The Explicit Density Functional and Its Connection with Entropy Maximization

The intrinsic Helmholtz free energy, commonly used as a basis for density functional theories, is here given explicitly as a cluster diagram expansion with density field points. Also given are explicit variational procedures for determining the chemical potential for a given density, the pair potential for a given pair correlation function, and the pair correlation function for a given pair potential. The physical meaning of the density functional is established within the context of a new derivation of statistical mechanics based on entropy that supplies a variational principle for equilibrium by generalizing the thermodynamic potential to nonequlibrium states. This shows that the conventional density functional determines not only the equilibrium density, but also the probability of fluctuations about that density.     

A First Order Generalized Thomas-Fermi Approximation for the Electron Density in Inversion Layers

An operator evaluation of the one-particle density matrix of a degenerate system of independent particles in first order with respect to the gradient of the potential developed by Macke and Rennert yields an analytic expression for the particle density. This method is extended here to potentials with an infinite step and to finite temperatures – a situation which is characteristic for inversion electrons in MIS-systems. The resulting density can be expressed as the Airy transform of the zeroth order (local density approximation). The first order yields both the tunneling into the classically forbidden region and oscillations of the density near the step of the potential. The operator evaluation of the density matrix is shown to be equivalent to solving a Schrödinger like equation. The first order density yields results for the subband structure of (100)Si inversion and accumulation layers at OK in remarkable agreement to density functional calculations of Ando.     

Density profiles and solvation force for a liquid in a slit

Computer simulations and density functional theory results are reported for a Lennard-Jones liquid in a slit or pore formed by two parallel hard walls. Both density profiles and solvation forces are computed. Two classes of calculation are performed. In the first class, a high bulk density is selected and, starting from a high temperature, the temperature is reduced until the temperature corresponding to bulk liquid—vapour coexistence is reached. For small slit widths or exceedingly large widths, the density in the slit decreases continuously until the slit is virtually empty or ‘dry’. When the slit width is somewhat larger than a molecular diameter, but still finite, the density in the slit decreases continuously as the temperature is decreased until there is an abrupt change in the density in the slit. Below this temperature, the density is smaller. Further decreases in the temperature, result in a continuous decrease in the slit density until the slit is virtually empty. In the second class, the density and temperature for bulk coexistence are chosen and the bulk density is increased. At the temperature and bulk density for bulk coexistence, the slit is virtually empty and remains so for all widths that we consider. As the bulk density is increased at constant temperature, the slit remains empty as the width is increased until some specific width is reached and then starts to fill abruptly. The agreement of the density functional and simulation results is qualitative but good.     

Influence of electrode separation on ion density in the vacuum arc

The density of singly ionized chromium shortly before and after forced extinction of vacuum arcs between chromium-copper electrodes was measured by laser-induced fluorescence for 2- and 10-mm contact gaps and currents between 200 A and 1 kA. In all cases studied, the ion density was constant before ramping down to the current and decayed exponentially after current zero. The ion density at current zero was found to be lower and to decay faster for a short gap than for a longer one, clearly indicating the effect of the contact separation on the charge carrier density. The variation of the time constant for the ion density decay with contact separation is closely analogous to the influence of contact separation on the recovery time of a switch gap. Furthermore, the recovery of dielectric strength of a chromium-copper gap proceeds on the same timescale as the decay of the density of singly ionized chromium. Both of these findings confirm that the ion density has a strong impact on the recovery of a vacuum gap     

Narrowband and broadband active control in an enclosure using the acoustic energy density

An active control system based on the acoustic energy density is investigated. The system is targeted for use in three-dimensional enclosures, such as aircraft cabins and rooms. The acoustic energy density control method senses both the potential and kinetic energy densities, while the most popular control systems of the past have relied on the potential energy density alone. Energy density fields are more uniform than squared pressure fields, and therefore, energy density measurements are less sensitive to sensor location. Experimental results are compared to computer-generated results for control systems based on energy density and squared pressure for a rectangular enclosure measuring 1.5 x 2.4 x 1.9 m. Broadband and narrowband frequency pressure fields in the room are controlled experimentally. Pressure-field and mode-amplitude data are presented for the narrowband experiments, while spectra and pressure-field data are presented for the broadband experiment. It is found that the energy density control system has superior performance to the squared pressure control system since the energy density measurement is more capable of observing the modes of a pressure field. Up to 14.4 and 3.8 dB of cancellation are achieved for the energy density control method for the narrowband and broadband experiments presented, respectively.     

On the stability of the Hartree-Fock homogeneous density solution for nuclear matter

The nuclear matter energy density used by Overhauser is shown not to be realistic. The consequence of a static density fluctuation thus seems doubtful. The application of the method of Baym, Bethe and Pethik, developed for neutron star matter problems, shows that for a more realistic nuclear energy density containing the Thomas-Fermi part plus gradient terms, both spatially periodic compression and decompression about the saturation density, augment the energy. In addition, positive gradient terms tend to prevent a rippled density.     

Density Matrix in Quantum Mechanics and Distinctness of Ensembles Having the Same Compressed Density Matrix

We clarify different definitions of the density matrix by proposing the use of different names, the full density matrix for a single-closed quantum system, the compressed density matrix for the averaged single molecule state from an ensemble of molecules, and the reduced density matrix for a part of an entangled quantum system, respectively. We show that ensembles with the same compressed density matrix can be physically distinguished by observing fluctuations of various observables. This is in contrast to a general belief that ensembles with the same compressed density matrix are identical. Explicit expression for the fluctuation of an observable in a specified ensemble is given. We have discussed the nature of nuclear magnetic resonance quantum computing. We show that the conclusion that there is no quantum entanglement in the current nuclear magnetic resonance quantum computing experiment is based on the unjustified belief that ensembles having the same compressed density matrix are identical physically. Related issues in quantum communication are also discussed.     

Integral equation theory of a one dimensional hard-ellipse fluid between hard walls

Density functional theory is used to study the structure of a one dimensional fluid model of hard-ellipse molecules with their axes freely rotating in a plane, confined between hard walls. A simple Hypernetted chain (HNC) approximation is used for the density functional of the fluid and the integral equation for the density is obtained from the grand potential. The only required input is the direct correlation function of the one dimensional hard-ellipse fluid. For this model, the pressure, sum rule and the density at the walls are obtained. The Percus Yevick (PY), for lower density, and HNC, for higher density, integral equations are also solved to obtain the direct correlation function of hard-ellipse model introduced here. We obtain the average density at the wall as well as the radial density profile. We compare these with Monte Carlo simulations of the same model and find reasonable agreement.     

Neutrino oscillations with three flavors in matter of varying density

In this paper, we discuss the evolution operator and the transition probabilities expressed as functions of the vacuum mass squared differences, the vacuum mixing angles, and the matter density parameter for three flavor neutrino oscillations in matter of varying density in the plane wave approximation. The applications of this to neutrino oscillations in a model of the earth's matter density profile, step function matter density profiles, constant matter density profiles, linear matter density profiles, and finally in a model of the sun's matter density profile are discussed. We show that for matter density profiles which do not fluctuate too much, the total evolution operator consisting of n operators can be replaced by one single evolution operator in the semi-classical approximation. Received: 23 March 2001 / Published online: 8 June 2001     

Spatial structure of an incompressible quantum Hall strip

The incompressible quantum Hall strip is sensitive to charging of localized states in the cyclotron gap. We study the effect of localized states by a density functional approach and find electron density and the strip width as a function of the density of states in the gap. Another important effect is electron exchange. By using a model density functional which accounts for negative compressibility of the QH state, we find electron density around the strip. At large exchange, the density profile becomes nonmonotonic. Both effects, localized states and exchange, lead to a substantial increase of the strip width.     

On the slow dynamics of density fluctuations near the colloidal glass transition

Slow dynamics of density fluctuations near the colloidal glass transition is discussed from a new viewpoint by numerically solving a nonlinear stochastic diffusion equation for the density fluctuations recently proposed by one of the present authors (MT). The effects of spatial heterogeneities on the dynamics of density fluctuations are then investigated in an equilibrium system. The spatial heterogeneities are generated by the nonlinear density fluctuations, while in a nonequilibrium system they are described by a nonlinear deterministic equation for the average number density. The dynamics of equilibrium density fluctuations is thus shown to be quite different from that of nonequilibrium ones, leading to a logarithmic decay followed by less distinct α- and β-relaxation processes. Received 9 March 2002 and Received in final form 19 September 2002     

Determination of Particle Mass Density Distribution

A new method for the determination of two characteristics of a sample of particles, the correlation of particle mass density with particle size and the distribution of particle mass density, is presented. The new method to meet these requirements is based on the combination of two optical particle sizing techniques where the measured particle characteristics have a different dependence on particle mass density. Photosedimentation and laser diffraction were chosen as suitable techniques for this goal. The determination of particle mass density by photosedimentation and laser diffraction is based on the fact that for each particle size class of the sample to be analysed the mass density can be calculated by an application of the Lambert-Beer law. The particle size distribution of the sample has to be known for the determination of particle mass density, and it is measured by laser diffraction. From this, two particle characteristics, the relationship of particle mass density and particle size and the distribution of particle mass density, are obtained. The capacity of the algorithm and its limitations are demonstrated by computational simulations including an error propagation analysis. Experimental results are shown for homogeneous and heterogeneous materials.     

A perturbation approach to the density functional theory of adsorption

A modified treatment of an exact density functional theory for non-uniform fluids due to Saam and Ebner is presented and a perturbation method of solution is proposed which avoids the need for a local density approximation. For hard-core fluids near a hard wall the equation for the equilibrium density reduces tothe wall-particle version of the RHNC approximation.     

On the summation of the virial expansion for the local density of a gas in contact with a solid

We investigate the density profile of a fluid in contact with a wall. Our analysis is based on the summation of the virial expansion for the local density and the resulting integral equation for the density profile involves the two particle direct correlation function of a non-uniform fluid.     

Instationary Electric Fields,Ion Transport and Strong Density Fluctuations in Tokamaks with Dominant Anomalous Electron Transport

A common explanation is given for ion transport and strong broadband density fluctuations in tokamaks as a result of large anomalous electron transport near dominant magnetic surfaces (resp. in small magnetic islands). The main mechanism is local density flattening connected with an anomalous electron transport induced instationary radial electric field, which forces the ions via polarization drift to follow the electrons. For the density flattening process an exact solution of the time-dependent diffusion equation for a linear initial profile over the island width is used. From this we also derive an expression for a temporal growing radial electric field. This positive field reaches its maximum at the density plateau. Strong viscous diffusion or instability-induced transport between high and low electric field regions may now reverse the density flattening. Therefore relaxation oscillations result which may also explain the observed strong density and potential fluctuations in tokamaks. Several details of recent measurements of impurity ion behaviour and density fluctuations in tokamaks may be better explained with the theory given here.     

Generalized acoustic energy density

The properties of acoustic kinetic energy density and total energy density of sound fields in lightly damped enclosures have been explored thoroughly in the literature. Their increased spatial uniformity makes them more favorable measurement quantities for various applications than acoustic potential energy density (or squared pressure), which is most often used. In this paper, a generalized acoustic energy density (GED), will be introduced. It is defined by introducing weighting factors into the formulation of total acoustic energy density. With an additional degree of freedom, the GED can conform to the traditional acoustic energy density quantities, or it can be optimized for different applications. The properties of the GED will be explored in this paper for individual room modes, a diffuse sound field, and a sound field below the Schroeder frequency.     

HL－1电子密度行为在各种条件下的实验研究

在ＨＬ－１装置电子密度测量中，进一步改进了密度相移信号的处理方法。在氘放电、氦补充送气条件下得到了ＨＬ－１最高电子密度１０．８×１０１３ｃｍ－３。总结了密度在各种实验条件下的行为，并对各种实验条件对密度的影响进行了分析。     

非理想背光照相对靶壳阿贝尔密度反演的影响

建立了背光照相的模拟手段,研究了记录屏像素尺寸、背光强度分布、背光光谱非单色、针孔弥散及针孔形状对惯性约束聚变中常用塑料球壳的阿贝尔密度反演的影响。结果表明:较大的记录屏像素尺寸会掩盖密度分布的细节;高斯型的背光空间分布会使密度分布低于真实值,可能导致非物理的负密度分布;采用Mo的L带谱线作为背光源也会导致反演密度偏离真实值;当壳层厚度小于针孔尺寸时,针孔弥散效应会显著降低峰值密度,利用维纳滤波法处理背光图像后密度反演的结果得到明显改善;相同针孔面积条件下,椭圆形针孔给出的峰值密度要低于圆形针孔的结果。