Confinement regime

The energy spectrum for the small confinement regime (a>z = 0.1) is displayed on the right hand side of Figure 2. It shows a band structure... 

In order to explain the band structure for the small confinement regime the nature of the potential energy function in the Hamiltonian has been examined in the internal space. Since, for quasi-one-dimensional quantum dots, the electrons can only move along the z coordinate, their x and y dependence is neglected in the analysis. The internal space is defined by a unitary transformation from the independent electron coordinates (z, Z2, , zn) into the correlated electron coordinates (za, zp,...). The coordinate za represents the totally symmetric center-of-mass coordinate za = 7=(zi + Z2 + + zn), and the remaining correlated electron coordinates zp,..., zn represent the internal degrees of freedom of the N electrons [20,21]. In the case of two electrons the correlated coordinates are defined by... 

In order to analyze the origin of this difference between the energy spectra of quasi one- and two-dimensional quantum dots in the small confinement regime, the internal space for two electrons is considered as in the quasi-one-dimensional cases. Using a harmonic approximation to the Gaussian confining potential, and neglecting the dependence on the z coordinate, the Hamiltonian of Equation (1) for two electrons takes the form... 

The energy spectrum of two electrons confined in a quasi-fwo-dimensional Gaussian potential has also been studied for the same set of the strengths of confinement as the corresponding quasi-one-dimensional cases, and are compared to them. The energy spectrum of the quasi-two-dimensional quantum dot is qualitatively different from that of the quasi-one-dimensional quantum dot in the small confinement regime. The origin of the differences is due to the difference in the structure of the internal space. 

The pion-nucleon interaction has been subject both to experimental and theoretical studies since the very beginning of the development of particle physics. On the theoretical side the description of the pion-nucleon system with QCD is considered to be a fundamental issue in the development of this theory. The understanding of strong interaction in the confinement regime has advanced recently, as chiral perturbation theory was developed to perform calculations at low energies [1,2]. 

Under these assumptions, the total injection rate is independent of nanoparticle size for particles that are not in the quantum-confined regime, and can be expressed as... 

Considerable amount of research has gone into the development and characterization of surfactant templated silica, in order to produce various mesophases and nanowire geometries with well-controlled pore diameters within the quantum confinement regime (i.e. 2-20 nm). Lu and coworkers have characterized one of the more promising methods, a sol-gel dip-coating method for rapid (tens of seconds) template generation. The fabrication process involves evaporation-induced self assembly of liquid crystal domains dominated by inward growth from the solid-liquid... 

Moller, K. J. Am. Chem. Soc in press.)(17). This is of interest from the standpoint that such small pieces of a bulk semiconductor lattice cannot fully develop the normal semi- conductor band structure and so reside in the so called size-quantized or quantum-confined regime. This is where the electron-hole pair of an excited semiconductor particle has a radius(18) larger than the actual particle size. The electron then behaves as a particle in a box and novel optical properties result. We decided, therefore, to look at preparation of CdS inside the zeolite cavities and then to explore the photo-oxidation chemistry of these species with absorbed olefins. 

A new coarse grained molecular dynamics model was developed to study the role of thermal, mechanical and chemical reactions in the onset of the ablation process of PMMA [58]. In this model, the laser energy is absorbed in different ways, i.e. pure heating and Norrish type I and II reactions. Mechanical stresses and pressure are dominant for very short pulses in the stress confinement regime and can initiate... 

The quantum confined nature of carriers in these systems strongly manifests itself in the optical properties of these materials. To fully realise the possibilities offered by these materials, it is crucial to not just understand the underlying physics but also to be able to accurately predict the material behaviour over a broad range of conditions. The central theme of quantum confinement, that is, the evolution of physical properties with size, determines not just the basic photophysics, but also provides the opportunities for addressing a wide range of applications. Experimentally, the onset of quantum confined regime is most easy to detect in the absorption and fluorescence spectra. Both techniques further provide rich information on other aspects of the electronic properties of these finite sized solids, including aspects such as mid gap states, traps, etc. 

Zhong HZ, Wang ZB, Bovero E, Lu ZH, Van Veggel FCJM, Scholes GD (2011) Colloidal CuInSc2 nanocrystals in the quantum confinement regime synthesis, optical properties, and electroluminescence. J Phys Chem C 115 12396... 

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