The transition of a fluid to a rigid glass upon cooling is a common route of transformation from liquid to solid that embodies the most poorly understood features of both phases 1,2,3 . From the liquid perspective, the puzzle is to understand stress relaxation in the disordered state. From the perspective of solids, the challenge is to extend our description of structure and its mechanical consequences to materials without long range order. Using computer simulations, we show that the localized low frequency normal modes of a configuration in a supercooled liquid are causally correlated to the irreversible structural reorganization of the particles within that configuration. We also demonstrate that the spatial distribution of these soft local modes can persist in spite of significant particle reorganization. The consequence of these two results is that it is now feasible to construct a theory of relaxation length scales in glass-forming liquids without recourse to dynamics and to explicitly relate molecular properties to their collective relaxation.A crucial concept 4-9 for the transition between liquid and glass is that the dramatic increase in viscosity of a supercooled liquid as it approaches vitrification is caused by the growth of localized domains of particles that must rearrange for the liquid to flow. Locating a causal link between local structure and such dynamical heterogeneities has proven elusive 10,11 .Recently, a fruitful computational approach to isolating the structural origin of dynamical heterogeneity has been put forward in the dual notions of an "isoconfigurational ensemble" and "propensity for motion" 12. The iso-configurational ensemble refers to the ensemble of trajectories that are run from an identical configuration of particles with random initial momenta sampled from the equilibrium Boltzmann distribution. Propensity refers to the mean squared displacement of individual particles when averaged over the ensemble at a given time scale. The heterogeneous character and increased clustering exhibited in the spatial propensity maps established that the spatial distribution of these dynamic heterogeneities can be explicitly attributed to structural features, as yet unidentified.Our goal is to understand that aspect of dynamic heterogeneity directly associated with structural relaxation. To this end we are interested in motions that a) involve local reorganisation of particle configurations (here measured in terms of changes in nearest neighbour pairings 13 ) and b) are irreversible over some observation time 14 and, hence, contribute to relaxation. To investigate this we consider a two dimensional binary

We present a quantum phase-space model of the Bose-Einstein condensate ͑BEC͒ in a double-well potential. In a quantum two-mode approximation we examine the eigenvectors and eigenvalues and find that the energy correlation diagram indicates a transition from a delocalized to a fragmented regime. Phase-space information is extracted from the stationary quantum states using the Husimi distribution function. We show that the mean-field phase-space characteristics of a nonrigid physical pendulum arises from the exact quantum states, and that only 4-8 particles per well are needed to reach the semiclassical limit. For a driven double-well BEC, we show that the classical chaotic dynamics is manifest in the dynamics of the quantum states. Phase-space analogy also suggests that a phase-displaced wave packet put on the unstable fixed point on a separatrix bifurcates to create a superposition of two pendulum rotor states-a macroscopic superposition state of BEC. We show that the choice of initial barrier height and ramping, following a phase imprinting on the condensate, can be used to generate controlled entangled number states with tunable extremity and sharpness.

The tectosphere, namely the portions of Earth's mantle lying below cratons, has a thermochemical structure that differs from average suboceanic mantle. The tectosphere is thought to be depleted in its basaltic components and to have an intrinsic buoyancy that balances the mass increase associated with its colder temperature relative to suboceanic mantle. Inversions of a large set of geodynamic data related to mantle convection, using tomography-based mantle flow models, indicate that the tectosphere is chemically depleted and relatively cold to 250 kilometers depth below Earth's surface. The approximate equilibrium between thermal and chemical buoyancy contributes to cratonic stability over geological time.

Using computer simulations, we show that the localized low frequency normal modes of a configuration in a supercooled liquid are strongly correlated with the irreversible structural reorganization of the particles within that configuration. Establishing this correlation constitutes the identification of the aspect of a configuration that determines the heterogeneity of the subsequent motion. We demonstrate that the spatial distribution of the summation over the soft local modes can persist in spite of particle reorganization that produces significant changes in individual modes. Along with spatial localization, the persistent influence of soft modes in particle relaxation results in anisotropy in the displacements of mobile particles over the timescale referred to as β relaxation.

[1] Measurements of heat flow and U, Th, K concentrations are used to determine the amount of heat generated in various belts of the Superior Province, the largest Archean craton on Earth. These data allow estimates of the average crustal heat production and indicate compositional differences between upper and lower crustal assemblages. The bulk average heat production of the Superior Province crust is 0.64 mW m À3 and is almost the same in different belts of slightly different ages, illustrating the remarkable uniformity of crust-building mechanisms. In the wider context of the North American continent, the bulk crustal heat production decreases from 1.0 mW m À3 in the oldest Slave Province to a minimum of 0.55 mW m À3 in the Paleo-Proterozoic Trans-Hudson Orogen. It increases in younger provinces, culminating with a high value of 1.05 mW m À3 in the Phanerozoic Appalachian Province. In all provinces, U and Th enrichment is systematically associated with sedimentary accumulations. A crustal differentiation index is obtained by calculating the ratio between the average values of heat production at the surface and in the bulk crust. The differentiation index is correlated with the bulk average heat production, which suggests that crustal differentiation processes are largely driven by internal radiogenic heat.