Gaussian Confinement Research Articles

Molecular Simulation Study of Water Mobility in Aerosol-OT Reverse Micelles

In this work, we present results from molecular dynamics simulations on the single-molecule relaxation of water within reverse micelles (RMs) of different sizes formed by the surfactant aerosol-OT (AOT, sodium bis(2-ethylhexyl)sulfosuccinate) in isooctane. Results are presented for RM water content w(0) = [H(2)O]/[AOT] in the range from 2.0 to 7.5. We show that translational diffusion of water within the RM can, to a good approximation, be decoupled from the translation of the RM through the isooctane solvent. Water translational mobility within the RM is restricted by the water pool dimensions, and thus, the water mean-squared displacements (MSDs) level off in time. Comparison with models of diffusion in confined geometries shows that a version of the Gaussian confinement model with a biexponential decay of correlations provides a good fit to the MSDs, while a model of free diffusion within a sphere agrees less well with simulation results. We find that the local diffusivity is considerably reduced in the interfacial region, especially as w(0) decreases. Molecular orientational relaxation is monitored by examining the behavior of OH and dipole vectors. For both vectors, orientational relaxation slows down close to the interface and as w(0) decreases. For the OH vector, reorientation is strongly affected by the presence of charged species at the RM interface and these effects are especially pronounced for water molecules hydrogen-bonded to surfactant sites that serve as hydrogen-bond acceptors. For the dipole vector, orientational relaxation near the interface slows down more than that for the OH vector due mainly to the influence of ion-dipole interactions with the sodium counterions. We investigate water OH and dipole reorientation mechanisms by studying the w(0) and interfacial shell dependence of orientational time correlations for different Legendre polynomial orders.

Optical properties of an off-center hydrogenic impurity in a spherical quantum dot with Gaussian potential

Optical absorption coefficients and refractive index changes associated with intersubband transition of an off-center hydrogenic impurity in a spherical quantum dot (QD) with Gaussian confinement potential are theoretically investigated. Our results show that the optical absorption coefficients in a spherical QD are 2–3 orders of magnitude higher than those in quantum wells and are 2–3 orders smaller than those in a disk-like QD. It is found that the optical absorptions and the optical refractive index are strongly affected not only by the confinement barrier height, dot radius but also by the position of the impurity.

Few-electron semiconductor quantum dots with Gaussian confinement

Abstract We have performed Hartree-Fock calculations of the electronic structure of N ≤ 10 electrons in a quantum dot modeled with a confining Gaussian potential well. We discuss the conditions for the stability of N bound electrons in the system. We show that the most relevant parameter determining the number of bound electrons is V 0 R 2. Such a feature arises from widely valid scaling properties of the confining potential. Gaussian Quantum dots having N = 2, 5, and 8 electrons are particularly stable in agreement with the Hund rule. The shell structure becomes less and less noticeable as the well radius increases.

Effect of confinement potential shape on exchange interaction in coupled quantum dots

Exchange interaction has been studied for electrons in coupled quantum dots(QDs) by a configuration interaction method using confinement potentials withdifferent profiles. The confinement potential has been parametrized by a two-centrepower-exponential function, which allows us to investigate various types of QDsdescribed by either soft or hard potentials of different ranges. For the soft (Gaussian)confinement potential the exchange energy decreases with increasing interdotdistance due to the decreasing interdot tunnelling. For the hard (rectangular-like)confinement potential we have found a non-monotonic behaviour of the exchangeinteraction as a function of distance between the confinement potential centres. In thiscase, the exchange interaction energy exhibits a pronounced maximum for theconfinement potential profile which corresponds to the nanostructure composedof the small inner QD with a deep potential well embedded in the large outerQD with a shallow potential well. This effect results from the strong localizationof electrons in the inner QD, which leads to the large singlet–triplet splitting.Implications of this finding for quantum logic operations have been discussed.

Polaronic effects in a Gaussian quantum dot

Abstract The problem of an electron interacting with longitudinal-optical (LO) phonons is investigated in an N -dimensional quantum dot with symmetric Gaussian confinement in all directions using the Rayleigh–Schrodinger perturbation theory, a variant of the canonical transformation method of Lee–Low–Pines, and the sophisticated apparatus of the Feynman–Haken path-integral technique for the entire range of the coupling parameters and the results for N = 2 and N = 3 are obtained as special cases. It is shown that the polaronic effects are quite significant for small dots with deep confining potential well and the parabolic potential is only a poor approximation of the Gaussian confinement. The Feynman–Haken path-integral technique in general gives a good upper bound to the ground state energy for all values of the system parameters and therefore is used as a benchmark for comparison between different methods. It is shown that the perturbation theory yields for the ground state polaron self-energy a simple closed-form analytic expression containing only Gamma functions and in the weak-coupling regime it provides the lowest energy because of an efficient partitioning of the Gaussian potential and the subsequent use of a mean-field kind of treatment. The polarization potential, the polaron radius and the number of virtual phonons in the polaron cloud are obtained using the Lee–Low–Pines–Huybrechts method and their variations with respect to different parameters of the system are discussed.

Two-electron singlet states in semiconductor quantum dots with Gaussian confinement: asingle-parameter variational calculation

The problem of two electrons in a three-dimensional quantum dot with Gaussianconfinement is investigated for the singlet pairing by a variational method with a verysimple wavefunction containing only a single parameter and a Jastrow-like factor, which isshown to yield fairly good results for deep confining potentials. The calculation is alsoperformed for a few realistic semiconductor quantum dots and the phase diagrams for thetwo-electron singlet states are obtained for these materials. The pair density function iscalculated for several parameter values and its peak positions are obtained as a function ofthe confinement length and the depth of the potential to study the behaviour ofthe electron-pair size. The size of the bound pair of electrons is also obtainedby directly calculating the average distance between the two electrons in threedifferent ways and compared with the pair correlation results. It is furthermoreshown that, other properties remaining the same, the two-electron energy and theelectron-pair size depend crucially on the effective electronic mass and the dielectricconstant of the material. Finally, the ways of improving the wavefunction are alsoindicated.

GAUSSIAN CONFINEMENT IN A JKJ DECAY MODEL

In microscopic decay models, one attempts to describe hadron strong decays in terms of quark and gluon degrees of freedom. We begin by assuming that strong decays are driven by the same interquark Hamiltonian which determines the spectrum, and that it incorporates gaussian confinement. An A → BC decay matrix element of the JKJ Hamiltonian involves a pair-production current matrix elements times a scatering matrix element. Diagrammatically this corresponds to an interaction between an initial line and produced pair.

Gaussian quantum dots of type II in in-plane electric field

The growing interest is recently focusing on QDs of type II, which contrary to type I QDs attract electrons and repulse holes (or conversely). In such QDs an electron–hole pair (X exciton) can still be traped due to electron–hole Coulomb attraction, resulting in significantly more complex structure of excitonic states. We consider an X exciton in QD of type II defined by electrostatic focusing in a narrow quantum well, in the presence of additional external in-plane electric field. The dependence of PL spectrum on dot size and in-plane electric field is analysed within the Hartree approach for model planar Gaussian confinement. The exciton ground state and its energy red-shift are found as a function of electric field and dot size. Corresponding rearrangement of PL spectrum is described. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Hydrogenic impurity in double quantum dots

The ground state binding energy and the average interparticle distances for a hydrogenic impurity in double quantum dots with Gaussian confinement potential are studied by the variational method. The probability density of the electron is calculated, too. The dependence of the binding energy on the impurity position is investigated for GaAs quantum dots. The result shows that the binding energy has a minimum as a function of the distance between the two quantum dots when the impurity is located at the center of one quantum dot or at the center of the edge of one quantum dot. When the impurity is located at the center of the two dots, the binding energy decreases monotonically. (c) 2006 Elsevier B.V. All rights reserved.

Confined Phonons in Si Nanowires

Raman microprobe studies of long crystalline Si nanowires reveal for the first time the evolution of phonon confinement with wire diameter. The Raman band at approximately 520 cm-1 in bulk Si is found to downshift and asymmetrically broaden to lower frequency with decreasing wire diameter D, in good agreement with a phenomenological model first proposed by Richter et al. An adjustable parameter (alpha) is added to the theory that defines the width of the Gaussian phonon confinement function. We find that this parameter is not sensitive to diameter over the range 4-25 nm.

Raman scattering investigations of nanocrystalline thorium oxide.

Raman scattering investigations are carried out on nanocrystalline thorium oxide powders. Shift and broadening of the Raman peak associated with F2g phonons are observed for the nanocrystalline samples as compared with those of the bulk. The peak shift and broadening are found to increase further as the particle size decreases. A quantitative analysis of the Raman line shape is carried out with a Gaussian confinement model, and the estimated size is found to be consistent with that obtained from X-ray diffraction and transmission electron microscopy.

Excitonic trions in single and double quantum dots

Excitonic trions in quantum dots with Gaussian confinement potential are studied by the variational method. We show that the photoluminescence line associated with the negative trion is always shifted towards lower energies with respect to the exciton line, and that this shift is larger for smaller dots. The qualitative behavior of the photoluminescence line of the positive trion is the same only in dots which resemble quantum wells or quantum wires. In other dots the size dependence of the positive-trion shift is more complex. In particular, we show that the order of the positive-trion line and the exciton line can be changed. The present approach has been generalized to the trion states in vertically coupled dots. We discuss the trion energy-level splitting induced by the coupling between the dots, as well as the relation between the photoluminescence-line shift with the binding energy of the trion in the double quantum dots.

Nature of confinement of phonons in nanocrystalline CVD diamond

Self-standing nanocrystalline CVD diamond sheets are investigated using Raman spectroscopy and X-ray diffraction. The sheets are composed of diamond phase and an amorphous-carbon-like non-diamond phase whose content increases with increasing gas pressure in the growth chamber. In the samples synthesised at high pressures the 1332 cm −1 diamond Raman peak exhibits asymmetric broadening. Although the scattering from defects can account for the symmetric part of the line-width, the asymmetry is much more than expected for a confined phonon line-shape calculated according to the Gaussian confinement model for the particle sizes obtained from X-ray diffraction. An alternative model for the confinement of phonons is discussed which involves the standing waves arising from the reflection of the phonons from the elastic-dielectric boundary. The calculated line-shapes arising from the contributions from the allowed q-points in the Brillouin-zone are found to agree with the measured spectra.

Polymer confinement in undulated membrane boxes and tubes

We consider quantum particle or Gaussian polymer confinement between two surfaces and in cylinders with sinusoidal undulations. In terms of the variational method, we show that the quantum-mechanical wave equations have lower ground-state energy in these geometries under long wavelength undulations, where bulges are formed and waves are localized in the bulges. It turns out correspondingly that Gaussian polymer chains in undulated boxes or tubes acquire higher entropy than in exactly flat or straight ones. These phenomena are explained by the uncertainty principle for quantum particles, and by a polymer confinement rule for Gaussian polymers. If membrane boxes or tubes are flexible, polymer-induced undulation instability is suggested. We find that the wavelength of undulations at the threshold of instability for a membrane box is almost twice the distance between two walls of the box. Surprisingly, we find that the instability for tubes begins with a shorter wavelength compared to the "Rayleigh" area-minimizing instability.

Output from Bose condensates in tunnel arrays: the role of mean-field interactions and of transverse confinement

We present numerical studies of atomic transport in 3D and 1D models for a mode-locked, pulsed atom laser as realized by Anderson and Kasevich [Science 281 (1998) 1686] using an elongated Bose condensate of 87Rb atoms poured into a vertical optical lattice. From our 3D results we ascertain in a quantitative manner the role of mean-field interactions in determining the shape and the size of the pulses in the case of Gaussian transverse confinement. By comparison with 1D simulations we single out a best-performing 1D reduction of the mean-field interactions, which yields quantitatively useful predictions for all main features of the matter output.

Visible light emission from Si materials

The photoluminescence of electrochemically etched silicon under excitation in the wavelength range from 325 to 514 nm is described by a single energy gap (of order of 1.9 eV). The Raman spectra can be explained by a Gaussian phonon confinement to a geometrical structure size of about 3 nm. In addition, the novel method of spark erosion for a non-liquid preparation of light-emitting silicon has been used, and it is shown that the light emission spectrum, apart from its overall intensity, is independent of environment gas species (N 2, O 2 or H 2). In areas of higher electric field strength, presumably leading to a smaller effective size, a blue shift is observed in all these cases. This appears to rule out any siloxene-derivate models and suggests a quantum confinement as the basic phenomenon.

The Discussion on Solving the Coupling Equations with Color Van Der Waals Force in the Quark Potential Model

The second order homogeneous ordinary differential equations were derived by introducing the Gaussian type quark confinement potential in order to study color-analog Van der Waals force in N-N interaction. In this paper, it is proved theoretically that the existence and uniqueness of non-zero solution of problem of boundary value in this kind of equations and the non-zero solution are calculated by numerical method (Gill method).