Resonant tunneling modes

The total tunneling current then consists of a resonance tunneling current and the direct elastic current. These two currents are shown plotted separately in Figs. 56 and 57 and it can be seen that the most important qualitative result is that the resonance tunneling mode gives a maximum in the current distribution, though this maximum may be difficult to observe in practice. 

The situation is more subtle for the antisymmetrically coupled mode. As shown in fig. 17, this vibration, in contrast to the symmetric mode, asymmetrizes the potential and violates the resonance. This should lead to a decrease in the splitting. Consider this problem perturbatively. If the vibration and the potential V Q) were uncoupled, each tunneling doublet Eq, Ei (we consider only the lowest one) of the uncoupled potential V Q) would give rise to a progression of vibrational levels with energies... 

The requirement I > 2 can be understood from the symmetry considerations. The case of no restoring force, 1=1, corresponds to a domain translation. Within our picture, this mode corresponds to the tunneling transition itself. The translation of the defects center of mass violates momentum conservation and thus must be accompanied by absorbing a phonon. Such resonant processes couple linearly to the lattice strain and contribute the most to the phonon absorption at the low temperatures, dominated by one-phonon processes. On the other hand, I = 0 corresponds to a uniform dilation of the shell. This mode is formally related to the domain growth at T>Tg and is described by the theory in Xia and Wolynes [ 1 ]. It is thus possible, in principle, to interpret our formalism as a multipole expansion of the interaction of the domain with the rest of the sample. Harmonics with I > 2 correspond to pure shape modulations of the membrane. 

A number of methods are available for the characterization and examination of SAMs as well as for the observation of the reactions with the immobilized biomolecules. Only some of these methods are mentioned briefly here. These include surface plasmon resonance (SPR) [46], quartz crystal microbalance (QCM) [47,48], ellipsometry [12,49], contact angle measurement [50], infrared spectroscopy (FT-IR) [51,52], Raman spectroscopy [53], scanning tunneling microscopy (STM) [54], atomic force microscopy (AFM) [55,56], sum frequency spectroscopy. X-ray photoelectron spectroscopy (XPS) [57, 58], surface acoustic wave and acoustic plate mode devices, confocal imaging and optical microscopy, low-angle X-ray reflectometry, electrochemical methods [59] and Raster electron microscopy [60]. 

By inelastic resonances we mean resonances which decay via energy redistribution between the internal vibrational-rotational modes or a transition from a quasi-bound to a continuum state. Elastic resonances, on the other hand, decay via tunneling through a potential barrier without the necessity of internal transitions. 

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