Dynamic tunnelling

Thus, with a free-electron metal tip, the dynamic tunneling conductance is proportional to the DOS of the sample. 

In other words, with a flat-DOS tip, the dynamic tunneling conductance is proportional to the sample DOS. This simple situation requires a special procedure to treat the tip. On the other hand, a reproducible sample surface is easier to prepare than a reproducible tip. In this case, the sample DOS as a function... 

By contrast, in heavy-light-heavy molecules such as HMuH, C1HC1, or IHI, a very extended elliptic island exists in the classical phase space [150]. In such cases, the elliptic island may be the support of several metastable states that can be obtained by Bohr-Sommerfeld quantization. Their lifetime is determined by dynamical tunneling from inside the elliptic island to the outside regions. 

The other important scenario in multidimensional tunneling is of the dynamical tunneling that is observed in 1.5D and 2D systems [21]. In this case, the classical phase space is separated not by the energy barrier but by the invariant surface (e.g., KAM tori). Such a situation is realized, for example, in periodically perturbed one-dimensional (1.5D) barrier potentials and also in 2D barrier systems when the total energy is taken over the potential saddle. In a series of recent articles [22-25], we have found a new class of tunneling phenomena... 

In thermally activated ET we are interested in the electronic states at the transition state (TS). When the system is at equilibrium in either the initial or final state (where D and A are well out of resonance), the diabatic states, xj/j and i/y, can be taken to be essentially the same as their adiabatic counterparts, xj/ and xj/2. When the system with weakly coupled D and A is suddenly carried into the TS by a fluctuation, we adopt the picture that the system remains in the (now nonstationary) xf/ state until (with some finite probability) it dynamically tunnels (see below) to i/y and irreversibly relaxes to the equilibrium product. The required resonance of D and A is a statement of the Franck-Condon control of thermally activated electron transfer [6, 8, 60] that is, at the TS,... 

E.E.Nikitin, Vibrational relaxation and vibrational predissociation as dynamical tunneling processes, Uspekhi Khimii 62,3 (1993)... 

We calculate the ratio of the classical to quantum VP rates, determine the conditions when the rates of quantum dynamical tunneling is close to the classical diffusional rates across the chaotic sea and establish a classical counterpart of quantum perturbation approach. 

Z.7 Dynamics, Tunneling and Related Nuclear Quantum Mechanical Effects 11195... 

However, we have also seen that some of the properties of quantum spectra are intrinsically non-classical, apart from the discreteness of quantum states and energy levels implied by the very existence of quanta. An example is the splitting of the local mode doublets, which was ascribed to dynamical tunnelling, i.e. processes which classically are forbidden. We can ask if non-classical effects are ubiquitous in spectra and, if so, are there manifestations accessible to observation other than those we have encountered so far If there are such manifestations, it seems likely that they will constitute subtle peculiarities in spectral patterns, whose discernment and interpretation will be an important challenge. 

In this survey, we will not be concerned with the dynamic aspects of the JT theorem. In fact the concepts of symmetry destruction and symmetry conservation, to which the epikernel principle refers, are properties of the adiabatic potential energy surface only. When the kinetic energy of the nuclei is included, the JT coupling does not destroy the initial symmetry, but just replaces the electronic degeneracy by a vibronic degeneracy, due to dynamic tunneling between the different equivalent minima on the JT surface. 

S. Keshavamurthy and P. Schlagheck (eds.). Dynamical Tunneling Theory and Experiment (Taylor and Francis, Boca Raton, 2011)... 

Finally, the states trapped in the local mode-wells actually come in nearly degenerate even and odd pairs. That is, there is dynamical tunneling between the classically isolated local-mode trajectories This effect is probably occurring in the water molecule. 

Fig. 13. Quantum eigenstates for symmetric-asymmetric pair of states separated by 10 in energy (top row). Adding the two wavefunctions before squaring them, we get the lower left figure. Subtracting, the lower right figure is obtained. The bottom row states correspond to the stable periodic classical trajectories, but while they are strictly separate and periodic, the wavefunction on the lower right will dynamically tunnel and become the one on the lower left after vibrational periods.

M. J. Davis and E. J. Heller, Quantum dynamical tunneling in bound states, J. Chem. Phys., submitted for publication. 

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