Glasses are solid materials whose constituent atoms are arranged in a disordered manner. The transition from a liquid to a glass remains one of the most poorly understood phenomena in condensed matter physics, and still no fully microscopic theory ex
ists that can describe the dynamics of supercooled liquids in a quantitative manner over all relevant time scales. Here we present such a theoretical framework that yields near-quantitative accuracy for the time-dependent correlation functions of a supercooled system over a broad density range. Our approach requires only simple static structural information as input and is based entirely based on first principles. Owing to this first-principles nature, the framework offers a unique platform to study the relation between structure and dynamics in glass-forming matter, and paves the way towards a systematically correctable and ultimately fully quantitative theory of microscopic glassy dynamics.
The mode-coupling theory of the glass transition treats the dynamics of supercooled liquids in terms of two-point density correlation functions. Here we consider a generalized, hierarchical formulation of schematic mode-coupling equations in which th
e full basis of multipoint density correlations is taken into account. By varying the parameters that control the effective contributions of higher-order correlations, we show that infinite hierarchies can give rise to both sharp and avoided glass transitions. Moreover, small changes in the form of the coefficients result in different scaling behaviors of the structural relaxation time, providing a means to tune the fragility in glass-forming materials. This demonstrates that the infinite-order construct of generalized mode-coupling theory constitutes a powerful and unifying framework for kinetic theories of the glass transition.
We investigate the ultracold reaction dynamics of magnetically trapped NH($X ^3Sigma^-$) radicals using rigorous quantum scattering calculations involving three coupled potential energy surfaces. We find that the reactive NH + NH cross section is dri
ven by a short-ranged collisional mechanism, and its magnitude is only weakly dependent on magnetic field strength. Unlike most ultracold reactions observed so far, the NH + NH scattering dynamics is non-universal. Our results indicate that chemical reactions can cause more trap loss than spin-inelastic NH + NH collisions, making molecular evaporative cooling more difficult than previously anticipated.
We present a detailed analysis of the role of the magnetic dipole-dipole interaction in cold and ultracold collisions. We focus on collisions between magnetically trapped NH molecules, but the theory is general for any two paramagnetic species for wh
ich the electronic spin and its space-fixed projection are (approximately) good quantum numbers. It is shown that dipolar spin relaxation is directly associated with magnetic-dipole induced avoided crossings that occur between different adiabatic potential curves. For a given collision energy and magnetic field strength, the cross-section contributions from different scattering channels depend strongly on whether or not the corresponding avoided crossings are energetically accessible. We find that the crossings become lower in energy as the magnetic field decreases, so that higher partial-wave scattering becomes increasingly important textit{below} a certain magnetic field strength. In addition, we derive analytical cross-section expressions for dipolar spin relaxation based on the Born approximation and distorted-wave Born approximation. The validity regions of these analytical expressions are determined by comparison with the NH + NH cross sections obtained from full coupled-channel calculations. We find that the Born approximation is accurate over a wide range of energies and field strengths, but breaks down at high energies and high magnetic fields. The analytical distorted-wave Born approximation gives more accurate results in the case of s-wave scattering, but shows some significant discrepancies for the higher partial-wave channels. We thus conclude that the Born approximation gives generally more meaningful results than the distorted-wave Born approximation at the collision energies and fields considered in this work.
Elastic and spin-changing inelastic collision cross sections are presented for cold and ultracold magnetically trapped NH. The cross sections are obtained from coupled-channel scattering calculations as a function of energy and magnetic field. We spe
cifically investigate the influence of the intramolecular spin-spin, spin-rotation, and intermolecular magnetic dipole coupling on the collision dynamics. It is shown that $^{15}$NH is a very suitable candidate for evaporative cooling experiments. The dominant trap-loss mechanism in the ultracold regime originates from the intermolecular dipolar coupling term. At higher energies and fields, intramolecular spin-spin coupling becomes increasingly important. Our qualitative results and conclusions are fairly independent of the exact form of the potential and of the size of the channel basis set.
We present elastic and inelastic spin-changing cross sections for cold and ultracold NH($X,^3Sigma^-$) + NH($X,^3Sigma^-$) collisions, obtained from full quantum scattering calculations on an accurate textit{ab initio} quintet potential-energy surfac
e. Although we consider only collisions in zero field, we focus on the cross sections relevant for magnetic trapping experiments. It is shown that evaporative cooling of both fermionic $^{14}$NH and bosonic $^{15}$NH is likely to be successful for hyperfine states that allow for s-wave collisions. The calculated cross sections are very sensitive to the details of the interaction potential, due to the presence of (quasi-)bound state resonances. The remaining inaccuracy of the textit{ab initio} potential-energy surface therefore gives rise to an uncertainty in the numerical cross-section values. However, based on a sampling of the uncertainty range of the textit{ab initio} calculations, we conclude that the exact potential is likely to be such that the elastic-to-inelastic cross-section ratio is sufficiently large to achieve efficient evaporative cooling. This likelihood is only weakly dependent on the size of the channel basis set used in the scattering calculations.
We present four-dimensional ab initio potential energy surfaces for the three spin states of the NH-NH complex. The potentials are partially based on the work of Dhont et al. [J. Chem. Phys. 123, 184302 (2005)]. The surface for the quintet state is o
btained at the RCCSD(T)/aug-cc-pVTZ level of theory and the energy diferences with the singlet and triplet states are calculated at the CASPTn/aug-cc-pVTZ (n = 2; 3) level of theory. The ab initio potentials are fitted to coupled spherical harmonics in the angular coordinates, and the long range is further expanded as a power series in 1/R. The RCCSD(T) potential is corrected for a size-consistency error prior to fitting. The long-range coeficients obtained from the fit are found to be in good agreement with perturbation theory calculations.
