We illustrate how path-integral molecular dynamics can be used to calculate ground-state tunnelling splittings in molecules or clusters. The method obtains the splittings from ratios of density matrix elements between the degenerate wells connected by the tunnelling. We propose a simple thermodynamic integration scheme for evaluating these elements. Numerical tests on fully dimensional malonald...

tunnelling through cities underlain by soft soil, commonly associated with soil movement around the tunnels and subsequent surface settlement. the predication of ground movement during the tunnelling and optimum support pressure could be based on analytical, empirical or the numerical methods. the commonly used earth pressure balance (epb) tunneling machines, uses the excavated soil in a pressu...

Abstract. The geometric theory of vortex tunnelling in superfluid liquids is developed. Geometry rules the tunnelling process in the approximation of an incompressible superfluid, which yields the identity of phase and configuration space in the vortex collective co-ordinate. To exemplify the implications of this approach to tunnelling, we solve explicitly for the two-dimensional motion of a po...

For almost 15 years, our Pathway model has been the most powerful model in terms of predicting the tunnelling mechanism for electron transfer (ET) in biological systems, particularly proteins. Going beyond the conventional Pathway models, we have generalized our method to understand how protein dynamics modulate not only the Franck-Condon factor, but also the tunnelling matrix element. We have ...

Individual atoms and ions are now routinely manipulated using scanning tunnelling microscopes or electromagnetic traps for the creation and control of artificial quantum states. For applications such as quantum information processing, the ability to introduce multiple atomic-scale defects deterministically in a semiconductor is highly desirable. Here we use a scanning tunnelling microscope to f...

The title reaction is involved in the formation of ammonia in the interstellar medium. We have calculated thermal rates including atom tunnelling using different rate theories. Canonical variational theory with microcanonically optimised multidimensional tunnelling was used for bimolecular rates, modelling the gas-phase reaction and also a surface-catalysed reaction of the Eley-Rideal type. Ins...

In the First Part of this paper [that was submitted for pub. in 1991 and appeared in print in Phys. Reports 214 (1992) 339] we critically review and analyse the main theoretical definitions and calculations of the sub-barrier tunnelling and reflection times. Moreover, we propose a new definition of such durations, on the basis of a recent general formalism of ours (already tested for other type...