Classical kinetic energy, quantum fluctuation terms and kinetic-energy functionals

We employ a recently formulated dequantization procedure to obtain an exact expression for the kinetic energy which is applicable to all kinetic-energy functionals. We express the kinetic energy of an N-electron system as the sum of an N-electron classical kinetic energy and an N-electron purely quantum kinetic energy arising from the quantum fluctuations that turn the classical momentum into the quantum momentum. This leads to an interesting analogy with Nelson's stochastic approach to quantum mechanics, which we use to conceptually clarify the physical nature of part of the kinetic-energy functional in terms of statistical fluctuations and in direct correspondence with Fisher Information Theory. We show that the N-electron purely quantum kinetic energy can be written as the sum of the (one-electron) Weizsacker term and an (N-1)-electron kinetic correlation term. We further show that the Weizsacker term results from local fluctuations while the kinetic correlation term results from the nonlocal fluctuations. For one-electron orbitals (where kinetic correlation is neglected) we obtain an exact (albeit impractical) expression for the noninteracting kinetic energy as the sum of the classical kinetic energy and the Weizsacker term. The classical kinetic energy is seen to be explicitly dependent on the electron phase and this has implications for the development of accurate orbital-free kinetic-energy functionals. Also, there is a direct connection between the classical kinetic energy and the angular momentum and, across a row of the periodic table, the classical kinetic energy component of the noninteracting kinetic energy generally increases as Z increases.Comment: 10 pages, 1 figure. To appear in Theor Chem Ac

Kinetic Turbulence

The weak collisionality typical of turbulence in many diffuse astrophysical plasmas invalidates an MHD description of the turbulent dynamics, motivating the development of a more comprehensive theory of kinetic turbulence. In particular, a kinetic approach is essential for the investigation of the physical mechanisms responsible for the dissipation of astrophysical turbulence and the resulting heating of the plasma. This chapter reviews the limitations of MHD turbulence theory and explains how kinetic considerations may be incorporated to obtain a kinetic theory for astrophysical plasma turbulence. Key questions about the nature of kinetic turbulence that drive current research efforts are identified. A comprehensive model of the kinetic turbulent cascade is presented, with a detailed discussion of each component of the model and a review of supporting and conflicting theoretical, numerical, and observational evidence.Comment: 31 pages, 3 figures, 99 references, Chapter 6 in A. Lazarian et al. (eds.), Magnetic Fields in Diffuse Media, Astrophysics and Space Science Library 407, Springer-Verlag Berlin Heidelberg (2015

Finding the key transition states and intermediates controlling net reaction rates and selectivity

In this paper Campbell's degree of rate control is extended to introduce the concepts of degree of kinetic rate control, degree of kinetic selectivity control, degree of thermodynamic rate control and degree of thermodynamic selectivity control. It is demonstrated by applying hypothetical but realistic kinetic models of varying complexity that the new methods offers a rigorous framework to analyze the importance of kinetic and thermodynamic parameters i.e. establishing the critical parameters of the kinetic model. The methods are general and can be applied to complex reaction networks with multiple overall reactions not only in heterogeneous catalysis but for all sorts of chemical kinetic models

Emergence of Kinetic Behavior in Streaming Ultracold Neutral Plasmas

We create streaming ultracold neutral plasmas by tailoring the photoionizing laser beam that creates the plasma. By varying the electron temperature, we control the relative velocity of the streaming populations, and, in conjunction with variation of the plasma density, this controls the ion collisionality of the colliding streams. Laser-induced fluorescence is used to map the spatially resolved density and velocity distribution function for the ions. We identify the lack of local thermal equilibrium and distinct populations of interpenetrating, counter-streaming ions as signatures of kinetic behavior. Experimental data is compared with results from a one-dimensional, two-fluid numerical simulation.Comment: 8 pages, 6 figure

Atomic simulations of kinetic friction and its velocity dependence at Al/Al and alpha-Al_2O_3/alpha-Al_2O_3 interfaces

Kinetic friction during dry sliding along atomistic-scale Al(001)/Al(001) and alpha-Al2O3(0001)/alpha-Al2O3(0001) interfaces has been investigated using molecular dynamics (MD) with recently developed Reactive Force Fields (ReaxFF). It is of interest to determine if kinetic friction variations predicted with MD follow the macroscopic-scale friction laws known as Coulomb's law (for dry sliding) and Stokes' friction law (for lubricated sliding) over a wide range of sliding velocities. The effects of interfacial commensuration and roughness on kinetic friction have been studied. It is found that kinetic friction during sliding at commensurate alpha-Al2O3(0001)/alpha-Al2O3(0001) interfaces exceeds that due to sliding at an incommensurate alpha-Al2O3(0001)/alpha-Al2O3(0001) interface. For both interfaces, kinetic friction at lower sliding velocities deviates minimally from Coulombic friction, whereas at higher sliding velocities, kinetic friction follows a viscous behavior with sliding damped by thermal phonons. For atomically smooth Al(001)/Al(001), only viscous friction is observed. Surface roughness tends to increase kinetic friction, and adhesive transfer causes kinetic friction to increase more rapidly at higher sliding velocities