Influence of an anisotropic parabolic potential on the quantum dot qubit

To study the influence of an anisotropic parabolic potential （APP） on the properties of a quantum dot （QD） qubit, we obtain the eigenenergies and eigenfunctions of the ground and first excited state of an electron, which is strongly coupled to the bulk longitudinal optical （LO） phonons, in a QD under the influence of an APP by the celebrated Lee-Low-Pines （LLP） unitary transformation and the Pekar type variational （PTV） methods. Then, this kind of two-level quantum system can be excogitated to constitute a single qubit. When the electron locates at the superposition state of its related eigenfunctions, we get the time evolution of the electron＇s probability density. Finally, the influence of an APP on the QD qubit is investigated. The numerical calculations indicate that the probability density will oscillate periodically and it is a decreasing function of the effective confinement lengths of the APP in different directions. Whereas its oscillatory period is an increasing one and will diminish with enhancing the electron-phonon （EP） coupling strength.

Effects of an anisotropic parabolic potential and Coulomb’s impurity potential on the energy characteristics of asymmetrical semi-exponential CsI quantum wells

Because of its unique optoelectronic properties,people have studied the characteristics of polarons in various quantum well(QW)models.Among them,the asymmetrical semiexponential QW(ASEQW)is a new model for studying the structure of QWs in recent years.It is of great significance to study the influences of the impurity and anisotropic parabolic confinement potential(APCP)on the crystal’s properties,because some of the impurities,usually regarded as Coulomb’s impurity potential(CIP),will exist in the crystal more or less,and the APCP has flexible adjustment parameters.However,the energy characteristics of the ASEQW under the combined actions of impurities and APCP have not been studied,which is the motivation of this paper.Using the linear combination operation and Lee-Low-Pines unitary transformation methods,we investigate the vibrational frequency and the ground state energy of the strong coupling polaron in an ASEQW with the influences of the CIP at the origin of coordinates and APCP,and make a comparison between our results and previous literature’s.Our numerical results about the energy properties in the ASEQW influenced by the CIP and APCP may have important significances for experimental design and device preparation.

A Local Tb Theorem for Square Functions and Parabolic Layer Potentials

In this paper,we give a locally parabolic version of Tb theorem for a class of vector-valued operators with off-diagonal decay in L^(2) and certain quasi-orthogonality on a subspace of L^(2),in which the testing functions themselves are also vector-valued.As an application,we establish the boundedness of layer potentials related to parabolic operators in divergence form,defined in the upper half-space Rn+2+:={(x,t,λ)∈R^(n+1)×(0,∞)},with uniformly complex elliptic,L^(∞),t,λ-independent coefficients,and satisfying the De Giorgi/Nash estimates.

From parabolic approximation to evanescent mode analysis on SOI MOSFET

Subthreshold conduction is governed by the potential distribution. We focus on full two-dimensional（2D） analytical modeling in order to evaluate the 2D potential profile within the active area of Fin FET structure.Surfaces and interfaces, which are key nanowire elements, are carefully studied. Different structures have different boundary conditions, and therefore different effects on the potential distributions. A range of models in Fin FET are reviewed in this paper. Parabolic approximation and evanescent mode are two different basic math methods to simplify the Poisson＇s equation. Both superposition method and parabolic approximation are widely used in heavily doped devices. It is helpful to learn performances of MOSFETs with different structures. These two methods achieved improvement to face different structures from heavily doped devices or lightly doped devices to junctionless transistors.