Quantum tunneling indicators

Tunneling may be conceptualized in several ways. For example, the wave-particle duality of quantum mechanics indicates that particles of mass m and velocity v have an associated de Broglie wavelength given in Eq. 10.6, where h is Planck s constant."... 

Quantum tunneling in enzyme-catalyzed reactions early indications 35 The rule of the geometric mean ( no isotope effects on isotope effects ) The Swain-Schaad relationship 36... 

QUANTUM TUNNELING IN ENZYME-CATALYZED REACTIONS EARLY INDICATIONS... 

Kinetic complexity definition, 43 Klinman s approach, 46 Kinetic isotope effects, 28 for 2,4,6-collidine, 31 a-secondary, 35 and coupled motion, 35, 40 in enzyme-catalyzed reactions, 35 as indicators of quantum tunneling, 70 in multistep enzymatic reactions, 44-45 normal temperature dependence, 37 Northrop notation, 45 Northrop s method of calculation, 55 rule of geometric mean, 36 secondary effects and transition state, 37 semiclassical treatment for hydrogen transfer,... 

A. H. Zewail For the base pair, we did the deuteration of both protons and observed transients for HH, DD, and HD species, indicating the nature of quantum tunneling. Please note that the experiments were performed in a molecular beam and the initial temperature is low. The motion is induced by the finite energy deposited microcanonically. 

In contrast, the x component of the susceptibility reflects directly the relaxation behavior under the applied field. For both samples, the maxima of X , measured at a given frequency, shift to lower temperature for increasing bias field. It also shifts to lower temperature for decreasing excitation frequency, and fixed field. Incidentally, this behavior indicates that the relaxation follows the classical predictions, and that no quantum tunneling relaxation is discernible since the trend would be of a shift to higher temperatures with increasing field. The dependence on H that we have adopted is... 

Specific heat measurements40 indicate that the assumption of static frozen glass disorder at low temperatures may be too restrictive and that the intra-H-bond hydrogen motion may still persist in the form of quantum tunnelling. To check this hypothesis, 2D deuteron NMR and 87Rb and 2H SLR measurements were carried out at low temperatures. With site-specific NMR measurements, it was also hoped to identify the microscopic nature of the "two-level" states which determine the low T glassy properties of these systems. 

Here amJ is the operator of proton creation (annihilation) in a position that is characterized by indices m and /defined above. Hrot is the transfer integral that describes the interbond proton hopping as a quantum tunneling. Once again we would like to emphasize that the parameter llro( does not characterized the direct overlapping of the wave functions of protons located at the nearest sites. Hro( is associated with the rotational motion of ion groups, which in the first approximation one can consider as a proton tunneling of some sort. 

Quantum mechanical features, however, remain by the quantum mechanical indices v and w. The tunneling features thus remain by the modified -form... 

In Fig. 4.12 we compare the experimental results of the internal fiiction with the numerical calculations for frequencies at 535 Hz and at 15 MHz using Efjke = 10 K, tq = 10 s, and a rather small distribution width relative value in comparison with the plateau [24]. It is worth pointing out, that for PMMA, since the changes produced by the free parameters Eq, tq and oq compete with each other, it is not possible to find another set of values which can explain the results as well as we can. It is important to note that the internal friction data for both polymers indicate a much smaller thermally activated contribution to the phonon attenuation for PMMA than for PS, in spite of the fact that in the quantum tunneling regime both samples show similar results. This difference may influence the low-temperature heat release because the number of excited states that are available after the cooling process will be different. 

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