We study the dynamics of the Bogoliubov wave packet in superconductors and calculate the supercurrent carried by the wave packet. We discover an anomalous contribution to the supercurrent, related to the quantum metric of the Bloch wave function. This anomalous contribution is most important for flat or quasiflat bands, as exemplified by the attractive Hubbard models on the Creutz ladder and sawtooth lattice. Our theoretical framework is general and can be used to study a wide variety of phenomena, such as spin transport and exciton transport.

Complete sets of quadratic and cubic force constants calculated for four isotopomers of dioxirane (CH2OO) are used to estimate vibration-rotation interaction contributions to observed values of rotational constants (B″), thereby yielding empirical estimates of the corresponding equilibrium values (Be). At the highest levels of theory, least-squares refinements of atomic coordinates to both the empirical Be values and the associated isotope shifts yield consistent sets of structural parameters. Recommended values are re(CO)=1.3846±0.0005 Å; re(OO)=1.5133±0.0005 Å; re(CH)=1.0853±0.0015 Å and θe(HCH)=117.03±0.20°. Semidiagonal quartic force constants (in the normal coordinate representation) also calculated for CH2OO are used to estimate anharmonic contributions to the fundamental vibrational frequencies. Arguments based on the latter set of results support those made in a previous theoretical study and clearly show that two infrared features assigned to dioxirane in a matrix-isolation experiment must be due to a different carrier.

A computational model is presented for the simulation of three-dimensional electrodiffusion of ions. Finite volume techniques were used to solve the Poisson-Nernst-Planck equation, and a dual Delaunay-Voronoi mesh was constructed to evaluate fluxes of ions, as well as resulting electric potentials. The algorithm has been validated and applied to a generalized node of Ranvier, where numerical results for computed action potentials agree well with cable model predictions for large clusters of voltage-gated ion channels. At smaller channel clusters, however, the three-dimensional electrodiffusion predictions diverge from the cable model predictions and show a broadening of the action potential, indicating a significant effect due to each channel's own local electric field. The node of Ranvier complex is an elaborate organization of membrane-bound aqueous compartments, and the model presented here represents what we believe is a significant first step in simulating electrophysiological events with combined realistic structural and physiological data.

The quantum trajectory method (QTM) is extended to the dynamics of electronic nonadiabiatic collisions. Equations of motion are first derived for the probability density, velocity, and action function for wave packets moving on each of the coupled electronic potential surfaces. These discretized equations are solved in the Lagrangian (moving with the fluid) picture to give the trajectory dynamics of fluid elements evolving on each potential surface. This trajectory method is fully quantum mechanical and does not involve “trajectory surface hopping.” The method is applied to nonadiabiatic collision models involving two coupled electronic states. The quantum trajectory results are in excellent agreement with solutions computed (using space-fixed grid methods) directly from the time-dependent Schrödinger equation.