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关键词： 量子力学  

ISBN: (纸本)9787554446287

摘要： 量子力学基础理论及若干相关前沿领域的进展，内容涉及量子力学概率诠释的问题，波粒二相性，波函数的几何相、拓扑相，量子力学与经典力学的界限与宏观水平量子力学，腔量子电动力学，量子霍尔效应。

关键词： Partial difference transforms   Heat semigroup   Discrete Laplacian   Maximal operators  

摘要： We analyze the convergence of the following type of series T-N f(n) = Sigma(N2)(j=N1) v(j)(e(aj+1 Delta d) f(n) - e(aj Delta d) f(n)), n is an element of Z, where {e(t Delta d)}(t>0) is the heat semigroup of the discrete Laplacian Delta(d), N = (N-1, N-2) is an element of Z(2) with N-1 < N-2, {v(j)}(j is an element of Z) is a bounded real sequence and {a(j)}(j is an element of Z) is an increasing real sequence. Our analysis will consist in the boundedness on l(p)(Z, omega) of the operators T-N and its maximal operator T * f(n) = sup(N) vertical bar T-N f(n)vertical bar, where 1 <= p < infinity and omega is a discrete Muckenhoupt weight. Moreover, we also get the alternative behavior of the maximal operator T* on l(infinity)(Z).

关键词： Fractional p(x, .)-Laplacian operator   Nonlocal problems   Nehari manifold   Embeddings results  

摘要： In the present paper, we study the existence of two non-negative solutions for a class of fractional p(x, .)-Laplacian problems with non-negative weight functions. The main tool is the Nehari manifold approach. Moreover, under some suitable assumptions, continuous and compact embeddings results are established.

关键词： Anisotropy   Position-dependent mass   Modified momentum operator   Low-dimensional nanocrystals  

摘要： In this study, a quantum mechanical system characterized by the product-like fractal geometry constructed by Li and Ostoja-Starzewski in order to explore physical properties of porous and anisotropic media and a positiondependent mass is constructed. We have derived the modified Schro center dot dinger equation and we have discussed some of its main consequences for different forms of potentials. Due to the particular forms of fractal gradient and Laplacian operators in Li and Ostoja-Starzewski approach, the potentials are characterized by fractional powers. For particular choices of the free parameters introduced in the theory, it was observed that both the commutation relation and the uncertainty principle are not altered although the momentum operator is modified. We have discussed a number of particular effective potentials and we have derived their associated energy eigenvalues which hold a number of new features. For a particular value of the fractal parameter, we have analyzed the case of low-dimensional nanocrystals of semiconductor materials characterized by particles sizes close to the exciton Bohr radius of the material. The results obtained are strongly affected by the anisotropic properties of Li and Ostoja-Starzewski approach. We have considered, as an application, the Cadmium selenide and we have evaluated the corresponding density of states and it is found to be extremely less than the standard result. Besides, the group velocity is enhanced and such an enhancement is detected in a homogenized dielectric medium in its component material phases due to anisotropy.

关键词： CdBr2   SiO2 interfaces   Optical conductivity   Band offsets   Microwave resonators  

摘要： Herein, the structural, optical, dielectric and optical conductivity parameters of the CdBr2/SiO2 interfaces are reported. Thin films of CdBr2 are coated with 50 nm thick SiO2 under a vacuum pressure of 10-5 mbar. The structural morphological and optical investigations have shown that CdBr2 exhibit hexagonal structure of lattice parameters of a = b = 7.20A and = 13.86 A, energy band gap of 3.32 eV and Urbach energy of 0.84 eV. The interfacing of CdBr2 films with SiO2, shortened the lattice parameters, blue-shifted the energy band gap and decreased the Urbach energy value. The electron affinity of CdBr2 which is determined here is found to be 3.27 eV. The CdBr2/SiO2 interfaces displayed a conduction and a valence band offsets of 2.37 eV and 3.21 eV, respectively. In addition, the dielectric dispersion and optical conduction analyses using the Drude-Lorentz approach have shown that the drift mobility and plasmon frequency (Wpi) of the free charge carriers at the CdBr2/SiO2 interfaces varies in the range of 28.59-22.87 cm2/Vs and 0.41-6.47 GHz, respectively. The effectiveness of the plasmon frequency to limit signal propagation in the heterojunction devices is confirmed by the impedance spectroscopy technique which showed radiowave (RF) band filter characteristics at the targeted Wpi. The energy band offsets, the optical conductivity parameters and the RF filtering properties nominates the CdBr2/SiO2 heterojunctions for use in thin film transistor technology.

关键词： Phase field   Spherical growth   Equiaxed growth   Globulitic solidification  

摘要： A one-dimensional quantitative phase-field model (thin-interface approximation) considering the effects of interface curvature and attachment kinetics was implemented to simulate the solidification of a solid sphere (globulitic solidification) of a pure substance in an undercooled infinite melt, beginning from the critical nucleus. The classical sharp interface model for the same problem was also solved and the growth velocity and interface temperature were calculated and compared with the results of the phase-field model. Numerical conditions of the phase-field model, namely interface thickness, numerical mesh spacing, and critical nucleus model, that give close agreement with the sharp interface model (quantitative modeling) were determined. The possibility of a unique controlling step of the overall solidification kinetics by heat transfer or interface attachment kinetics or even of a mixed control was analyzed by defining relative undercoolings at the solid-liquid interface. For both metallic and non-metallic materials, growth is initially controlled by interface attachment kinetics, but, as the solid sphere grows and the melt heats up, it changes to the mixed control regime with heat transfer before spherical growth becomes unstable. The spherical radius for the change to mixed control increases when the kinetic coefficient or the magnitude of melt undercooling increases, because the heat transfer step is facilitated relative to that of attachment kinetics.

关键词： 量子力学  

ISBN: (纸本)9787030700001

摘要： 本书讲述非相对论量子力学, 内容新颖, 阐述清晰, 分析深入, 不回避问题 ; 包括量子力学的物理基础、Schrodinger万程、一维问题、中心场束缚态问题、量子力学的表象与表示、对称性分析和应用、电子自旅、定态微扰论、电磁作用分析和应用、势散射理论、含时问题与量子跃迁等。

关键词： Primary Secondary Key Words and Phrases   Riemann-Liouville and Caputo derivatives   fractional diffusion   regularity   fractional Laplacian   double-sided  

摘要： This paper investigates the structure of solutions to the BVP of a class of fractional ordinary differential equations involving both fractional derivatives (R-L or Caputo) and fractional Laplacian with variable coefficients. This family of equations generalize the usual fractional diffusion equation and fractional Laplace equation. We provide a deep insight to the structure of the solutions shared by this family of equations. The specific decomposition of the solution is obtained, which consists of the "good" part and the "bad" part that precisely control the regularity and singularity, respectively. Other associated properties of the solution will be characterized as well.

关键词： 量子力学  

ISBN: (纸本)9787030696816

摘要： 本书注重内容的精选、概念的准确和叙述方式的可读性，是适合于利用零星时间，碎片式学习的基础资料。各专题叙述的重要内容之间有一些必要的重复，从不同角度和不同内容的联系方面进行阐述，但又相对独立和完整，便于读者随时随地阅读、学习和深化对专题的理解。

关键词： alloyed quantum dots   Auger recombination   carrier dynamics   light-emitting devices  

摘要： Light-emitting devices based on alloyed quantum dots have reached external quantum efficiencies above 20% in red, green, and blue emission devices. Their outstanding performances including high efficiency, long-term device stability, and suppressed efficiency roll-off identify alloyed-quantum-dot based light-emitting devices as good candidates for next generation solid-state lightings and displays. All these advantages stem from the chemical composition gradient of alloyed quantum dots in radial direction. The chemical composition gradient enables the lattice strain to be released gradually, eventually decreasing interface defects and suppressing Auger recombination. Carrier dynamics play a crucial role in the fundamental properties and functionalities of quantum dots for solid-state devices and light-emitting devices. A more in-depth understanding of carrier dynamics in quantum dots is therefore of both fundamental and technological significance. This review article provides an overview on recent advances in the study and understanding of carrier dynamics of alloyed quantum dots and alloyed-quantum-dot based light-emitting devices. Particular emphasis is placed on the relationship between Auger recombination and optical properties and optoelectronic properties. This review is expected to encourage further research in alloyed quantum dots and related devices and to stimulate new synthesis efforts to produce stable alloyed quantum dots with further improved control of carrier dynamics.