Diffusion quantum

3 After correction with a Debye-Waller factor (see section 8.4), the following Lorentzian halfwidths could be determined from time-of-flight spectra of He-atoms scattered from a surface covered with diffusing CO-molecules. 

Quantum tunneling has been considered using the flux-flux correlation function and a Monte-Carlo path integral method by Jaquet and Miller [45]. Metiu et al. have considered quantum diffusion of hydrogen atoms also using the flux-flux correlation method [46]. 

In the flux-flux correlation method [47] the rate constant is obtained as 

At the simplest level of the discussion, the coupling between the diffusion process and phonon excitation/deexcitation processes can be thought of as adding a time-dependent frictional or dissipative force to the equations of motion for 

4 Determine the diffusion constant Do and the activation energy Et, from the following data (adapted from [48]) for hydrogen diffusing on Pt(l 11). The table gives values of F in units of 10 eV as a function of temperature and in A- . 

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This clearly indicates quantum diffusion of H and D atoms, rather than molecular diffusion. In mixed crystals of D2 and HD (with the H2/D2 ratio being from 20 1 to 7 1) the concentration of... 

Such a rough comparison of real mixtures with ideal solutions is definitely not perfect but it allows the authors of [230] to proceed using conventional theory. The general conclusion following this comparison is that the quantum. /-diffusion model just slightly differs from its... 

The effects of transfer of atoms by tunneling may play an essential role in a number of phenomena involving the transfer of atoms and atomic groups in the condensed phase. One may expect that these effects may exist not only in the proton transfer reactions considered above but also in such processes as the diffusion of hydrogen atoms and other light ions (e.g., Li+) in liquids, tunnel inversion and isomerization in some molecules, quantum diffusion of defects and light atoms in the electrode at cathodic incorporation of the ions, ion transfer across the liquid/solid interface, and low-temperature chemical reactions. 

Poulsen, J. A. Nyman, G. Rossky, P. J., Quantum diffusion in liquid para-hydrogen an application of the Feynman-Kleinert linearized path integral approximation, J. Phys. Chem. B 2004,108, 19799-19808... 

Fig. 6. The hop rate of muonium in KC1 as a function of temperature. The crossover from stochastic to quantum diffusion occurs at about 70 K, as evidence by a dramatic increase in the hop rate at lower temperatures. From Kiefl et al. (1989a).

The interpretation of these unconventional conduction properties is still a challenge for condensed matter physicists. Several models have been proposed including thermally activated hopping [10] band structure effects due to small density of states and narrow pseudo-gap [11,12] or anomalous quantum diffusion [13,14]. Yet all these models are difficult to compare in a quantitative way with experiments. 

In this paper we present preliminary results of an ab-initio study of quantum diffusion in the crystalline a-AlMnSi phase. The number of atoms in the unit cell (138) is sufficiently small to permit computation with the ab-initio Linearized Muffin Tin Orbitals (LMTO) method and provides us a good starting model. Within the Density Functional Theory (DFT) [15,16], this approach has still limitations due to the Local Density Approximation (LDA) for the exchange-correlation potential treatment of electron correlations and due to the approximation in the solution of the Schrodinger equation as explained in next section. However, we believe that this starting point is much better than simplified parametrized tight-binding like s-band models. 

The phenomenon of backscattering leads to unusual quantum diffusion, ft is illustrated on the plot of the average spreading of states (equation (2)) versus time t (figure 4). It shows that results in two term a... 

At T < 11K, the self-diffusion of H2 in an H2 crystal is due to tunneling of a molecule from a lattice node to a vacancy, the formation of which requires 0.22 kcal/mol [Weinhaus and Meyer, 1973]. If diffusion of H and D were caused by motion of H2 or D2 through the lattice, then the process would be expected to be thermally activated, contrary to the experimental results. This discrepancy strongly suggests that the mechanism of the quantum diffusion of H and D atoms is not a molecular one,... 

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