Colligative Properties of Solutions: II. Vanishing Concentrations

We continue our study of colligative properties of solutions initiated in ref. 1. We focus on the situations where, in a system of linear size L, the concentration and the chemical potential scale like c=ξ/L and h=b/L, respectively. We find that there exists a critical value ξt such that no phase separation occurs for ξ≤ξt while, for ξ>ξt, the two phases of the solvent coexist for an interval of values of b. Moreover, phase separation begins abruptly in the sense that a macroscopic fraction of the system suddenly freezes (or melts) forming a crystal (or droplet) of the complementary phase when b reaches a critical value. For certain values of system parameters, under “frozen” boundary conditions, phase separation also ends abruptly in the sense that the equilibrium droplet grows continuously with increasing b and then suddenly jumps in size to subsume the entire system. Our findings indicate that the onset of freezing-point depression is in fact a surface phenomenon.     

Statistical Ensemble and Quantization of Thermodynamics

We derive the equations of quantized thermodynamics from the Gibbs ensemble and obtain a representation of the new equations which permits a formal passage to the Bardeen--Cooper--Schrieffer equations.     

A new approach for the justification of ensembles in quantum statistical mechanics — I

In this and the following paper, a new approach for the justification of ensembles in statistical mechanics is given. The essential physical idea is that a measurement is an average of values arising from disjoint regions in three-space. This idea is given a mathematical basis in terms of a class of operators called local operators, and the first paper is devoted primarily to the development of the properties of local operators. In particular, a complete characterization of the bounded local operators on ₂ spaces of finite measure is given. Two results of importance for statistical mechanics are also derived. First, it is shown that the observables of quantum mechanics are local operators. Second, it is shown that the expectation value of an observable for a pure state can be written formally as an ensemble average. In the following paper, these results are used to develop a new approach for the justification of statistical ensembles.This work was supported in part by research grants from the National Science Foundation and the U.S. Public Health Service. The material of this paper is contained in a doctoral dissertation submitted by the author to the University of Oregon (1969).     

A statistical theory of excitable membranes. Nonlinear force-flux relation and fluctuation

A statistical theory of an excitable membrane is proposed under the assumptions that the membrane is composed of an ensemble of a number of active patches, and that the flip-flop transition of an active patch is governed by the dissipative interaction caused by an electric eddy current. By the method of expanding the master equation in the system size together with the Gaussian approximation, the time course of an excitation and the steady N-shaped relation between current and voltage are derived from the ensemble theory of open systems. The fluctuation of electric current under a fixed voltage becomes anomalously large in the marginal state at the threshold potential. The fluctuation associated with an action potential increases sharply at the jump-up transition, but it is not so large at the flip-back catastrophe. The fluctuation-dissipation relation at the steady state of the membrane system is discussed on the basis of a variational principle.This study was supported partly by a grant from the Ministry of Education, Japan.     

利用冷原子系综制备窄线宽三光子频率纠缠态

从理论上提出了一种制备窄线宽三光子频率纠缠态的实验方案,该三光子纠缠态利用在两个冷原子系综中的四波混频和电磁诱导透明来产生.利用二阶微扰理论完成了相关计算,并通过分析光子符合计数,研究了该三光子纠缠态的特性,证明其具有类似于离散变量三粒子W态的基本性质,并具有光子反群聚效应.     

含噪混沌时间序列预测误差分析

对于含噪混沌时间序列预测问题, 传统方法存在较大的经验性, 对预测误差的构成分析不足, 因而忽略了混沌动态重建与预测模型建立之间的差异性. 本文将实际预测误差分解为预测器偏差和输入扰动误差, 并对整体最小二乘和正则化两种全局预测方法进行分析比较, 进而说明整体最小二乘适用于混沌动态的重建, 对预测器偏差影响较大, 而正则化方法能够改善预测器敏感性, 对输入扰动误差影响较大. 通过两个仿真实例, 展示了混沌动态重建与预测模型建立之间的差异, 在对比最小二乘和正则化方法的同时验证了实际预测误差受预测器偏差和输入扰动误差共同作用. 并指出, 在实际操作时应在二者间寻求平衡, 以便使模型预测精度达到最优. 关键词： 混沌时间序列预测 噪声 整体最小二乘 正则化     

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.