Bounds on Localized Modes in the Crystal Impurity Problem

Using general properties of the crystal site representation normal mode matrix, we provide some very simple bounds on localized modes in simple, body-centered and face-centered cubic crystals with substitutional point defects. We derive a trace condition constraint on the net change in crystal eigenfrequencies caused by the introduction of a defect, with the condition being a completely general one which holds for any combination of central and non-central crystal force-constants and for all-neighbor interactions. Using this condition we show that the sufficient condition for producing localized modes in an arbitrary cubic crystal by a mass change at the defect site is that the defect mass be less than one half of that of the host atom mass which it replaces, and that the sufficient condition for producing localized modes in an arbitrary cubic crystal by force-constant changes alone is that the defect site self force-constant be greater than twice that of the pure crystal self force-constant of the host atom which it replaces.Comment: 25 pages, 3 figures, revtex4. Updated version contains much more general bounds than original versio

Time-reversal symmetric work distributions for closed quantum dynamics in the histories framework

A central topic in the emerging field of quantum thermodynamics is the definition of thermodynamic work in the quantum regime. One widely used solution is to define work for a closed system undergoing non-equilibrium dynamics according to the two-point energy measurement scheme. However, due to the invasive nature of measurement the two-point quantum work probability distribution leads to inconsistencies with two pillars of thermodynamics: it breaks the first law and the time-reversal symmetry expected for closed dynamics. We here introduce the quantum histories framework as a method to characterise the thermodynamic properties of the unmeasured, closed dynamics. Extending the classical phase space trajectories to continuous power operator trajectories allows us to derive an alternative quantum work distribution for closed quantum dynamics that fulfils the first law and is time-reversal symmetric. We find that the work distribution of the unmeasured dynamics leads to deviations from the classical Jarzynski equality and can have negative values highlighting distinctly non-classical features of quantum work.Comment: 18 pages, 2 figures, comments welcom

Entropy production and time-asymmetry in the presence of strong interactions

It is known that the equilibrium properties of open classical systems that are strongly coupled to a heat bath are described by a set of thermodynamic potentials related to the system's Hamiltonian of mean force. By adapting this framework to a more general class of non-equilibrium states, we show that the equilibrium properties of the bath can be well-defined, even when the system is arbitrarily far from equilibrium and correlated with the bath. These states, which retain a notion of temperature, take the form of conditional equilibrium distributions. For out-of-equilibrium processes we show that the average entropy production quantifies the extent to which the system-bath state is driven away from the conditional equilibrium distribution. In addition, we show that the stochastic entropy production satisfies a generalised Crooks relation and can be used to quantify time-asymmetry of correlated non-equilibrium processes. These results naturally extend the familiar properties of entropy production in weakly-coupled systems to the strong coupling regime. Experimental measurements of the entropy production at strong coupling could be pursued using optomechanics or trapped ion systems, which allow strong coupling to be engineered.Comment: 8 pages, 1 figure, comments welcom

United States Nuclear Export Controls

This article will explore the U.S. nuclear export controls regime. It will initially discuss controls affecting the export of nuclear material, facilities, and specially designed components of nuclear facilities. This section will specifically consider export licensing procedures and requirements, agreements for nuclear cooperation, the specific export criteria for major nuclear cooperation, as well as the necessary policy determination. Then the Article will discuss the procedures and requirements for obtaining a license to export dual-use equipment, the authorization necessary for the export of nuclear technology and the subsequent arrangement process, which further aids in the implementation of U.S. non-proliferation policies