Non-Markovian binary theory

Quantum theory of spectral collapse 4.3 Non-Markovian binary theory 

The necessary generalization of the description is achieved by using instead of Eq. (4.3) the integral kinetic equation 

Here s is the time between the beginning of observation (t = 0) and the instant of closest approach where the intermolecular interaction V reaches its maximum. The operator U rules the alteration of the operator 

From Eq. (4.1) and Eq. (4.2) we find, omitting the bars over d for simplicity, that 

The evolution of the spectrum is thus reduced to inversion of the matrix Gik,tm(o ) and its convolution according to the recipe given in Eq. (4.7). 

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NMR see nuclear magnetic resonance non-Markovian binary theory 138-40 non-Markovian differential theory 38-45, 65... 

The quantum theory of spectral collapse presented in Chapter 4 aims at even lower gas densities where the Stark or Zeeman multiplets of atomic spectra as well as the rotational structure of all the branches of absorption or Raman spectra are well resolved. The evolution of basic ideas of line broadening and interference (spectral exchange) is reviewed. Adiabatic and non-adiabatic spectral broadening are described in the frame of binary non-Markovian theory and compared with the impact approximation. The conditions for spectral collapse and subsequent narrowing of the spectra are analysed for the simplest examples, which model typical situations in atomic and molecular spectroscopy. Special attention is paid to collapse of the isotropic Raman spectrum. Quantum theory, based on first principles, attempts to predict the. /-dependence of the widths of the rotational component as well as the envelope of the unresolved and then collapsed spectrum (Fig. 0.4). 

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