Correlation function

Abstract: This paper analyzes dynamic properties of hydrogen bonds in liquid water. We use molecular dynamics simulation to calculate different probability densities that govern the time evolution of the formation and rupture of hydrogen bonds. We provide analytical connections between these functions. Excellent agreement with our simulation results is observed. We prove transition state theory rate constant to be identical to the inverse of the associated mean first passage time (hydrogen bond lifetime). Hence, the analysis establishes its Arrhenius temperature dependence. We give the explicit relation between reactive flux correlation function for the relaxation dynamics of hydrogen bonds, and their first passage time probability densities. All the different observations in the existing literature, associated with various estimates of hydrogen bonding times in liquid water that are affected (or not affected) by particular bond criteria, as well as by different definitions of hydrogen bond lifetimes applied in sim...

Abstract: Some ideas of the new theory of Bardeen, Cooper and Schrieffer are expressed in a more transparent form. New collective fermion variables are introduced which are linear combinations of creation and annihilation operators of electrons, and describe elementary excitations. They lead to a simple classification of excited states and a great simplification in the calculations. The structure of the excitation spectrum is investigated without equating the matrix element of the interaction potential to a constant at an early stage, and new relationships and equations are derived. The temperature dependent problem is described by means of a statistical operator, and its relationship to that of the grand canonical ensemble is established. Simple new relationships are obtained for the correlation function.

Abstract: The long-distance properties of classical Heisenberg ferromagnets below the transition point are related to a continuous-field theory, the nonlinear $\ensuremath{\sigma}$ model. The renormalizability of this model in two dimensions and its ultraviolet asymptotic freedom are used to derive renormalization-group equations valid above $d=2$. It is argued that this model is renormalizable up to four dimensions. The scaling properties which incorporate critical and Goldstone singularities follow. Explicit calculations of exponents and of correlation functions in powers of $d\ensuremath{-}2$ are given. A technique is proposed to make calculations in the symmetric phase applicable even in two dimensions.

Abstract: The correlation between fluorescence photons emitted by an optically pumped single molecule of pentacene in a p-terphenyl host has been investigated at short times. The correlation function shows photon antibunching, a unique feature of a nonclassical radiation field, which decreases if two molecules rather than one are pumped at the same time. The peculiarities of the correlation function for a three-level molecule are discussed and the theoretical description outlined.