EFFECT OF IMAGE FORCES ON ELECTRONS CONFINED IN LOW-DIMENSIONAL STRUCTURES UNDER A MAGNETIC-FIELD

We consider the effect of image forces, arising due to a difference in dielectric permeabilities of the well layer and barrier layers, on the energy spectrum of an electron confined in a rectangular potential well under a magnetic field. Depending on the value and the sign of the dielectric mismatch, image forces can localize electrons near the interfaces of the well or in well centre and change the direct intersubband gaps into indirect ones. These effects can be controlled by variation of the magnetic field, offering possibilities for exact tuning of electronic devices.

Low dimensional fabrication of giant dielectric CaCu3Ti4O12 through soft e-beam lithography

We report low-dimensional fabrication of technologically important giant dielectric material CaCu3Ti4O12 (CCTO) using soft electron beam lithographic technique. Sol-gel precursor solution of CCTO was prepared using inorganic metal nitrates and Ti-isopropoxide. Employing the prepared precursor solution and e-beam lithographically fabricated resist mask CCTO dots with similar to 200 nm characteristic dimension were fabricated on platinized Si (111) substrate. Phase formation, chemical purity and crystalline nature of fabricated low dimensional structures were investigated with X-ray diffraction (XRD), energy dispersive X-ray spectroscopy (EDS) and selected area electron diffraction (SAED), respectively. Morphological investigations were carried out with the help of scanning electron microscopy (SEM) and transmission electron microscopy (TEM). This kind of solution based fabrication of patterned low-dimensional high dielectric architectures might get potential significance for cost-effective technological applications. (C) 2012 Elsevier B.V. All rights reserved.

Convex Relaxation for Low-Dimensional Representation: Phase Transitions and Limitations

There is a growing interest in taking advantage of possible patterns and structures in data so as to extract the desired information and overcome the curse of dimensionality. In a wide range of applications, including computer vision, machine learning, medical imaging, and social networks, the signal that gives rise to the observations can be modeled to be approximately sparse and exploiting this fact can be very beneficial. This has led to an immense interest in the problem of efficiently reconstructing a sparse signal from limited linear observations. More recently, low-rank approximation techniques have become prominent tools to approach problems arising in machine learning, system identification and quantum tomography.

In sparse and low-rank estimation problems, the challenge is the inherent intractability of the objective function, and one needs efficient methods to capture the low-dimensionality of these models. Convex optimization is often a promising tool to attack such problems. An intractable problem with a combinatorial objective can often be "relaxed" to obtain a tractable but almost as powerful convex optimization problem. This dissertation studies convex optimization techniques that can take advantage of low-dimensional representations of the underlying high-dimensional data. We provide provable guarantees that ensure that the proposed algorithms will succeed under reasonable conditions, and answer questions of the following flavor:

More specifically, i) Focusing on linear inverse problems, we generalize the classical error bounds known for the least-squares technique to the lasso formulation, which incorporates the signal model. ii) We show that intuitive convex approaches do not perform as well as expected when it comes to signals that have multiple low-dimensional structures simultaneously. iii) Finally, we propose convex relaxations for the graph clustering problem and give sharp performance guarantees for a family of graphs arising from the so-called stochastic block model. We pay particular attention to the following aspects. For i) and ii), we aim to provide a general geometric framework, in which the results on sparse and low-rank estimation can be obtained as special cases. For i) and iii), we investigate the precise performance characterization, which yields the right constants in our bounds and the true dependence between the problem parameters.

Symmetry and optical transition rule for low-dimensional semiconductor system with spin-orbit interaction and magnetic field

Starting from effective mass Hamiltonian, we systematically investigate the symmetry of low-dimensional structures with spin-orbit interaction and transverse magnetic field. The position-dependent potentials are assumed to be space symmetric, which is ever-present in theory and experiment research. By group theory, we analyze degeneracy in different cases. Spin-orbit interaction makes the transition between Zeeman sub-levels possible, which is originally forbidden within dipole approximation. However, a transition rule given in this paper for the first time shows that the transition between some levels is forbidden for space symmetric potentials. (C) 2009 Elsevier Ltd. All rights reserved.

Low-dimensional hydrogen-bonded structures in the 1:1 and 1:2 proton-transfer compounds of 4,5-dichlorophthalic acid with the aliphatic Lewis bases triethylamine, diethylamine, n-butylamine and piperidine

The structures of proton-transfer compounds of 4,5-dichlorophthalic acid (DCPA) with the aliphatic Lewis bases triethylamine, diethylamine, n-butylamine and piperidine, namely triethylaminium 2-carboxy-4,5-dichlorobenzoate C~6~H~16~N^+^ C~8~H~3~Cl~2~O~4~^-^ (I), diethylaminium 2-carboxy-4,5-dichlorobenzoate C~4~H~12~N^+^ C~8~H~3~Cl~2~O~4~^-^ (II), bis(n-butylaminium) 4,5-dichlorophthalate monohydrate 2(C~4~H~12~N^+^) C~8~H~2~Cl~2~O~4~^2-^ . H~2~O (III) and bis(piperidinium) 4,5-dichlorophthalate monohydrate 2(C~5~H~12~N^+^) C~8~H~2~Cl~2~O~4~^2-^ . H~2~O (IV)have been determined at 200 K. All compounds have hydrogen-bonding associations giving in (I) discrete cation-anion units, linear chains in (II) while (III) and (IV) both have two-dimensional structures. In (I) a discrete cation-anion unit is formed through an asymmetric R2/1(4) N+-H...O,O' hydrogen-bonding association whereas in (II), one-dimensional chains are formed through linear N-H...O associations by both aminium H donors. In compounds (III) and (IV) the primary N-H...O linked cation-anion units are extended into a two-dimensional sheet structure via amide N-H...O(carboxyl) and ...O(carbonyl) interactions. In the 1:1 salts [(I) and (II)], the hydrogen 4,5-dichlorophthalate anions are essentially planar with short intramolecular carboxylic acid O-H...O(carboxyl) hydrogen bonds [O...O, 2.4223(14) and 2.388(2)A respectively]. This work provides a further example of the uncommon zero-dimensional hydrogen-bonded DCPA-Lewis base salt and the one-dimensional chain structure type, while even with the hydrate structures of the 1:2 salts with the primary and secondary amines, the low dimensionality generally associated with 1:1 DCPA salts is also found.

Nanopowder management and plasma parameters in nanofabrication of low-dimensional quantum structures in reactive silane-based plasmas

Management of nanopowder and reactive plasma parameters in a low-pressure RF glow discharge in silane is studied. It is shown that the discharge control parameters and reactor volume can be adjusted to ensure lower abundance of nanopowders, which is one of the requirements of the plasma-assisted fabrication of low-dimensional quantum nanostructures. The results are relevant to micro- and nanomanufacturing technologies employing low-pressure glow discharge plasmas of silane-based gas mixtures.

Photoluminescence of low-dimensional semiconductor structures under pressure

Photoluminescence of some low-dimensional semiconductor structures has been investigated under pressure. The measured pressure coefficients of In0.55Al0.45 As/Al0.5Ga0.5As quantum dots with average diameter of 26, 52 and 62 nm are 82, 94 and 98 meV/GPa, respectively. It indicates that these quantum dots are type-I dots. On the other hand, the measured pressure coefficient for quantum dots with 7 nm in size is -17meV/GPa, indicating the type-II character. The measured pressure coefficient for Mn emission in ZnS:Mn nanoparticles is -34.6meV/GPa, in agreement with the predication of the crystal field theory. However, the DA emission is nearly independent on pressure, indicating that this emission is related to the surface defects in ZnS host. The measured pressure coefficient of Cu emission in ZnS: Cu nanoparticles is 63.2 meV/GPa. It implies that the acceptor level introduced by Cu ions has some character of shallow level. The measured pressure coefficient of Eu emission in ZnS:Eu nanoparticles is 24.1 mev/GPa, in contrast to the predication of the crystal field theory. It may be due to the strong interaction between the excited state of Eu ions and the conduction band of ZnS host.

Low-Dimensional Dynamical Systems for a Wake-Type Shear Flow with Vortex Dislocations

Low-dimensional systems are constructed to investigate dynamics of vortex dislocations in a wake-type shear flow. High-resolution direct numerical simulations are employed to obtain flow snapshots from which the most energetic modes are extracted using proper orthogonal decomposition (POD). The first 10 modes are classified into two groups. One represents the general characteristics of two-dimensional wake-type shear flow, and the other is related to the three-dimensional properties or non-uniform characteristics along the span. Vortex dislocations are generated by these two kinds of coherent structures. The results from the first 20 three-dimensional POD modes show that the low- dimensional systems have captured the basic properties of the wake-type shear flow with vortex dislocation, such as two incommensurable frequencies and their beat frequency.

Optical and electrical investigation of low dimensional self-assembled InAs quantum dot field effect transistors

Self-assembled InAs QD dot-in-a-well (DWELL) structures were grown on GaAs substrate by MBE system, and heterojunction modulation-doped field effect transistor (MODFET) was fabricated. The optical properties of the samples show that the photoluminescence of InAs/GaAs self-assembled quantum dot (SAQD) is at 1.265 mu m at 300 K. The temperature-dependence of the abnormal redshift of InAs SAQD wavelength with the increasing temperature was observed, which is closely related with the inhomogeneous size distribution of the InAs quantum dot. According to the electrical measurement, high electric field current-voltage characteristic of the MODFET device were obtained. The embedded InAs QD of the samples can be regard as scattering centers to the vicinity of the channel electrons. The transport property of the electrons in GaAs channel will be modulated by the QD due to the Coulomb interaction. It has been proposed that a MODFET embedded with InAs QDs presents a novel type of field effect photon detector.

Synthesis and structure of new low dimensional polymeric haloplumbate(II) complexes [Pb4Br12(C40H40N8)] and [Pb4Cl12(C40H40N8)]center dot H2O

New low dimensional polymeric haloplumbate(II) complexes of the dication of (4,4'-bis(imidazolyl-ylmethyl)biphenyl) were synthesised and their crystal structures determined. Complex 1, [Pb4Br12(C40H40N8)], has cis-edge-shared, octahedral, lead bromide double chains. In compound 2 [Pb4Cl12(C40H40N8)]center dot H2O, the inorganic chains are corner-shared, square pyramidal chains of lead chloride. In both compounds the organic ammoniums form regular layers that alternate with the inorganic chains.

Control of self-organized low-dimensional morphology in Poly(styrene-b-4vinylpyridine)/polystyrene blend thin films

The surface morphologies of poly(styrene-b-4vinylpyridine) (PS-b-P4VP) diblock copolymer and homopolystyrene (hPS) binary blend thin films were investigated by atomic force microscopy as a function of total volume fraction of PS (phi(PS)) in the mixture. It was found that when hPS was added into symmetric PS-b-P4VP diblock copolymers, the surface morphology of this diblock copolymer was changed to a certain degree. With phi(PS) increasing at first, hPS was solubilized into the corresponding domains of block copolymer and formed cylinders. Moreover, the more solubilized the hPS, the more cylinders exist. However, when the limit was reached, excessive hPS tended to separate from the domains independently instead of solubilizing into the corresponding domains any longer, that is, a macrophase separation occurred. A model describing transitions of these morphologies with an increase in phi(PS) is proposed. The effect of composition on the phase morphology of blend films when graphite is used as a substrate is also investigated.

Ground state of low-dimensional dipolar gases: Linear and zigzag chains

We study the ground-state phase diagram of ultracold dipolar gases in highly anisotropic traps. Starting from a one-dimensional geometry, by ramping down the transverse confinement along one direction, the gas reaches various planar distributions of dipoles. At large linear densities, when the dipolar gas exhibits a crystal-like phase, critical values of the transverse frequency exist below which the configuration exhibits transverse patterns. These critical values are found by means of a classical theory, and are in full agreement with classical Monte Carlo simulations. The study of the quantum system is performed numerically with Monte Carlo techniques and shows that the quantum fluctuations smoothen the transition and make it completely disappear in a gas phase. These predictions could be experimentally tested and would allow one to reveal the effect of zero-point motion on self-organized mesoscopic structures of matter waves, such as the transverse pattern of the zigzag chain.