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The microscopic motion of water is a central question, but gaining experimental information about the interfacial dynamics of water in fields such as catalysis, biophysics and nanotribology is challenging due to its ultrafast motion, and the complex interplay of intermolecular and molecule-surface interactions. Here we present an experimental and computational study of the nanoscale-nanosecond motion of water at the surface of a topological insulator (TI), Bi 2 Te 3. Understanding the chemistry and motion of molecules on TI surfaces, while considered a key to design and manufacturing for future applications, has hitherto been hardly addressed experimentally. By combining helium spin-echo spectroscopy and density functional theory calculations, we are able to obtain a general insight into the diffusion of water on Bi 2 Te 3. Instead of Brownian motion, we find an activated jump diffusion mechanism. Signatures of correlated motion suggest unusual repulsive interactions between the water molecules. From the lineshape broadening we determine the diffusion coefficient, the diffusion energy and the pre-exponential factor.

We derive an analytical expression for the intermediate scattering function of a particle on a flat surface obeying the Generalised Langevin equation, with exponential memory friction. Numerical simulations based on an extended phase space method confirm the analytical results. The simulated trajectories provide qualitative insight into the effect that introducing a finite memory timescale has on the analytical line shapes. The relative amplitude of the long-time exponential tail of the line shape is suppressed, but its decay rate is unchanged, reflecting the fact that the cutoff frequency of the exponential kernel affects short-time correlations but not the diffusion coefficient which is defined in terms of a long-time limit. The exponential sensitivity of the relative amplitudes to the decay time of the chosen memory kernel is a very strong indicator for the prospect of inferring a friction kernel and the physical insights from experimentally measured intermediate scattering functions. t

We present a package using Simulink and MATLAB to perform molecular dynamics simulations of interacting particles obeying a Generalized Langevin Equation. The package, which accounts for three spatial dimensions and rigid-body like rotation, is tuned to explore surface diffusion of co-adsorbed species. The physical parameters are species specific, and include userdefined colored noise spectra and memory friction kernels acting independently on translational and rotational degrees of freedom. We benchmark the simulations using established analytical results for dynamical correlation functions, and we use the package to numerically verify novel analytical results concerning dissipative rotational motion and mutli-exponential friction kernels. The package provides a straightforward way to expand the modeling of ultra-fast surface diffusion problems at the atomic scale.

Exact expressions are derived for the intermediate scattering function (ISF) of a quantum particle diffusing in a harmonic potential and linearly coupled to a harmonic bath. The results are valid for arbitrary strength and spectral density of the coupling. The general, exact non-Markovian result is expressed in terms of the classical velocity autocorrelation function, which represents an accumulated phase during a scattering event. The imaginary part of the exponent of the ISF is proportional to the accumulated phase, which is an antisymmetric function of the correlation time t. The expressions extend previous results given in the quantum Langevin framework where the classical response of the bath was taken as Markovian. For a special case of non-Markovian friction, where the friction kernel decays exponentially in time rather than instantaneously, we provide exact results relating to unconfined quantum diffusion, and identify general features that allow insight to be exported to more complex examples. The accumulated phase as a function of the t has a universal gradient at the origin, depending only on the mass of the diffusing system particle. At large t the accumulated phase reaches a constant limit that depends only on the classical diffusion coefficient and is therefore independent of the detailed memory properties of the friction kernel. Non-Markovian properties of the friction kernel are encoded in the details of how the accumulated phase switches from its t → −∞ to its t → +∞ limit, subject to the constraint of the universal gradient. When memory effects are significant, the transition from one limit to the other becomes non-monotonic, owing to oscillations in the classical velocity autocorrelation. The result is interpreted in terms of a solvent caging effect, in which slowly fluctuating bath modes create transient wells for the system particle.

Nanoscopic clustering in a 2D disordered phase is observed for oxygen on Ru(0001) at low coverages and high temperatures. We study the coexistence of quasi-static clusters (with a characteristic length of ∼ 9Å) and highly mobile atomic oxygen which diffuses between the energy-inequivalent, threefold hollow sites of the substrate. We determine a surprisingly low activation energy for diffusion of 385 ± 20 meV. The minimum of the O − O interadsorbate potential appears to be at lower separations than previously reported.

The classical Langevin dynamics of a particle in a periodic potential energy landscape are studied via the intermediate scattering function (ISF). By construction, the particle performs coupled vibrational and activated jump motion with a wide separation of the vibrational period and the mean residence time between jumps.The long time limit of the ISF is a decaying tail proportional to the function that describes ideal jump motion in the absence of vibrations. The amplitude of the tail is unity in idealized jump dynamics models, but is reduced from unity by the intrawell motion. Analytical estimates of the amplitude of the jump motion signature are provided by assuming a factorization of the conditional probability density of the particle position at long times, motivated by the separation of time scales associated with inter-cell and intra-cell motion. The assumption leads to a factorization of the ISF at long correlation times, where one factor is an ideal jump motion signature, and the other component is the amplitude of the signature. The amplitude takes the form of a single-particle anharmonic Debye-Waller factor. The factorization approximation is exact at the diffraction conditions associated with the periodic potential. Numerical simulations of the Langevin equation in one and two spatial dimensions confirm that for a strongly corrugated potential the analytical approximation provides a good qualitative description of the trend in the jump signature amplitude, between the points where the factorization is exact. Published full-text https://doi.

The use of helium diffraction patterns to study desorption processes is explored as a novel extension to traditional methods based on helium specular reflection. The sample, cyclooctatetraene, adsorbed on Cu(111) provides a rich but complex structure. The modulation of cyclooctatetraene by Cu(111) is manifested as a convolution in the diffraction pattern, displaying an averaged super cell symmetry of . The adlayer expands during isothermal desorption, and the change in lattice constant provides a direct measure of the coverage as a function of time. We find a desorption energy of 0.96 ± 0.01 at saturation of the first layer and an upper limit of 1.62 ± 0.07 for isolated molecules. These values and details of the assigned structure indicate chemisorbed molecules with a planar conformation.

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