Quantum resonances vibrational resonance

Long progressions of feature states in the two Franck-Condon active vibrational modes (CC stretch and /rani-bend) contain information about wavepacket dynamics in a two dimensional configuration space. Each feature state actually corresponds to a polyad, which is specified by three approximately conserved vibrational quantum numbers (the polyad quantum numbers nslretch, "resonance, and /total, [ r, res,fl)> and every symmetry accessible polyad is initially illuminated by exactly one a priori known Franck-Condon bright state. 

In particular, irregular vibrational spectra with Wignerian level spacing statistics have been observed this last decade for a number of highly excited molecules [3-7]. On the other hand, many recent works have characterized the reactive dynamics in terms of quantum resonances, which allows a rigorous definition of metastable states with finite lifetimes and hence of dissociation rates [4, 8-10]. 

In view of Figure 7.11 (and similar plots for all other resonances) the peaks in the absorption spectrum can be assigned to a set of two quantum numbers (m, n ), where m is the quantum number for excitation along the dissociation bond R and n is the quantum number for excitation of the N-0 vibrational bond r. The asterisk indicates that these quantum numbers designate resonance, i.e., quasi-bound, states rather than true bound states. Asymptotically, n becomes the vibrational quantum number of the free NO molecule while m has no counterpart in the product channel. The main progression is built upon m = 0 and the second, much weaker progression corresponds to m = 1. 

Since there are only four atoms, this case can act as a useful bridge between classical and quantum dynamics calculations. Since nonadiabatic effects are expected to be minor, the quantum calculations are limited by the PES and the computational precision. Consequently, they will ultimately offer the most meaningful comparison between experiment and theory. However, the quantum dynamics calculations carried out to date have been limited to two dimensions. Therefore, they have little to do with the HOCO system per se, except in the general sense of exploring the physics of vibrational resonances coupled to continua. 

In the preceding discussion we observed non-monotonic behaviour of F as either a vibrational quantum number, e.g., V2 in HCO (Fig. 16), or a rotational quantum number, e.g., J in HOCl (Figs. 22 and 23), was varied. The origin of these structures is rather universal and was already discussed in 2.3 the mixing between resonances. Two resonances with widths Fj and F2 (Fi <3< F2) may interact, i.e., the narrow state acquires character of the... 

Evgueni s current interests lie in the theoretical study of vibrational relaxation at ultra-low energies where quantum suppression and resonance enhancement are... 

We see that the resonance vibrations of the wall cause an effective cooling of the lowest electromagnetic modes (provided y < 1). The total number of quanta and the total energy in this example are formally infinite, due to the equipartition law of the classical statistical mechanics. In reality both these quantities are finite, since v (0) [Pg.331]

Vibrational Relaxation. Stochastic processes, including vibrational relaxation in condensed media, have been considered from a theoretical standpoint in an extensive review,502 and a further review has considered measurement of such processes also.503 Models have been presented for vibrational relaxation in diatomic liquids 504 and in condensed media,505 using a master-equation approach. An extensive development of quantum ergodic theory for relaxation processes has been published,506 and quantum resonance effects in electronic to vibrational energy transfer have been considered.507 A paper has also considered the coupling between vibrational relaxation and molecular electronic transitions.508 A theory has also been outlined for the time-resolved electronic absorption spectrum of a molecule undergoing collisional vibrational relaxation.509... 

In this relation, Vj is the vibrational quantum number of a non-stable negative iort, and Fq, (in s ) are probabilities of transitions between vibrational states. The cross section of the resonant vibrational excitation process (2-148) can be found in the quasi-steady-state approximation using the Breit-Wigner formula ... 

Non-resonant vibrational energy exchange between molecules of a different kind is usually referred to as W exchange. Let us first consider the W exchange for diatomic molecules A and B with slightly different vibrational quanta ftcoA > Similar to W exchange of anharmonic molecules of the same kind, the adiabatic factors here also mainly determine the smallness of the probability. If a molecule A transfers a quantum (wa -f-1 m va) to a molecule B (vb + 1 vb),... 

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