Resonant dynamics

Kellman, M. E. (1985), Algebraic Resonance Dynamics of the Normal/Local Transition from Experimental Spectra of ABA Triatomics, J. Chem. Phys. 83,3843. 

Martens, C. C., and Ezra, G. S. (1987), Classical, Quantum Mechanical, and Semiclassi-cal Representations of Resonant Dynamics A Unified Treatment, J. Chem. Phys. 87, 284. 

We first consider the AN regime of a two-level system coupled to a thermal bath. We will use off-resonant dynamic modulations, resulting in AC-Stark shifts (Figure 4.5(a)). The Hamiltonians then assume the following form ... 

Obviously, much information on the resonance dynamics should normally be gained by close examination of the structure of the wavefunction in the internal region of the configuration space. However, it is often possible also to infer either the dominant roles or the secondary roles of the interaction potentials in resonance processes without going into details of the wave-function. The inspection of the potentials can often lead to transparent visual understanding of the essential dynamics. 

Edwards, T. E., and Sigurdsson, S. T. (2002). Electron paramagnetic resonance dynamic signatures of TAR RNA—Small molecule complexes provide insight into RNA structure and recognition. Biochemistry 41, 14843-14847. 

The methods of level dynamics can be extended to resonance dynamics in case the energy levels En acquire a width in the presence of a continuum. Resonance dynamics of the one-dimensional helium atom is discussed in Section 10.5.2. 

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These five cases are excellent examples of the additional challenges that can arise In the study of shape resonance phenomena. They should not diminish the simplicity and power of the fundamental shape resonance dynamics but, rather, should show how the fundamental framework showcases more complicated (and Interesting) photolonlzatlon dynamics which. In turn, require a more sophisticated framework for full understanding. 

Near the resonant energy E = 1.806 eV, the channels which participate most In the resonance dynamics are clearly "0 of the H2 reactants and Vp>2 of the HF products. 

Sessin and Ferraz-Mello, 1984). This integral of the resonant dynamics means that ai and a2 vary in anti-phase. When one of the semi-axis increases, the other necessarily decreases. 

Figure 8.5 Coherence resonance. Dynamics of an excitable system perturbed by stochastic fluctuations for different values of the noise amplitude increasing from top to bottom. At intermediate noise levels, nearly periodic spikes occur (from Pikovsky and Kurths (1997)).

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