arXiv subjects

Nguyen Anh Tuan

Publications and source records attributed to Nguyen Anh Tuan.

5 recordsLinked to original sources

arXiv2024

Effects of magnetic field and structural parameters on multi-photon absorption spectra in Morse quantum wells with electron-phonon interactions

We present a systematic theoretical study of the multi-photon nonlinear optical absorption properties of a $\text{GaAs/A}{\text{l}_{x}}\text{G}{\text{a}_{1-x}}\text{As}$ based quantum well (QW) structure with Morse confinement potential under the influence of a magnetic field. Based on the stationary states due to the electron confinement in Morse QWs and the Landau levels obtained by solving the Schrodinger equation in the effective mass approximation, we have developed calculations for the optical absorption power with MPA using second-order perturbation theory. Our model accounts for electron-phonon interactions and considers both optical and acoustic phonon mechanisms in the MPA process. Our findings show that the one-photon absorption (1PA) peaks are larger and appear to the right of the two-photon absorption (2PA) peaks, whereas 2PA peaks are larger and occur to the right of three-photon absorption (3PA) peaks. The resonance peak positions follow the magneto-phonon resonance condition and are temperature-independent. Increasing the magnetic field and aluminum concentration induces a blue shift in the absorption spectra, whereas increasing the QW width leads to a red shift. Variations in magnetic field, aluminum concentration, and QW width also affect the peak intensities and full-width at half maximum (FWHM), with increasing values of the former two enhancing the FWHM, while expanding the QW width reduces it. Thermal excitations increase peak intensity without shifting their positions. Our study highlights the significance of nonlinear absorption processes (2PA, 3PA) in understanding optical absorption, despite their smaller FWHM compared to linear absorption (1PA). Overall, the Morse QW model demonstrates promising magneto-optical properties, making it a strong candidate for future optoelectronic device applications.

cond-mat.mes-hall↗

arXiv2021

Global well-posedness for fractional Sobolev-Galpern type equations

This article is a comparative study on an initial-boundary value problem for a class of semilinear pseudo-parabolic equations with the fractional Caputo derivative, also called the fractional Sobolev-Galpern type equations. The purpose of this work is to reveal the influence of the degree of the source nonlinearity on the well-posedness of the solution. By considering four different types of nonlinearities, we derive the global well-posedness of mild solutions to the problem corresponding to the four cases of the nonlinear source terms. For the advection source function case, we apply a nontrivial limit technique for singular integral and some appropriate choices of weighted Banach space to prove the global existence result. For the gradient nonlinearity as a local Lipschitzian, we use the Cauchy sequence technique to show that the solution either exists globally in time or blows up at finite time. For the polynomial form nonlinearity, by assuming the smallness of the initial data we derive the global well-posed results. And for the case of exponential nonlinearity in two-dimensional space, we derive the global well-posedness by additionally use of Orlicz space.

math.AP↗

arXiv2015

Classification of Real Solvable Lie Algebras Whose Simply Connected Lie Groups Have Only Zero or Maximal Dimensional Coadjoint Orbits

In this paper we study a special subclass of real solvable Lie algebras having small dimensional or small codimensional derived ideal. It is well-known that the derived ideal of any Heisenberg Lie algebra is 1-dimensional and the derived ideal of the 4-dimensional real Diamond algebra is 1-codimensional. Moreover, all the coadjoint orbits of any Heisenberg Lie group as well as 4-dimensional real Diamond group are orbits of dimension zero or maximal dimension. In general, a (finite dimensional) real solvable Lie group is called an $MD$-group if its coadjoint orbits are zero-dimensional or maximal dimensional. The Lie algebra of an $MD$-group is called an $MD$-algebra and the class of all $MD$-algebras is called $MD$-class. Simulating the mentioned above characteristic of Heisenberg Lie algebras and 4-dimensional real Diamond algebra, we give a complete classification of $MD$-algebras having 1-dimensional or 1-codimensional derived ideals.

math.RA↗

arXiv2014

K-theory for the Leaf Spaces of the Orbit Foliations of the co-adjoint Action of some 5-dimensional Solvable Lie groups

In this paper, combining Kirillov's method of orbits with Connes' method in Differential Geometry, we study the so-called MD(5,3C)-foliations, i.e. the orbit foliations of the co-adjoint action of MD(5,3C)-groups. First, we classify topologically MD(5,3C)-foliations based on the classification of all MD(5,3C)-algebras in [22] and the picture of co-adjoint orbits (K-orbits) of all MD(5,3C)-groups in [23]. Finally, we study K-theory for leaf space of MD(5,3C)-foliations and describe analytically or characterize Connes' C*-algebras of the considered foliations by KK-functors.

math.KT↗

arXiv2014

K-theory for the Leaf Space of Foliations Formed by the Generic K-orbits of a class of Solvable Real Lie Groups

The paper is a continuation of the works [17] of Vu and Shum, [18] and [19] of Vu and Hoa. In [17], Vu and Shum classified all the MD5-algebras having commutative derived ideals. In [18], Vu and Hoa considered foliations formed by the maximal dimensional K-orbits (for short, MD5-foliations) of connected MD5-groups such that their Lie algebras have 4-dimensional commutative derived ideals and gave a topological classification of the considered foliations. In [19], Vu and Hoa characterized the Connes' C*-algebras of some MD5-foliations considered in \cite{VU-HO09} by the method of K-functors. In this paper, we study K-theory for the leaf space of all MD5-foliations which are classified in [18] and characterize the Connes' C*-algebras of them by the method of K-functors.

math.KT↗