Microscopic dielectric response functions in semiconductor quantum dots

We calculate and model the microscopic dielectric response function for quantum dots using first principle methods. We find that the response is bulklike inside the quantum dots, and the reduction of the macroscopic dielectric constants is a surface effect. We present a model for the microscopic dielectric function which reproduces well the directly calculated results and can be used to solve the Poisson equation in a nanosystem.     

Electron-phonon interaction in polar solids with application to the tungsten bronzes

We investigate the interaction between electrons and lattice vibrations in polar solids taking into account their microscopic dielectric properties and constructing in a semi-phenomenological manner the nonlocal dielectric function, ?_GG'(q). The results of earlier, phenomenological theories, such as the Clausius-Mossotti formula for the macroscopic screening constant and Fröhlich's electron-phonon coupling parameter α are obtained from the RPA dielectric function when the dipole approximation is used to calculate the screening by the strongly localized valence electrons. For polar metals we also consider the screening by the free conduction electrons. We present and discuss the results of the screened electron-phonon interaction as a function of the phonon wavevector q for the sodium tungsten bronzes.     

On the theory of dielectric relaxation

The Kirkwood expression for the static dielectric constant of a polar substance is extended to non-zero frequencies by a means which avoids the introduction of spherical specimens and the connection between the dipoledipole correlation functions of distinct spatial regions. The procedure is based on a previously derived relation between the dynamic dielectric constant and the current-current susceptibility and on the use of the Callen-Welton theorem to relate the susceptibility to fluctuations. Surface effects are eliminated at the outset by consideration of media which are infinite in extent. A general relation between the long-range dipole-dipole correlations (which fall off as the inverse cube of the distance) and short-range correlations in a specimen composed of non-polarizable molecules is found from a consistency relation. It is shown that the two microscopic relaxation times which result from the existence of but one relaxation time in the dielectric constant correspond to the transverse and longitudinal relaxation times with the longitudinal time being screened relative to the transverse time by the static dielectric constant.     

Induced polarization charge density and microscopic local field for a covalent semiconductor

A model calculation of the static macroscopic dielectric function is presented for diamond in which the consequence of the localised and plane wave features of the band structure on the polarizability are separated. Microscopic local field and polarization charge density induced by an uniform external field are analyzed in real space. Although the macroscopic dielectric function is essentially intensitive to small changes in the parameters of the model, microscopic quantities can be rather sensitive suggesting that one should be carefull in constructing a microscopic dielectric matrix to be used in calculating, for instance, phonon frequencies.     

Interaction of electrons with polar optical phonons in semiconductor superlattices

On the basis of the microscopic theory of lattice dynamics, simulation of the electric potentials created by optical phonons in semiconductor superlattices is performed. It is shown that the spatial distribution of the amplitudes of electric potentials differs from that in a dielectric continuum predicted by the conventional macroscopic model without dispersion. A modified macroscopic continuum theory is proposed that takes into account the dispersion of short-range interatomic forces and allows one to obtain analytical expressions for the potentials of electron-phonon interaction.     

Polarization as a Berry Phase

The macroscopic polarization of a crystalline dielectric is best defined as a Berry phase of the electronic Bloch wavefunctions, a feature that is best exemplified by the spontaneous polarization of a ferroelectric crystal for which a microscopic theory was previously unavailable.     

Microscopic Origin of Universality in Casimir Forces

The microscopic mechanisms for universality of Casimir forces between macroscopic conductors are displayed in a model of classical charged fluids. The model consists of two slabs in empty space at distance d containing classical charged particles in thermal equilibrium (plasma, electrolyte). A direct computation of the average force per unit surface yields, at large distance, the usual form of the Casimir force in the classical limit (up to a factor 2 due to the fact that the model does not incorporate the magnetic part of the force). Universality originates from perfect screening sum rules obeyed by the microscopic charge correlations in conductors. If one of the slabs is replaced by a macroscopic dielectric medium, the result of Lifshitz theory for the force is retrieved. The techniques used are Mayer expansions and integral equations for charged fluids.     

The method of local fields: A bridge between molecular modelling and dielectric theory

At the nanoscale, the charge distribution in a cluster of several atoms or molecules can be calculated ab initio, i.e. without free parameters. Molecular modelling is limited to a relatively small number of atoms compared to macroscopic materials with myriads of atoms. On the other hand, dielectric and ferroelectric properties of macroscopic matter are described by classical theory using mean-field approximations, e. g. the formula of Clausius–Mossotti for dielectrics and the Landau–Ginzburg–Devonshire theory or rather the molecular field theory by Weiss for ferroelectrics. In the context of multiscale simulations we present a microscopic model for dielectrics and ferroelectrics consisting of discrete atoms and / or dipoles. Parameters calculated from molecular modelling can be used here as input to our simulations in order to calculate bigger systems now. All electrostatic interactions are considered and the electrodes are taken into account using the method of images. Based on thermally activated processes, permanent dipoles fluctuate in double well potentials according to the Boltzmann statistics. Neutral atoms are modelled by induced dipoles having dipole moments proportional to the locally prevailing field. The numerical calculations are based on deterministic local field computations and on weighted probabilistic dynamic Monte Carlo steps.     

Electromagnetic stress and momentum in matter

Whether the momentum density associated with an electromagnetic wave in a refracting medium is solely determined by its intensity or its dependent on the refractive index is perhaps of little practical importance, and probably beyond the power of present experimental techniques to decide. Nevertheless, since this question was first propounded by Abraham and Minkowski, it has continued to attract physicists' attention and, to judge by current literature, is still regarded as an open and quite possibly insoluble question. This article expounds some of the approaches to its solution that have been proposed, and shows that one of them leads to a complete solution of both the Abraham-Minkowski controversy and the more general problem of describing the distribution of stress in a material medium in the presence of an electromagnetic disturbance. The treatment emphasizes the significance of the electrostrictive and magnetostrictive terms in the stress tensor. These relatively unfamiliar effects are neither small nor unimportant. They express, in macroscopic terms, consequences of the microscopic structure of a medium which are not adequately described by the usual constitutive relations involving only the relative dielectric constant and the relative magnetic permeability. Their presence in the macroscopic theory ultimately reflects the fact that the individual microscopic charges in matter are subject to forces which, though purely electromagnetic, cannot adequately be described in terms of macroscopic fields, even if these fields are modified by the inclusion of a Lorentz local-field correction. As a result they form a crucial link in the connection between macroscopic and microscopic treatments.     

Microscopic derivation of fluctuation formulas for calculating dielectric constants by simulation

A microscopic derivation using the average Maxwell electric field is given for fluctuation formulas for the dielectric constant of a simulation sample for both periodic and reaction field boundary conditions. The reaction field case is for a spherical cavity reaction field. The derivations put both boundary conditions on an equal footing of microscopic theory and the only nonrigorous part of the derivation is the assumption that the region used to average the electric field is large enough. The fluctuation formula for reaction field boundary conditions is rather different from that used heretofore. The method is applied to a subregion of an isolated spherical system.     

模耦合理论计算纳米粒子在聚合物熔体中的含时扩散系数与常规扩散常数 (cited: 2)

分析和计算了纳米粒子在聚合物熔体中的含时扩散系数与常规扩散常数. 采用广义朗之万方程描述扩散动力学,并通过模耦合理论计算摩擦记忆内核.为简单起见,只考虑了来自两体碰撞和溶剂密度涨落耦合作用两类微观因素对摩擦记忆内核的贡献. 采用聚合物参考作用点模型以及Percus-Yevick闭合条件计算了聚合物-纳米粒子复合溶液的平衡态结构信息函数;详尽分析了纳米粒子的尺寸与聚合物链的尺寸对扩散动力学的影响. 揭示了结构函数、摩擦记忆内核以及扩散系数等随着纳米粒子半径和聚合物链长的变化关系. 结果表明,对于小尺寸的纳米粒子或者短链的聚合物,短时间的非马尔可夫扩散 动力学特征比较显著,含时扩散系数需要更长的时间弛豫到常规扩散常数. 微观因素对扩散常数的贡献随着纳米粒子尺寸的增加而减小,却随着聚合物链长的增加而增大. 此外,模耦合理论得到的扩散常数与Stokes-Einstein关系的预测值进行比较,发现对于小尺寸的纳米粒子或者长链的聚合物,微观因素对扩散常数的的贡献占主导地位. 相反,当纳米粒子较大或者聚合物链长较短时,流体力学的贡献会发挥重要作用.     

Reaction dynamics for heavy particle charge transfer reactions in polar solvents and ion dielectric friction

The authors' theory of a solvent's influence on heavy particle charge transfer reactions in polar solvents with complex frequency-dependent dielectric constant is applied to treat the dielectric friction on a moving ion. The aim is to demonstrate a relation between the approach used in the theory and other approaches used for treating solute-solvent Coulomb interactions. As a result Zwanzig's formula is recovered. In addition, because this formula is derived by the other method, the relationship between the dielectric friction and the dynamics of nonequilibrium solvent polarization is demonstrated in a very transparent manner.     

The elastic dielectric

Macroscopic field equations, boundary conditions and equations of state are derived for the non-linear, macroscopic elastic and dielectric response of an insulator. A centrosymmetric polynomial representation of order four is introduced for the energy density; the equations of state for the electric field and stress tensor are then deduced as polynomials of degree three in the displacement gradients and electric displacement field. The results are applied to the special case of m3m material symmetry.

A finite, point-charge model of a centrosymmetric ionic crystal is introduced and used to determine 0°K microscopic expressions for the electric field and stress tensor equation of state coefficients introduced in the macroscopic analysis. The results are used to calculate the full set of second and third-order non-linear coefficients for NaI, based on a Born-Mayer potential and the 4·2°K elastic stiffness data of Claytor and Marshall.     

Dielectric constant of solvents at nano to bulk regimes: linear response theory and statistical mechanics-based approaches

Statistical mechanics and generalised linear response theory based approaches are employed to derive the analytical expressions for size-dependent dielectric constant and normalised orientation polarisation of solvents. As an illustrative example, water is considered and the dielectric constants for the same are calculated over the entire range of water clusters. Our results reveal that the dielectric constant and normalised orientation polarisation are monotonically increasing with the increase in the number of solvent molecules and converge to the respective bulk values in the thermodynamic limit. More importantly, the dielectric constant of water is found to be independent of the nature, geometry and microscopic charges of the non-spherical ions. This finding offers a new platform for calculating the hydration energy and orientation polarisation based on linear response theory for different kinds of ions in the solvent medium.     

Microscopic theory of formation of macroscopic order

A general microscopic theory for the formation process of macroscopic order is proposed. The existence of a finite on-set time is shown in our framework. The relation between the previous scaling theory and the present one is also discussed.     

A microscopic model of triangular arbitrage

We introduce a microscopic model which describes the dynamics of each dealer in multiple foreign exchange markets, taking account of the triangular arbitrage transaction. The model reproduces the interaction among the markets well. We explore the relation between the parameters of the present microscopic model and the spring constant of a macroscopic model that we proposed previously.     

Collective Excitations in Quasi-Zero-Dimensional GaAs-Al1-xGaxAs Superlattices

The linear-respononae theory is used to calculate the dielectric response of tunneling dot superlattice with a simple model including the many-body effect to an external perturbation in a reasonable way. Explicit analytical results for the dispersion relation are derived. The transition behaviour from one-dimensional chain to quasitwo-dimensional tunneling semiconductor superlattice is discussed.     

Solvation energy of multiply charged anions and dielectric constant for finite system: a microscopic theory based bottom-up and top-down approach

This is the first time a microscopic theory-based bottom-up approach has been implemented to derive an analytical expression for the solvation energy for a finite (N) system, including the bulk. This bottom-up approach provides the information on solvation energies of anionic solutes in finite-size clusters, including the bulk (N = ∞), from the knowledge of the detachment energies for the system containing a few numbers of solvent molecules. However, in the case of dielectric constant, a microscopic theory-based top-down approach has been prescribed to derive an analytical expression for the static dielectric constant for the finite system. In this approach, the knowledge of the dielectric constant for the bulk provides a scheme to obtain the same quantity for a wide numbers of solvent molecules. As an illustrative example, the hydrated doubly charged anions, SO^?2 ₄.NH₂O and C₂O^?2 ₄.NH₂O, have been considered, and the calculated bulk solvation energy for the SO^?2 ₄.NH₂O system is found to be in very good agreement (within 5%) with the available experimental result. However, the same quantity calculated based on the Born model is found to be largely deviating (32%) from the experimental result. The calculated results of the dielectric constant for these two systems support the linear theory of dielectric constant.     

超导电性的量子特征

大量实验事实及量子力学理论已证明微观粒子的运动会表现出一系列量子化特征．因此,过去人们通常认为量子效应是微观粒子所独有的．在本文中,我们通过超导体的一些奇特现象,论述了超导电性的量子特征;阐明在一定条件下由大量微观粒子组成的宏观物体也具有量子化效应,宏观可测量也可以是量子化的,这种宏观量子效应仍可用量子力学理论来研究．     

基于亲电/亲核反应描述符的气体介质绝缘强度预测

研究分子微观参数与气体介质绝缘强度的关联,可为SF₆替代气体筛选提供方向.本文基于密度泛函理论,采用M06-2X泛函与def2系列基组,计算了73种气体分子的亲电/亲核反应描述符,包括轨道能量参数、概念密度泛函理论的参数、不同电子概率密度等值面的静电势参数等;分析了各描述符与气体介质绝缘强度的相关性,以及描述符的独立性,最终提出了绝缘强度预测模型.最低空轨道能量、正负静电势表面积、静电势平均偏差、简缩局部亲电指数最小值与绝缘强度相关性较强,且彼此间相关性较低.预测模型在电子概率密度0.0002 a.u.时精度最优,其可决系数R²为0.809,均方误差MSE为0.096.