Resonant couplings

We have seen that resonance couplings destroy quantum numbers as constants of the spectroscopic Hamiltonian. Widi both the Darling-Deimison stretch coupling and the Femii stretch-bend coupling in H2O, the individual quantum numbers and were destroyed, leaving the total polyad number n + +... 

The question of non-classical manifestations is particularly important in view of the chaos that we have seen is present in the classical dynamics of a multimode system, such as a polyatomic molecule, with more than one resonance coupling. Chaotic classical dynamics is expected to introduce its own peculiarities into quantum spectra [29, 77]. In Fl20, we noted that chaotic regions of phase space are readily seen in the classical dynamics corresponding to the spectroscopic Flamiltonian. Flow important are the effects of chaos in the observed spectrum, and in the wavefiinctions of tire molecule In FI2O, there were some states whose wavefiinctions appeared very disordered, in the region of the... 

Venanzi T J 1982 Nuclear magnetic resonance coupling constants and electronic structure in molecules J. Chem. Educ. 59 144-8... 

The natural structural frequencies of most large systems are also in the low-frequency range, and care must be exercised to avoid resonant couplings between the structure and the foundation. The excitation in rotating machinery comes from rotating unbalanced masses. These unbalances result from four factors ... 

Two-dimensional constant matrix, transition state trajectory, white noise, 203-207 Two-pathway excitation, coherence spectroscopy atomic systems, 170-171 channel phases, 148-149 energy domain, 178-182 extended systems and dissipative environments, 177-185 future research issues, 185-186 isolated resonance, coupled continuum, 168-169... 

Photons in quantum optical cavities also constitute excellent qubit candidates [52]. Resonant coupling of atoms with a single mode of the radiation field was experimentally achieved 25 years ago [53], and eventually the coherent coupling of quantum optical cavities with atoms or (simple) molecules was suggested as a means to achieve stable quantum memories in a hybrid quantum processor [54]. There might be a role to play for molecular spin qubits in this kind of hybrid quantum devices that combine solid-state with flying qubits. 

As a further illustration of the phenomenon of H-bond resonance coupling let us consider the intramolecular H-bond of (3-hydroxyacrolein (0=CHCH=CH0H), a prototypical enolone (2-en-3-ol-l-one, or enol isomer of (3-diketone).55 This molecule may be envisioned as existing in two distinct isomeric forms, according to the position of the proton in the O- H—O hydrogen bond ... 

Fig. 2.16 (a) A schematic drawing of polymer microring resonator couple to a side polished optical fiber, (b) A microscope image of the fabricated EO polymer electric field sensor, (c) SEM image of resonators fabricated on the polished flat of a free standing fiber. The scale bar in the picture represents 100 pm. Reprinted from Ref. 15 with permission. 2008 Institute of Electrical and Electronics Engineers... 

Liang, W. Yang, L. Poon, J. K. Huang, Y. Vahala, K. J. Yariv, A., Transmission char acteristics of a Fabry Perot etalon microtoroid resonator coupled systems, Opt. Lett. 2006, 31, 510 512... 

We start by recalling that the framework of diahatic states depicts a competition in solution between the electronic resonance coupling [5 — which tends to delocalize the solute electronic charge — and the solvent polarization — which tries to localize it, to better solvate the reaction sys-... 

Hence, one should expect that, along the ESP at sufficiently large inter-nuclear separation, the solvent will overcome the delocalizing effects of the electronic resonance coupling, and localize the solute charge distribution... 

Fig. 2. Resonant coupling between atom state 0> and band states i> in a solid. Full (broken) lines represent the filled (unfilled) part of the band.

Figure 5. Schematics of (a) a bandstop (all-pass) and (b) add/drop filter designs, and (c) a transmission eharacteristic of a 3.0-pm-diameter GaAs microring resonator coupled to a bus waveguide.

Hammer M., 2002, Resonant coupling of dielectric optical waveguides via rectangular microcavities the coupled guided mode perspective, Opt.Communicat. 214(1-6) 155-170. 

Electron Spin Resonance Coupling Constants (Gauss) of Radicals of Some Aromatic Nitrocompounds, Produced Electrochemically and Photochemically, in Protic and Aprotic Media... 

Resonance coupling, Fe—S dimers, 38 446-451 Resonance delocalization, 38 426 Resonance effects, of astatophenols, 31 66 Resonance fluorescence, 46 156 nuclear, 6 438-445 theory of, 6 433 38... 

We note that the AZE can only come about when the peaks of Ffco) and G co) do not overlap, that is, the resonant coupling is shifted from the maximum of G co). If, by contrast, the peaks of Ffo)) and G co) do coincide, any rate of interruptions would result in QZE (Eigure 4.4c). This can be understood by viewing Ffco) as an averaging kernel of G co) around . If G mf) is the maximum of the spectmm, any averaging can only be lower than this maximum, which is the GR decay rate. Hence, any rate of intermptions can only decrease the decay rate with respect to the GR rate, that is, cause the QZE. 

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