The Many-Body Approach to Materials Science
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The Many-Body Approach to Materials Science Minko Balkanski Laboratoire de Physique des Solides de i'Universite Pierre et Marie Curie, associe au CNRS I would like to express my gratitude to the Awards Committee and its chairman for bringing me here today. One of the effects, and not the least, of this award is to call on my earliest recollections from the United States. In the Fall of 1956, I arrived in Boston at the Massachusetts Institute of Technology (MIT) as a postdoctoral fellow in the laboratory of Prof, von Hippel. My stay in the Materials Research Laboratory of MIT was a determining influence in my future work. The many-body problem is the study of the effects of interaction between bodies on the behavior of a many-body system. The importance of the many-body problem derives from the fact that almost any real physical system is composed of a set of interacting particles. Another essential aspect is that the many-body problem is not a branch of solid-state or atomic or nuclear physics but deals with general methods applicable to all many-body systems. Because of the complexity of the manybody problem, one of the preferred solutions is simply to ignore it. One can always say, "Let us admit that the particles forming the system do not interact or that their interaction is so weak that the effect can be considered negligible." In many cases, this method produced good results, and one of the great mysteries is why. The breakthrough in the many-body approach came in 1956-57 with a series of pioneering papers showing that the methods of quantum field theory provide a powerful, unified way of attacking the many-body problem. Since then much of the most exciting and fundamental research into the nature of matter has been based on quantum field theory methods. A new, simple picture of matter has emerged in which systems of interacting real particles are described in terms of approximately noninteracting fictitious bodies called "quasi-particles" and "collective excitations." The properties of quasi-particles are directly observable experimentally; the properties of real particles can then be inferred. A quasi-particle is an excited energy level of the many-body system; hence it is referred to as an "elementary excitation" of the system. The interaction of the radiation field with matter results in the transformation
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taking into account the statistical nature of such systems and applicability at arbitrary temperatures requires the use of manybody theory.
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of the system from its ground state to an excited energy state. In this process a photon from the electromagnetic field can be absorbed by the solid, creating an "elementary excitation." The elementary excitation can involve the electron or the nuclei of the solid. For electrons, the elementary excitations include the single particle excitations — electrons in the conduction band and holes in the valence band, the collective excitations known as plasmons, and the electron-hole excitations known as excitons. F
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