The Radiation Field Theory

In order to understand the concept of Molecular Photonics, it is crucial for the reader to undertake a study of fundamental principles. Chapter 1 Fundamentals of Molecular Photonics includes four sections dedicated to optics, the molecular field theory, the radiation field theory, and the interactions between the molecular field and the radiation field. Fundamental principles are often treated in an introductory chapter, leading the reader to think that they are of little importance and that they can be understood with ease. This trend of relegating the fundamentals to a brief introduction is getting increasingly common in natural... 

The theories of photo- and opto-related areas can be classified into three categories the fundamentals of optics, the molecular field theory, and the radiation field theory. As we defined molecular photonics by Equation (0.1) which relates the interaction of the radiation field with the molecular field, it may seem sufficient to restrict our discussion to the molecular field theory and the radiation field theory. However we believe that the fundamentals of optics are also very important to understand and appreciate all the photo and opto concepts described in this book. To support this view, consider the following. 

To this point, we have considered only the radiation field. We now turn to the interaction between the matter and the field. According to classical electromagnetic theory, the force on a particle with charge e due to the electric and magnetic fields is... 

The application of microdosimetry to medical physics derives from biological models of radiation action (primarily, the Theory of Dual Radiation Action [14]) that explicitly utilize for their predictions a microdosimetric description of the radiation field. Specifically, they concern the following two problems ... 

Various theories have been proposed for horizontal transfer at the isoenergetic point. Gouterman considered a condensed system and tried to explain it in the same way as the radiative mechanism. In the radiative transfer, the two energy states are coupled by the photon or the radiation field. In the nonradiative transfer, the coupling is brought about by the phonon field of the crystalline matrix. But this theory is inconsistent with the observation that internal conversion occurs also in individual polyatomic molecules such as benzene. In such cases the medium does not actively participate except as a heat sink. This was taken into consideration in theories proposed by Robinson and Frosch, and Siebrand and has been further improved by Bixon and Jortner for isolated molecules, but the subject is still imperfectly understood. 

We now consider the effect of exposing a system to electromagnetic radiation. Our treatment will involve approximations beyond that of replacing (3.13) with (3.16). A proper treatment of the interaction of radiation with matter must treat both the atom and the radiation field quantum-mechanically this gives what is called quantum field theory (or quantum electrodynamics). However, the quantum theory of radiation is beyond the scope of this book. We will treat the atom quantum-mechanically, but will treat the radiation field as a classical wave, ignoring its photon aspect. Thus our treatment is semiclassical. 

It is very important, in the theory of quantum relaxation processes, to understand how an atomic or molecular excited state is prepared, and to know under what circumstances it is meaningful to consider the time development of such a compound state. It is obvious, but nevertheless important to say, that an atomic or molecular system in a stationary state cannot be induced to make transitions to other states by small terms in the molecular Hamiltonian. A stationary state will undergo transition to other stationary states only by coupling with the radiation field, so that all time-dependent transitions between stationary states are radiative in nature. However, if the system is prepared in a nonstationary state of the total Hamiltonian, nonradiative transitions will occur. Thus, for example, in the theory of molecular predissociation4 it is not justified to prepare the physical system in a pure Born-Oppenheimer bound state and to force transitions to the manifold of continuum dissociative states. If, on the other hand, the excitation process produces the system in a mixed state consisting of a superposition of eigenstates of the total Hamiltonian, a relaxation process will take place. Provided that the absorption line shape is Lorentzian, the relaxation process will follow an exponential decay. 

A comprehensive theory of radiative transfer, which governs the radiation field in a medium that absorbs, emits, and scatters... 

In the first part of this introductory section, we summarize the main collective phenomena acquired by the dipolar exciton from the lattice-symmetry collectivization of molecular properties. The crystal is considered as an assembly of electrically neutral systems, the molecules, physically separated from each other and in electromagnetic interaction. This /V-body problem will be treated quantum-mechanically in the limit of low exciton densities. We redemonstrate the complete equivalence of this treatment with the theories of Lorentz and Ewald, as well as with the semiclassical approximation. In Section I.A, in a more compact but still gradual way, we establish the model of the rigid lattice of dipoles and the general theory of low-exciton-density systems in interaction with the radiation field. Coulombic excitons, photons,... 

The electron and its charge can hence be identified with a local maximum in the radiation field, embedded in a sea of virtual photons. The amplitude corresponds to the electric potential of the electron and significantly does not become infinite as r — 0, but approaches 4>0. The interference between divergent and convergent waves therefore achieves the same, and more, as renormalization in field theory. 

Another possibility to obtain direct information from such a collision system is the observation of Molecular orbital (MO) X-rays resulting from electronic de-excita-tions between the molecular levels during the collision under emission of noncharacteristic photons. The result of our many-particle calculation is given in Fig. 10 where the spectrum of the collision system 20 MeV CP on Ar is compared with the experiment. In this calculation the radiation field was coupled to the system by first order perturbation theory but the wavefunctions were taken from the solution ot the time-dependent relativistic DV-Xa calculations . 

The Rayleigh-Jeans picture of the radiation field as an ensemble of different modes of vibration confined to an enclosure was applied to the blackbody problem in Chapter 1. The quantum theory of radiation develops this correspondence more explicitly, identifying each mode of the electromagnetic field with an abstract harmonic oscillator of frequency coa- The Hamiltonian for the entire radiation field can be written... 

Brillouin proceeds to apply these ideas to the resistance of the electrons in the metal. The radiation field is replaced by the vibration field of a solid body consisting of one kind of atom, as given by Debye s theory the moving particle is the electron. Then as... 

A relatively unexplored extension of the Kramers theory is the escape of a Brownian particle out of a potential well in the presence of an external periodic force. Processes such as multiphoton dissociation and isomerization of molecules in high-pressure gas or in condensed phases/ laser-assisted desorption/ and transitions in current-driven Josephson junctions under the influence of microwaves " may be described with such a model, where the pieriodic force results from the radiation field. 

Dirac s 1929 comment [227] The underlying physical laws necessary for the mathematical theory for a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too difficult to be soluble has become a part of the Delphic wisdom of our subject. To this confident statement Richard Feynman [228] added in 1985 a codicil But there was still the problem of the interaction of light and matter , and . .. the theory behind chemistry is quantum electrodynamics . He goes on to say that he is writing of non-covariant quantum electrodynamics, for the interaction of the radiation field with the slow-moving particles in atoms and molecules. 

Many dynamical processes of interest are either initiated or probed by light, and their understanding requires some knowledge of this subject. This chapter is included in order to make this text self contained by providing an overview of subjects that are used in various applications later in the text. In particular, it aims to supplement the elementary view of radiation-matter interaction as a time-dependent perturbation in the Hamiltonian, by describing some aspects of the quantum nature of the radiation field. This is done on two levels The main body of this chapter is an essentially qualitative overview that ends with a treatment of spontaneous emission as an example. The Appendix gives some more details on the mathematical structure of the theory. 

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