Dynamical mechanisms leading to equilibration in two-component gases

Demonstrating how microscopic dynamics cause large systems to approach thermal equilibrium remains an elusive, longstanding, and actively-pursued goal of statistical mechanics. We identify here a dynamical mechanism for thermalization in a general class of two-component dynamical Lorentz gases, and prove that each component, even when maintained in a non-equilibrium state itself, can drive the other to a thermal state with a well-defined effective temperature.Comment: 5 pages, 5 figure

Chaotic Dynamics of a Free Particle Interacting Linearly with a Harmonic Oscillator

We study the closed Hamiltonian dynamics of a free particle moving on a ring, over one section of which it interacts linearly with a single harmonic oscillator. On the basis of numerical and analytical evidence, we conjecture that at small positive energies the phase space of our model is completely chaotic except for a single region of complete integrability with a smooth sharp boundary showing no KAM-type structures of any kind. This results in the cleanest mixed phase space structure possible, in which motions in the integrable region and in the chaotic region are clearly separated and independent of one another. For certain system parameters, this mixed phase space structure can be tuned to make either of the two components disappear, leaving a completely integrable or completely chaotic phase space. For other values of the system parameters, additional structures appear, such as KAM-like elliptic islands, and one parameter families of parabolic periodic orbits embedded in the chaotic sea. The latter are analogous to bouncing ball orbits seen in the stadium billiard. The analytical part of our study proceeds from a geometric description of the dynamics, and shows it to be equivalent to a linked twist map on the union of two intersecting disks.Comment: 17 pages, 11 figures Typos corrected to display section label

Adiabatic-Nonadiabatic Transition in the Diffusive Hamiltonian Dynamics of a Classical Holstein Polaron

We study the Hamiltonian dynamics of a free particle injected onto a chain containing a periodic array of harmonic oscillators in thermal equilibrium. The particle interacts locally with each oscillator, with an interaction that is linear in the oscillator coordinate and independent of the particle's position when it is within a finite interaction range. At long times the particle exhibits diffusive motion, with an ensemble averaged mean-squared displacement that is linear in time. The diffusion constant at high temperatures follows a power law D ~ T^{5/2} for all parameter values studied. At low temperatures particle motion changes to a hopping process in which the particle is bound for considerable periods of time to a single oscillator before it is able to escape and explore the rest of the chain. A different power law, D ~ T^{3/4}, emerges in this limit. A thermal distribution of particles exhibits thermally activated diffusion at low temperatures as a result of classically self-trapped polaronic states.Comment: 15 pages, 4 figures Submitted to Physical Review

IUGS–IUPAC recommendations and status reports on the half-lives of 87 Rb, 146 Sm, 147 Sm, 234 U, 235 U, and 238 U (IUPAC Technical Report)

The IUPAC–IUGS joint Task Group “Isotopes in Geosciences” (TGIG) has evaluated the published literature on the half-lives of six long-lived, geologically relevant radioactive nuclides. Where conflicting literature estimates are present, it is necessary to first identify any systematic bias in accordance with metrological traceability and to exclude the biased estimates from further consideration. The TGIG recommends three robust half-life estimates: 49.61±0.16 Ga for 87Rb, corresponding to a decay constant λ(87Rb) = (1.3972±0.0045)×10–11 a–1; 106.25±0.38 Ga for 147Sm, and a corresponding decay constant λ(147Sm) = (6.524±0.024)×10–12 a–1; 4.4683±0.0096 Ga for 238U, i.e. a decay constant λ(238U) = (1.55125±0.00333)×10–10 a–1. All cited uncertainties have a coverage factor k = 2. For other radionuclides of Sm and U no unambiguous consensus value can be endorsed at present by TGIG, which limits its evaluation to a status report highlighting unaccounted-for potential sources of bias. The improved repeatability of mass spectrometric measurements has revealed systematic bias effects that had been dismissed as subordinate in the past. These issues can only be resolved by future dedicated investigations

IUPAC-IUGS common definition and convention on the use of the year as a derived unit of time (IUPAC Recommendations 2011)

The units of time (both absolute time and duration) most practical to use when dealing with very long times, for example, in nuclear chemistry and earth and planetary sciences, are multiples of the year, or annus (a). Its proposed definition in terms of the SI base unit for time, the second (s), for the epoch 2000.0 is 1 a = 3.1556925445×107 s. Adoption of this definition, and abandonment of the use of distinct units for time differences, will bring the earth and planetary sciences into compliance with quantity calculus for SI and non-SI units of tim

On a semiclassical formula for non-diagonal matrix elements

Let $H(\hbar)=-\hbar^2d^2/dx^2+V(x)$ be a Schr\"odinger operator on the real line, $W(x)$ be a bounded observable depending only on the coordinate and $k$ be a fixed integer. Suppose that an energy level $E$ intersects the potential $V(x)$ in exactly two turning points and lies below $V_\infty=\liminf_{|x|\to\infty} V(x)$. We consider the semiclassical limit $n\to\infty$, $\hbar=\hbar_n\to0$ and $E_n=E$ where $E_n$ is the $n$th eigen-energy of $H(\hbar)$. An asymptotic formula for $$, the non-diagonal matrix elements of $W(x)$ in the eigenbasis of $H(\hbar)$, has been known in the theoretical physics for a long time. Here it is proved in a mathematically rigorous manner.Comment: LaTeX2

Normal Transport at Positive Temperatures in Classical Hamiltonian Open Systems

We study the transport properties of classical Hamiltonian models describing the motion of an unconfined particle coupled to vibrational degrees of freedom in thermal equilibrium at zero or positive temperature. We identify and discuss conditions under which, in such systems, the particle has a well-defined diffusion constant and mobility. We will in particular point out some marked differences with the situation where the particle is confined and described with a Caldeira-Leggett model. We will more specifically report on results obtained in a classical version of the Holstein molecular crystal model, speculate on their relevance in the corresponding quantum system and describe a number of open problems

Simple principles for metrology in chemistry: identifying and counting

Abstract We examine the problem of quantitative chemical measurement for well-identified substances, discuss the quantity called 'amount of substance', the means of expressing it, and its physical SI unit the mole. The everyday quantity which is a number of entities may be measured by the performance of two operations (identification and counting), the results of which may be communicated with two items of information (their name and the number of entities). We distinguish nominal, ordinal, interval and ratio scales of measurement and apply these to counting, referring to ordinal and cardinal numbers and Helmholtz' analysis of measurement. Counting may be by direct serial numeration, direct parallel numeration, or comparative numeration. We discuss the limitations of serial numeration, the possibilities of parallel numeration, and the advantages of comparative numeration where a unit for counting in multiples (such as the analyst's mole) may be used to define a scale on which equal numbers of objects correspond to equal values of some other physical quantity. We conclude that the numeration of very large numbers of objects is readily achieved but with unavoidable uncertainty, using operations which compare numbers of entities either to numbers of other entities or to some other quantity which accurately models numbers of entities