficiently general to include systems driven by both white and Ornstein-Uhlenbeck colored noises. We discuss applications of the main theorem to several physical phenomena, including the experimental study of Brownian motion in a diffusion gradient.
Open Access
Solid-angle factor in the magnetic-field integral equation
(John Wiley & Sons, 2005) Ergül, Özgür; Gürel, Levent
The magnetic-field integral equation (MFIE) contains a geometry-dependent solid-angle factor due to the limit value of the magnetic field at the source region. Determination of the solid-angle factor becomes bewildering, especially at the points of geometric discontinuities caused by the simultaneous discretization of the MFIE and the geometry. In this paper, we clarify the ambiguity by scrutinizing the magnetic-field radiation integrals of the MFIE formulation. We prove that the solid-angle factor can be implicitly determined if the singular source-region magnetic-field expressions are correctly treated, thus eliminating the need for guessing or explicitly inserting solid-angle values in the formulation.