External radiation field coupling

Figure 4. Techniques for coupling an external radiation field into optical waveguides (a) prism coupling, (b) grating coupling, and (c) end-fire coupling.

V(x) is assumed to be the usual symmetrical double-well potential [V(x) - 8x /2 + fix /4] the third term on the right-hand side of Eq. (77) is the coupling between the Brownian particle and the external radiation field, which is characterized through its autocorrelation function... 

In this approximation, the molecular hamiltonian is coupled to the radiation field by the three latter terms. They define the molecule-radiation field coupling opo ator, U. The linear term in A acts as external perturbation on the quantum states of Hm prompting for the passage among different eigenstates of Hm. 

This chapter considers the first group of instabilities and introduces the analysis of processes implying an interaction with external flow-field perturbahons. This is exemplified by investigations of coupling between pressure waves and plane flames and also between an external acceleration field and flame fronts. The coupling between flow perturbations and flames giving rise to heat release unsteadiness and coupling with acoushc modes is considered in Chapter 5.2, which deals with the relationship between perturbed flame dynamics and radiated acoustic field, a fundamental process of thermo-acoustic instabilities. 

A systematic development of relativistic molecular Hamiltonians and various non-relativistic approximations are presented. Our starting point is the Dirac one-fermion Hamiltonian in the presence of an external electromagnetic field. The problems associated with generalizing Dirac s one-fermion theory smoothly to more than one fermion are discussed. The description of many-fermion systems within the framework of quantum electrodynamics (QED) will lead to Hamiltonians which do not suffer from the problems associated with the direct extension of Dirac s one-fermion theory to many-fermion system. An exhaustive discussion of the recent QED developments in the relevant area is not presented, except for cursory remarks for completeness. The non-relativistic form (NRF) of the many-electron relativistic Hamiltonian is developed as the working Hamiltonian. It is used to extract operators for the observables, which represent the response of a molecule to an external electromagnetic radiation field. In this study, our focus is mainly on the operators which eventually were used to calculate the nuclear magnetic resonance (NMR) chemical shifts and indirect nuclear spin-spin coupling constants. 

We now describe a generic formalism for active control of a molecule coupled to the radiation field. That is, we examine how the control conditions for a variety of circumstances can be expressed in terms of the phase of the external field and the phase of the relevant dynamical variables. For simplicity, we consider a simple case, namely, when only two electronic states of the molecule play roles in the reaction dynamics we take these to be the ground electronic state and the first excited electronic state. The radiation that couples the two surfaces is the means of control. The internal state of the molecule is defined by the density operators pj, j e g, e, where g and e denote the ground and excited states, respectively. The combined density operator describing the state of the system can be represented as... 

As far as spontaneous fluctuations of orientation are concerned, that is within the frame of linear response, this function can be expressed in terms of measured susceptibilities respective to any external field coupled with the orientational degrees of freedom. Such is the case for hertzian electromagnetic radiation that couples with the molecular electric moments. Suitable expressions in terms of the susceptibilities have been proposed, duly incorporating a convenient internal field correction. One among them reads ... 

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